Hello, thank you. My name is Sebastian König. I'm here with my colleague Simeon Konsendorf We are from a small studio in Leipzig called blend FX. We are five people like three partners and we have two employees and We do a couple of things which I'm going to show you just very briefly So we do architectural visualization product visualization For example doors is a thing for us. I don't know why we are rendering lots of doors for a company and floors as well If we are not rendering doors and floors, we are doing a little bit of CG stuff There should be more in the video. I'm not sure why it's stopped. Maybe I can press next There is again So you can enjoy this again, maybe after that there Will be more stuff to see If not, I will just continue Telling you what we do. So this is like some CG stuff. We also do visual effects Which is what you hear for short films. So a little bit of compositing We also do Animations for TV and sometimes also cinema, but the other thing we do a lot is VR and This is what this talk is going to be about So VR is something that we really like especially mobile VR for cultural applications We've been here two years ago I think we had a little talk about one app that we did rochlitz VR Which is about a castle in Germany and they have a room which looks like that It's like very old and and rotten because they they wanted to show that the rooms in the castle go through different time periods and we are we have been reconstructing these time periods and People in the museum can go there and sit in a chair inside that room and then put on their glasses and see how the room looked like We like to do that a lot because we think it makes sense. It's not like just gaming It's it's for culture. It's people learn something from it So we really like doing that stuff So we were really happy when we got an email in March or February 2018 from from a producer and she wrote hey, I know your rochlitz project, which I like a lot since over a year I have been working on this project about Hotel Astoria. I just got the confirmation that I'm allowed to film there before it will be destroyed I would like to produce a VR app about it similar to rochlitz. I even got funding for a story development. Are you interested? Well, you have to know that the hotel Astoria is One of the most famous hotels in Leipzig is what it was built. It was built in 19 and 15 Especially in the GDR period it was a very famous place Fancy place like in in Leipzig in eastern Germany during the GDR period There were not many fancy places. So this was the thing Businessmen and celebrities from the west could then go there meet locals It had a nightclub in the basement, which was especially fancy there It might not look like much but back then this was really like wow so people go there especially the people from the West and meet with the locals there were also prostitutes allowed there But those prostitutes were working for the secret state police Because that was a thing there. There was a lot of surveillance in that nightclub So you have this fancy place, which was a little bit naughty as well But then always the subtle threat about surveillance and the secret state police So a super interesting place which has been abandoned since Yeah, since 20 years it has been empty and rotting along It was like the holy grail for geocaches in Leipzig or like adventures who like to go in lost places But it's really hard to get into it because it's very well guarded and so Yeah, are we interested? Yeah So We were happy to hear that Alina the film producer was inviting us to to visit the the place And at that time when she wrote us the email that was the stage of story development for for her She had been doing research about the hotel for a long time before and now she got funding for story development from the MDM the middle-deutsche median further on the mid German media fund and this funding goes in three steps so first there's story development and with that you can then apply for prototype development and If you finish a prototype where you can show the funding board that how your app or your product will look like Then you can apply for the next and last stage where we which will be a product development And that's where all the money will be so We were really happy that they were inviting us to collaborate with them Especially since they would do the paperwork Because applying for funding involves a lot of bureaucracy and paperwork. So yeah, we were lucky that this would be done by Alina Syuronek and Falk Schuster So from Huck films, that's the film company and they are they are the producers And they are doing two things the one thing is an animated documentary where they will animate and like a collage of interviews and snippets and the other thing will be the virtual reality app and both of these will Will not tell like a straight storyline or let one person the story of one person But they want to capture like the essence of the hotel and the how it was like being in that time period and Experiencing that nightclub So it's storytelling through story fragments. So to say so our job was to build an app that will Transform you and bring you to that place, but where we can also explore and watch different elements from that time so March 2018 that was the stage of story development and The production couldn't start yet, but we got the chance to visit the Astoria. So I will hand over to see me on now so I'm simian and As you heard we are very infected by the idea to create the Astoria in the 80s and We have the chance to visit this place, but only for some hours. So we have to be prepared So we have to rent a good camera. We have to prepare because there will be no light there's no power source in this room and We have to wear helmets and this is the day 14 days later after the email where we wear the blender branded helmet and Yes, we got a chance to visit this place and here's a little video snippet where you see Some parts of this day That's the moment we entered the nightclub and as you can see there's nothing more in You see the paintings on the walls, but no tables and yes No carpet nothing a very rotten place and Then we started and preparing our equipment here You see the special lamps we built these are in battery-powered flood lights floodlights pointing downwards to a big paper lamp and this this this big point lamps as you know Give us the chance to not have hard shadows in the whole area It's very soft lightened area and that's it's especially important to take and photos without shadows to use them as textures later words and most important the textures have been on the walls they are from a painter who made them in the 80s and Yes, folk take care of these and to preserve these pictures for our app and also for the future And at this point we gathered all the information we could from this room But still there was no money for us We have to wait until the next six months if there's a positive message from the MDM saying Okay, Alina and convinced us about the story now start the prototype and in end of 2018 we get a message or a phone call from Alina saying Okay, they liked the idea of reconstructing the Astoria. Let's start this prototype so in October we got the Message that we could continue working on it and then we did a little bit of planning and then in winter like November December 2018 we started building that thing so when I was there I took precise measurements with an industry standard note-taking device So I could have all the reference and heights and everything so I could start Reconstructing the room not the entire hotel of course just the nightclub and the bar I had an old ground plan that I could use as a reference and I Used that to to build the bar Also, we prepared the textures in Lightroom before to the especially the paintings to clear clear it up a little bit So that we could then project them on the wall with blender texture painting And you might wonder why we didn't just use photogrammetry, which is like a thing You can do that press a button sort of this laser scanning and then you have the entire room But yeah, then you also have just a very crappy Model with lots of vertices which you have to clean up in the end and since we wanted to Reconstruct the the building like it was Like back then like when it was still intact We had to remodel everything anyway, so we could just as well build it right from scratch And the room was so easy to build that it was quite straightforward anyway Also, we want to go to a game engine with with the architecture So you have to have clean geometry then so you have to model it anyway And of course we did it in 2.80. I mean what's good enough for this spring team will be good enough for us I assumed and I wasn't mistaken because everything was quite fine Is it stable I mean in winter that was not even better stage. Yeah, it was it was alright there were some problems but It went well and also we wanted to be future proof because we we knew that this project might go on for a long time so We want to have all the good stuff from 2.80 of course and it's not like Blender is unstable or more unstable than than other software In fact the blender 2.80 in alpha was still quite stable working not many crashes there I'm working and reconstructing the room was was kind of a detective game for us So we there were not that many references and we didn't really know how these Lamps for instance looked like exactly or what's that thing the pattern on that thing there? We didn't know so we we had to to dive in some references also that Wooden thing in the middle was totally unclear to us. What is it? It doesn't really fit there, but it was a thing where you put glasses and stuff on and we had to dive into some private photo albums from the Former personnel to really figure out how that stuff looked like Also Alina had been doing lots of research and they talked to the former personnel and some of them had some Props and some things there from the hotel so which you could pick to take pictures of this weird snail cutlery or or glasses So yeah, we built we reconstructed the room and all the assets with blender 2.8 ad and that it went well In November December and January there were some issues. I I couldn't really I Didn't really know how to use the collections and do the hiding hide from viewport hide render boss So I was lost There were also some bugs which made me like struggle a bit But thanks thanks to the developers and the fabricator side those issues were solved quite quickly So yeah, I really started to love blender 2.8 a lot especially the collections Like in this hotel room where we have all these assets and details doing this with layers in 2.7 You would be like a nightmare. So Thanks for the collections and in the 2.8 One thing that we are missing Sadly still is a queer rectangular rendering in in Evie. I mean Evie is nice But we have to output Stereo images a rectangular and we didn't have that also not spherical stereo rendering which is very important for us So maybe maybe in the future with Evie, but since until then we will use cycles Now just briefly about our 3d workflow For VR so the app will be for a mobile device So we can't have like that many that much geometry so we are pre rendering everything into 3d 360 stereo panoramas like that obviously not in an agliff but in top-bottom format and We of course we want to be able to exchange some elements. It should be an interactive app after all So what we do is to have like first our a queer rectangular camera and then we use a perspective camera With a very narrow field of view And then we can just render a snippet from that and within that area that this camera is rendering We can then change objects and render that so One thing that is important if you do that don't forget spherical stereo. It's important to have a seamless match but that allows us to have like a Small like interactive elements people drinking beer and we can just blend that in with the panorama in the game engine And this is the the interactive part that now Simion will talk about So now we have these beautiful So renderings panorama renderings out from blender, but then there is currently not able to create and virtual reality apps with interactivity so I choose unity as my game engine and you see on this side on your left side This is the something like the editor view the scene view and on the right side You see the game view what what the user would see And I don't start with the spherical renderings because they will appear later what at first I also import a low-poly or a Base mesh model from the hotel so that I have a reference in unity. We are to place the sound objects or other objects Basically when I have or at first when I start with the base model I start with the VR device and search for and the best positions where we want to render So I go through the room or a transport through the room and say this is this is a good position to See the pictures on a wall or to sit on the table I gave this positions to blender back and then we render the positions and this looks like this actually, I disabled now the The whole mesh and you see that the camera position is just inside on a sphere But some objects are real-time or the spatial audio Sources and you see there's the the ball above that the tiny ball. This is the disco ball and he's rotating so he's This is a real-time object. So everything that should be moving or which you should act and interact These are still 3d objects with a sphere When I move the position From one point to another point. I also move the camera and the sphere though. I always work in absolute space Same for the position of Interactive objects on a table. I take the table from blender important unity Then I can place the interactive objects on the table and in on runtime I remove the table just or disable the table and it gets in front of the sphere like you see here Actually, it's just floating objects in front of a sphere, but from the user perspective It looks like they are lying on the table You have to cheat a little bit like the shadows on the for the cigarettes I just use a blob shadow, which is a transparent transparent shadow But this gives you the illusion that it's really lying on a on the ground Let's see this in action This is an original receipt from we got from the employees And I copy the rotation of the controller that you can investigate the objects Yes, we just don't want to have only in 3d objects We also want to have a testimonial something like a testimonial in our app We want to add a character and not a game character. It wasn't fit We want to have a real person which worked at the Astoria which are still alive and This one this person mr. C was a bartender or bar mixer in the old times and he worked for many years in Astoria and That as we knew that there is a person and he want to work with us we had to prepare for this and This there's a recording from from mr. C in front of a green screen So we ordered the green screen you see behind him We ordered the lights and make many testing and the most important part is this this stereoscopic camera and This that's something special about because normally you would say okay take two diesel are or something similar and Make a stereoscopic Recording but because our eyes are in a certain distance of 0.3 centimeters These cameras must be very narrow Okay, it could be achieved with some lenses, but we have a very very wide field of view I want the person standing one meter in front of me That means a field of view of over 90 degrees and the lenses lenses wide angle lenses are very big We choose these cameras. These are from yee 4k plus is the model We printed 3d printed our own rig and these cameras have great features like 4,000 by 3,000 resolution and very wide angle and we can play back via in pysons script It was a good choice to take these and this is the output the camera standing one meter just in front of the person Which is Falk and he was my test person and Yes, we have this really I would compare it like we built cameras as They were our eyes. Yes, we have to be very Near to the reality and also the camera height where we film must be exact the same camera height Then we render the images then you get the perfect Illusion like the rendering Sebastian described we we make a perspective cut out from reality and This is you have to do some compositing like king and then There are not good and video codecs with alpha support which are running on mobile devices So we have to build in the key in the video file and the rest makes the shader So we you have color left eye color right eye and mask left eye mask right eye and the shader and combines this for for unity and Yes, when we prepared for some weeks to for this special day We invited mr. C to come to us in our office and we did the recording and in the middle. There's our Technical most important part the tiny setup for the camera and we had a great day and he also mixes us a cocktail He mixes 20 years ago called grüne Wiese Which is a green cocktail which is funny in front of a green screen, but because it was in front of him It was just a masking job And that's what it's look like in unity. You see we are showing a plane in front of a sphere Sounds very simple, but the illusion is like this If you not look to him he he makes some noise Good evening. I'm standing behind you Thank you now the part of the Yes, we made an app the people liked and they could interact with it and what's next? Yeah, so once we finished the The prototype Alina went to the funding board and showed it to them And then they had a little discussion and then you have to wait for a few weeks and then we finally got the message Yes, you will get the funding so We can now produce like The thing like the product which is super great Something that we didn't mention yet though is that we are producing for a special device Which is the the Oculus go which is a very nice device. It's it looks good. It feels good. The interaction is great So everything is really nice except for Oculus like they we need a kiosk mode Where you don't have to what the user doesn't have to interact with the Oculus interface So we just want to start our app and then you will never leave it you would just you can of course leave the and get rid of the HMD but You don't have to interact with the Oculus interface Sadly, they don't listen. So if you listen now, please kiosk mode is super important for us Anyway, we might switch to a different device if they don't listen to us so We got more money now, which is super great. We can now start working We have a little bit over half a year of time to to produce more Rooms like the bar is missing and then another part of the bar is missing We want to add more details, of course more interactivity and during that phase of working half a year, maybe more blender features would be nice. Maybe we get some Like for instance spherical stereo in Eevee would be great someone's listening or We are in blender. I mean we are all in blender, of course, but Like virtual reality in blender would be super great and apparently it's happening. So Julian Eisel is working on it today We had a little meeting about the future of VR and blender. So there is a team working on virtual reality interaction right inside blender, which for us would be of course amazing because we don't want to always go to unity and Have to interact with that game engine would be nice to to stay right inside blender to to do all these things that you have to do to to plan your scene and Place your objects So, thank you. Thank you, but no, no so there is there is a project going on and My Simion might want to talk a little bit more about that. We still have like 29 seconds. Oh really? Yeah But just fun 25 minutes That's the sound from Venus mixed reality starting at VR session This is demo I did for Julian Eisel where I test the open XR branch Which is currently only a special you have to compile it yourself But as Sebastian Sebastian said it was so interesting to meet these people like Yeah, Julian Eisel and Dalai Linto and William and the Ubisoft guys and I'm really looking forward to this because we need it stable and usable. We leave the material preview We need a controller input for transformations And the option to disable position tracking but we talked to them about all these features and I'm really Convinced that we are getting the best VR tool with blender in the next month and years and really they have a great Vision and this will be awesome Yes So no, thank you. Thank you Just to wrap it all up so what we are producing is like a something like a digital time-travel documentary I would call it so it all started with one Polaroid one one photo that someone back there in 1986 took and then through lots of effort and Interviews and research it ended up in in this like this future VR app, which we are really Happy to produce. It's been a lot of fun working with blender 2.8 It's going to be even more fun once we get the VR tools in blender The producers are nice Alina and folk are really nice to work with so that's it's a great project and Part of that was also like going to that place like back in time in a basement which in an abandoned building Super interesting and we even got to have like the last drink in the nightclub of the hotel Astoria. So Thank you for listening. Thank you


Altcoin of the day. Parental advisory. This is not investment advice. Roger Verz adopt the child, Bitcoin Cash. Born. August 1st, 2017, into a tumultuous world, named after his father, Bitcoin Cash, has always been in Bitcoin's shadow. Early life. It would later try and reinvent itself as B-Cash. Despite the remonstrations of a doting surrogate father. During this period, B-Cash began sleeping around with a number of exchanges, and getting involved with a number of users, hashtag YOLO. After this experimental period, BCH emerged with a clear goal in mind, to challenge his father for dominance as true peer-to-peer electronic cash, with an increased block size of 8MB. Leading to faster transaction, B-Cash has grown from humble beginnings to an almost 35 billion market cap, and a price of almost $2,000. Where is it today? B-Cash and Bitcoin have reconciled a bit. Bitcoin has retired as a store of value, and cleared the way for B-Cash to make a name for itself, and it is doing just that. Bitcoin.com has just announced a B-Cash Visa debit card, to be released soon. Which would allow you to say, order a pizza? Who knows? Could this be what sends B-Cash to the moon? Everyone is proud of an astronaut, right dad?


Let me explain what the nonce is in mining. We have talked about cryptographic hash functions. What cryptographic hash functions do is produce a specific fingerprint from data, such that if you make a tiny change to the data just a single bit, no matter how big the data is or how small the data is, it will produce a radical change in the fingerprint, allowing you to determine that the data has changed. When you produce a hash, the hash is a completely different number, even if all you changed was one bit in the input. What hash functions are doing is taking all of the bits of your data, pouring them into a bucket, and then stirring them algorithmically. Effectively, a cryptographic hash algorithm just stirs up the bits. If you look at how the algorithm works, what it is doing inside is a lot of addition. It is adding up binary numbers, and it is doing those additions with a modulo, so that if you add up to more than 32 bits, it wraps around and starts again, which mixes those bits effectively. As well as binary shift operations, where the cryptographic hash algorithm will take a chunk of bits, and will shift them left or right, and then add them to other bits. Essentially, what it is doing is shuffling, so it is a bit like shuffling cards. You take the data that you put into the cryptographic hash algorithm, and you cut it into chunks, and then you mix those chunks together, and you keep mixing them until eventually you get a 256-bit number, which is the output of your cryptographic hash, which is the fingerprint. Any point in that mixing process, if one of the bits of the data is different, causes the mixing process to go down a completely different path, which produces a completely different fingerprint. Just changing one bit changes the cryptographic hash function. If you think about it, the cryptographic hash function is output. The number it produces, the fingerprint it produces, is effectively a random number. It is a random number in that you cannot predict what it is going to be, but it is also a deterministic number, meaning that if you put the same data in, every time to the same algorithm, you will get the exact same fingerprint, which means it is very easy for anyone to verify. If you take the data, put it through the fingerprint algorithm, you get the same fingerprint as everybody else who puts the data into the hash algorithm. This is a very interesting trick. You put a data in, if you change it even by a tiny bit, it seemingly produces a completely different random number, but if you present the same data to someone else, and they put it through the fingerprint function, it is going to produce the same fingerprint. What if, when you are trying to pick these random fingerprints that are coming out there, you set a target and you say, I want my fingerprint to start with zero. What are the chances that your fingerprint starts with zero? Well, if you are looking at it in binary, and the first digit can either be zero or one, then if you just keep throwing fingerprints out there, half of them are going to start with zero, half of them are going to start with one. You have about a 50-50 chance. What about both of the first binary digits being zero? In that case, you have a 25% chance, because only one in four of the results will have both of the first binary digits being zero. You keep throwing fingerprints and you keep hashing. One out of every four hashing results will start with two binary zero digits at the beginning. Then you can keep going with that. Every time you add the requirement for one more zero, you get half as many of the hashes fit that target. Now you have gotten to 30 zeros. Now only one in a quintillion hashes will actually have all 30 of the first binary digits be zero. In order to find that one, what you have to do is take your data, which is your block, modify it slightly, calculate the hash, see if it has 30 leading zeros. It won't.  What is the nonce? The nonce is the part of the block that you are changing. If you think about the block, the block header contains a timestamp, a block number, the Merkle route of transactions, which is like a fingerprint of all of the transactions. It contains the hash of the previous block. All of this information is fixed. For a valid block, all of this information can only be one thing. You can't really change it. You can change the timestamp a tiny bit by a few seconds here and there, but the rest of this data can't be changed. The previous block is always going to be the same number. The fingerprint of all of the transactions is always going to be the same in that candidate block that you've built. Well, there's a special part of block that's 32 bits that doesn't do anything in the block. It's just sitting there, and you can put any number you want in there. Why does that space exist? It exists to allow you to change something in the block header so that you can produce a different hash. We call that the nonce. Let's say you take this 32-bit number and you start it with all zeros, and you hash the block header and you get some kind of hash. Does it have the necessary number of zeros in the beginning to meet your target? No. Try again. Instead of zero, let's make that 32-bit number one, then two, then three, then four, five, six, seven, eight, nine, ten. As you keep incrementing that 32-bit number, every time you hash it, it produces a completely different fingerprint. You do that five quadrillion times, and eventually you produce a hash that starts with 30 zeros just by chance. When you do, what you can then tell everyone is, here's a block, and look what I found. If you put this nonce in, and this nonce is, oh, it just happens to be the number 6,475,322. If you put 6,475,322 into the block header, watch what happens. You hash that, and the hash by complete coincidence has 30 leading zeros. How do you know that it took me a lot of time to find that? You know that the only way I could do that was by plugging numbers into the nonce and hashing, and waiting to see if the result matched. That's what a nonce is. It's simply the space in the block that has no meaning, where you can just plug in a random number and keep trying in order to find a specific fingerprint, to produce a fingerprint. Once you tell everybody that random number, they can all plug it into that space in the block, where it does nothing, and when they produce the fingerprint for the block. It's this magical fingerprint that has this special pattern of zeros in the beginning, and they're like, oh, wow, it must have taken a lot of work to find that random number that you have to plug in the nonce. That is proof that you did the work, proof of work. That's how a nonce works. Now, there are some complications. 32-bits is not enough to do all of the hashing you need. Miners actually use some additional space in the coin base that doesn't do anything, for changing some bits there. They also use part of the timestamp, because they need to move a lot of bits in the input to produce that. The nonce isn't just in one place, but that's more of an implementation detail. A couple of follow-up questions on that, which I find interesting. Really good questions in the chat room today. Talking about nonces, Luke asks, Do the miners know the amount of zeros required for the next block? Yes, that's the target difficulty. The target difficulty is, how many zeros does the hash have to have? In simple terms, that means in binary, but you can just think of it as a number. If I say that a number starts with so many zeros, effectively what I'm saying is that that number is less than x. So, x is the target. In order for your hash to be within the difficulty target for the next block, it has to start with a certain number of zeros. It has to be a smaller number than the difficulty target. That difficulty target is known by every node on the network, because every node on the network calculates that difficulty target using the same formula. Every 2016 block, every node puts the same numbers into that formula and produces the same answer. The way they do it is they say, What was the difficulty target for the previous two-week period? How many blocks did we mine and how long did those blocks take? So, we're looking to mine 2016 blocks, and because we're looking to mine them in 10 minutes each, that would take, theoretically, 20,160 minutes to mine these 2016 blocks. Let's look, how long did it take? Oh, it actually took 10% longer than 20,160, which means that miners are not able to find blocks every 10 minutes. They're a bit slower, they're 10% slower, which means it's 10% too difficult, which means that the difficulty needs to be adjusted by exactly 10%. So, the difficulty is reduced by 10%. Because the number of blocks 2016 is fixed, the time it took to mine those 2016 blocks is the same. Everybody knows the answer to how long it took in minutes, because they counted the same way. Therefore, they can do this division and find exactly how much to adjust the target difficulty. Everybody has the same target difficulty for the previous round, and that way everybody knows. Okay, the next block is in a new difficulty period. I expect the difficulty target for the next block, based on my calculations, to be x. I will only accept blocks whose hash is less than x. Everybody comes up with the same answer for x, and therefore everybody is looking for miners to achieve the same amount of proof of work for the next block, based on that. That's the difficulty retargeting algorithm, which happens every two weeks, or more specifically every 2016 block, which allows everyone on the network to know exactly what the difficulty of the next block should be at any moment in time, and arrive at the same conclusion. It allows miners to know what they need to do to succeed. They have a target, and all they have to do is say, is the hash less than the target? Yes, it's a valid block. No, keep hashing. Try more nonces. See if you can figure it out. Another question is, I wonder if it's possible to guess the nonce on the first try. Yeah, it's absolutely possible. You might find it on the first try, you might find it on the fifth quintillion time. It doesn't matter. The probabilities are exactly the same. The probability of finding it in your first try is exactly the same as the probability of finding it in your second try, the third try, the fourth try. These are independent events, meaning that the probability of each event does not affect the previous or the next event. There's no link between them. Just like if I flip a coin, whether it comes up heads or tails, the chances of it coming up heads the next time I flip it is still 50%. Even if I flip it a hundred times and it comes up tails a hundred times, the hundred and first time the probability is 50% that it will come up heads, 50% that it will come up tails, the probability doesn't change. The same thing for picking a nonce. The chance that the very first nonce I plug in produces a hash below the difficulty level is exactly the same as the second nonce I try. I could try them randomly. I could try them in order. I could try them in decreasing order. I could start from any value of nonce randomly and then just add one and keep going. It doesn't matter. It makes no difference what you choose as the starting nonce and how you move from nonce to nonce. You could just choose them randomly. However, choosing them randomly involves doing some more computation, because you have to figure out random numbers. And there's no reason to do that. There's plenty of randomness in the cryptographic hash. So instead, you could just increment them by one. That's the fastest way to do it, because incrementing by one in binary is something computers can do very fast. So what you do is you just pick a starting point for your nonce, and you just increment by one. And you have exactly the same chances of finding a valid nonce as everybody else on the network. And here comes an interesting question, which this is difficult to understand, but it's a very important concept on how pools work with lower difficulty. Sergio asks, Why does a pool work with a lower difficulty level for its nodes to solve? If my node finds a nonce that gives a hash lower than the expected difficulty set by the pool, how does that relate to the difficulty set on the Bitcoin network for that block? This is a really, really great question. This takes a bit of more discussion to answer, so that you can really grasp what's happening. But it's a really neat trick. Let's say you have a room full of people, and they each hold two dice. And you have a team who are working together, and their goal is to throw dice below a certain number. And if they find below that certain number, they win. So the team wins. Let's call that the difficulty target. And that's the difficulty target for the blockchain, the whole game. That's the actual difficulty target. So you tell all your players, Listen everybody, we can throw between two and twelve. Our dice, either you get two ones, is the lowest number you can throw, or two sixes, twelve, is the highest number you can throw. We win if we roll less than five total between the two dice. So that means that 6 and 6 don't work, 6 and 5 doesn't work, 5 and 5 doesn't work, 5 and 4 doesn't work, 4 and 4 doesn't work, 4 and 3 doesn't work, 3 and 3 doesn't work, 3 and 2 works, 2 and 2 works, 1 and 2 works, 1 and 1 works. Any of those throws below three and two work, below five. That is the target for the whole game. Your team starts throwing dice. You want to reward the people who are throwing dice most often, because they are doing more of the work for the team. How do you count whether they are throwing dice often enough? You could just wait until one of them wins. But if you just wait until one of them wins and give them all the winnings, then it is not really a pool. That is the same as if they were competing by themselves. What you do is come up with a pool strategy that involves giving them a portion of the reward. No matter who in the team throws less than five, or five and below, the whole team wins. But then you want to split those winnings based on how much everybody contributed to all of this dice throwing... that made you a winner. How do you do that? You set a different difficulty target and you say, Every time you throw less than ten, I count one share of contribution to the work for you as a team member. The team members are throwing dice. Twelve doesn't count, eleven doesn't count, ten doesn't count, nine. That is below the team difficulty, but it is not below the game difficulty. I count one share because I am doing work, because I threw nine, and I keep throwing. Because the team difficulty is anything below ten, that will give us a pretty good metric as to who is doing the most work. The people who are doing the most work will tend to throw more nine and below dice. They are going to get more shares, so we will be able to allocate shares based on them throwing low numbers. That means they are throwing enough dice, because the probability is the same. But here is the thing, a winning dice throw that is below five is also below nine. As long as your people are throwing dice, the chances of them throwing below nine are the same as the chances for any single throw, as them throwing below five. They are not losing anything by announcing, we didn't win the game, but I did win the pool difficulty. They announced that the dice throw is still helping you get closer to winning the game, because they might have thrown less than five, but it gives you a way to track their performance, because they threw less than ten. By setting these two difficulty levels, you have the difficulty at which we win the game, and then you have the difficulty at which your contribution as a team member is recognized and you count a share of the work. But that is less difficult to throw, then everybody can start throwing their dice and trying to win the game as a pool, and then you can allocate the winnings correctly by counting their shares. That is how the pool difficulty works. I hope that was understood. If I have an ASIC miner and I get a reward, how is this technically linked to a wallet of mine? Can you explain the process I should follow? That is a great question, Scott. How does the network know who to pay when you win a block? It is really quite simple when you think about it. When you have an ASIC miner, you construct a candidate block that is the block you are going to try to find a proof of work for. That candidate block is made by your own computer, so your computer that is connected to the ASIC miner, that is collecting transactions and blocks off the network, is going to construct a candidate block by taking a whole bunch of transactions that are currently unconfirmed, stuffing them into a block so you can make some fees, and basically building the block. You are proposing a new block to the network. You don't show this to anyone until you have proof of work, because no one is interested in a block that doesn't have proof of work. You just send it to your ASIC miner. Within that block, there is a special transaction called the Coinbase transaction. That is the transaction that pays the mining reward. Who creates that transaction? Your computer creates it. When you are a miner, your computer creates the candidate block, and your computer creates the Coinbase transaction, which represents your $12.5 Bitcoin reward plus whatever fees from all of the transactions that are in there. Therefore, you decide who that transaction pays out to. Your computer puts your own wallet's destination address into that candidate block when you are mining. If you are mining as part of a pool, the pool operator does that. But if you are mining by yourself, for example, which you probably would only do if you had a lot of mining equipment, you would have your computer construct candidate blocks that already have a Coinbase transaction in them that pays you. So you write that transaction. Effectively, miners write a check to themselves to collect the reward. The key to understand here is that that check isn't valid unless the block in which it was written is valid. That only happens if they find proof of work. When a miner verifies and finds a proof-of-work solution for a block through mining, once they've created a valid block, then the blank check they wrote to themselves for $12.5 Bitcoin plus fees in the Coinbase is now a valid transaction. If that block is accepted by the rest of the network, then that transaction exists in everybody's blockchain. It shows clearly that this miner is being paid their reward. Of course, the reward needs to be the correct amount. It needs to be exactly the same as the fees and the block subsidy at this level. Everything in the block has to be valid, otherwise it's rejected. But if it is valid, then there you go.  At that point, 100 blocks later, the miner can now spend that transaction. There's a 100 block limit for Coinbase transactions. They can't be spent until 100 blocks have passed. Essentially, a miner's own Coinbase transaction has to have 100 confirmations before it's spent. This rule is to prevent miners from using chain reorganizations to double-spend their own rewards. David asks, when a miner creates a block, am I right in thinking that this block is then transmitted to all other nodes on the network and is available for any miner to validate? No, not exactly. It is transmitted, but only after the proof of work is found. A miner only transmits a block to other people once that miner has already validated and proven that block by finding a nonce that creates proof of work for that block within the difficulty target. Meaning that the miner has to do quadrillions and quadrillions of hashes in order to find a suitable nonce. Only once that block contains a correct nonce that produces a correct proof of work can the miner send it to the rest of the network. The reason is that when the miner sends that block, the very first node they send it to will validate that block. If it doesn't have proof of work, it will reject it and, in fact, disconnect from the miner that lied. Every node on the network validates every transaction in every block, which means that miners cannot propagate blocks until those blocks have been made valid. That means they have valid proof of work.


you will be no longer required to have a border path and can freely travel into Queensland. A great thing for people coming into Queensland and particularly our neighbours across the border, it'll be back to normal for them so just cross the border as I always have without any passes or any hindrance. Members have been very committed to this you know that's a long haul nine months of standing on borders and keeping professional and keeping doing the right thing and I think the outcomes you know as I said that's a million vehicles actually intercepted many millions more of being wired through and checked in terms of just having their passes.


Okay, so let's try this one, the oxidation of lithium by oxygen to make lithium oxide. Okay, so the first thing you want to do is what? At show which atoms you have, right? So left side not gonna do it, right? Left side, Li, right? And what else? Very good, very good. And over here, do we have both of those elements? Especially if you only say yes and no, nobody's ever gonna know you, all right? Okay, so how many lithiums do we have? One, right? Over here, oxygens? Well, yeah, because it's O2, that's a molecule, right? So we always have to keep oxygen as O2, at least on this side of the reaction equation, okay? So we have two of them. We look over here, how many lithium? Two, very good. And oxygen, how many lithium? Okay, so let's step back and we look, okay, those are all scrambled up, right? We don't we don't got the right numbers of anything. And we would have to remember we want to balance these numbers. So the easiest way to do this one is well, I see I have two oxygens over here and one oxygen over here, so five foot of two there. Okay. Let's now figure out how many lithiums and oxygens we have on the products, okay? So remember when I'm putting the coefficient there, that's like saying this multiplied by that coefficient, okay? So the subscript here multiplied by the coefficient, so times two, so how many lithium are we gonna have? Both. And here, what are we gonna do? Very good, times two, all right, and what are we gonna get? Two. Okay, so do you see anything cool? Something's balanced, right? Oxygens are balanced, right? But lithiums aren't, right? So what are we gonna have to do to our lithiums over here? Make it a four. So what do I multiply one by to equal four? One times what? Equals four. Yeah, one times four Equals four. So that means four has to be our what? Coefficient, we call it, okay? Okay, so now just to check, right? Lithium-4, lithium-4, balanced. Oxygen-2, oxygen-2, balanced. Are we okay with that one?


You're watching Impulse on the Freedom Network, and now here's Anthony. Thank you so much. I appreciate you and I appreciate our audience. Today I wanted to talk to you about this. This is a headset specifically designed to work on mobile gaming platforms, however it does other things too. This headset says that it's designed for PlayStation 4, and as you can see here, it comes with one of the one-eighth inch Omni-Jax, which will both handle your microphone and your speakers here. So really, in essence, it'll also work on PC, it'll work on pretty much anything to some extent. Now I've got the cord crimped here, however the cord here is about three feet long. It doesn't seem that long, but let me show you this. It comes with an adapter. This adapter's cord is about eight feet long. What happens is if you're using it for mobile gaming, you simply plug this into the headset portion for your iPhone or Android device. So it's great for that. Or you can plug it in here, and just like any Turtle Beach headset that's of any quality, you can do a base boost. You can also adjust in-game volume and mute or unmute your microphone from this dongle. And then this dongle is actually USB. Oh, like I said, long cord. There we go. It's actually a USB dongle. So that's really nice. It gives it a lot of really cool ways that it can be used. I also personally enjoy the fact that it's blue. Blue is awesome. Blue is king, especially when we're using green screens. As far as the headset itself, when you move the microphone, you do get a really annoying clicking, which I'm not a huge fan of. However, once you get the main arm where you'd like it, repositioning the microphone itself is really easily easily done. But as you can tell, it's also very easy to trigger that clicking, which, like I said, is annoying. The ear padding is fairly soft. It also doesn't really cancel out any noise from outside the headset. In my personal experience, it's comfortable to wear and it's fairly well ventilated. But you know, like I said, outside noise kind of plays into a factor. Sound quality, as far as reproduction, I would place it at about a seven. And as far as the microphone quality, putting it at about a four. That's even after discounting for things like, you know, the fact that it's a more it's a headset, because those microphones are always really known to be the band. Overall, because of the price point and because of everything else, I think it's strong contender. It's not the most perfect headset that I've ever seen. However, I will say that if you're looking for something in a low price point anywhere about $30 or so, this is a decent one. So just keep that in mind when you're out there buying. If you have any experience with this headset or any headset like it, let me know in the comment section down below and we will talk about it. Overall quality of the headset, I put it about a six or so. But that's after taking consideration that it's got a low price point. If I had to compare it against some of the other higher end ones that I've been reviewing on this show, I would probably put it in about a four or a three. But as far as budget headsets go, this one's decent. I hope that this video has been helpful for you. If it has, let us know in the comment section down below. And until next time, I'm Anthony. Like, subscribe, comments, please. Oh, and also, remember, you can catch me at youtube.com slash a. The padding up top is very firm, but not uncomfortably. So the padding around the ears is rigid, but it's not uncomfortable to your ears. If you really look at yourself, you will be speechless. What happened to being doctors and teachers? What happened to being your brother's keeper? Nowadays kids won't worry about the


Fel gyntaf y toffi TV yw'r Eivarton News Daileey, Eivarton beat Berlun 31 y Gwlderswrn Parc last night o go into the top four in the Premier League. Rafa Benitez has said the hard work must continue. Benitez, talking about the formation last night, said that it was more down to the tactics rather than the shape why Eivarton were able to overcome a tough Berlun side last night. He is demanded that the player is way harder, this is being backed up by the likes of Andrews Tawnesend and Shea McChulman who are the manager is very demanding, is wants more and more from us. We did see an absolute goal of the season that could send off Andrews Tawnesend last night to put Everton to one of it. It was a fantastic strike, its F dışs Premier League goal for the club, what a way to get it! Tawnesend is absolutely delighted when his after-match interview felly eu r goin o'r maes yn feddwl. Pes ryw iawn i'ch golffol i'ch golygiad. Roedd'n amser yn ddull i, mae'r ddechrau. Rydym yn gweithio bod, gan y 5 o 6 ran, mae hynny yn ffai. Roedd o'r golygiad yn fwy o'r golygiad, yn byw i'r drafod ein golygiad, a mi'n clrwpio'r golygiad. Wyddech chi oherwydd ar y cofnod. Mae'n fwy hoffi eu dal yn y gychwyn ffynol. Rhywb bod y ffynol yn gweithio'r ei fyddechrau ar yr eistedding. Mae'r gwaith yn cyfrifio gyda Evernon a mae oedd weithio i Aston Villa yn ymwneud, sy'n 5.30 o'r cyfrifio, mae'n gweithio'n gweithio'n gweithio, a'r amser yn gweithio'n gweithio arall, a'r gweithio'n gweithio arall. Aston Villa yn gweithio'n gweithio'n gweithio'r Gweithredu Cynon Davies, a'r trezigau, mae'n gweithio'n gweithio'n gweithio'n gweithio'n gweithio. Leon Bailey yn ymddangos i gyd, mae'n ddau'r haneseng yng Nghymru, felly sio irli team newies from Villa dde, Everton, also with injury problems of their own, Fabian Delf out, Dominic Calderliffen, gonna be missing for at least a fort night's wrap-up, and he says said last night it could possibly be longer, which would basically mean he won't be back till after the international break, if it's longer than that. So, hopefully Dominic makes a speedy recovery and we can get him back into said. Everton today are still interested in Nathan Patterson, that is according to Scottish media, the Rangers right back was apparently subject to a couple of bids by Everton in the summer transfer window, they were rejected out of hand, Everton still hold an interest in that apparently, but other Scottish media are now reporting that Everton have switched their attention to 18-year-old Aberdeen right back Calvin Ramsey. He's played in all of Aberdeen's games so far this season, he's highly rated, 18-year-old, be interested in if Everton were to go for him, would he come straight into the side at that age, or would he just be back up to Coleman, would he play into many threes, it's an interest among what Everton are apparently watching him very closely with a view to a move in January so, want to keep an eye on there. And Everton and Sunderland are close to agreeing a fee for young striker Francis Ocaronco, the 16-year-old was included in the list of 59 under-21 plays that Everton submitted to the Premier League, the move hasn't been fully signed off, hence the negotiating over a fee for him, but he is a very, very highly rated 6-4-3 centre forward who's at Sunderland scored against Everton last season, the Blues impressed with him and look like they've won the race for him. So that's a good one as well, get the young players in as well and hopefully develop them to become 13 players. Make sure you download the ultimate fan app, get involved in that, there is a cross between fantasy football and FIFA's ultimate team, you can win a share of eight and a half grand prize money each week, so get involved in that, if you played toffy picks last year, go on to that, it'll direct you straight there, it's easy to play a free game, there's two subscription models as well, one of two 99-months, one of four 99-months, but you can play it absolutely free, you get three players each week to put in your team and see if they can get your points by the game, so go and get involved in that, the link is in the description below. So like I said, make sure you check out the final where that is live now, where is there, go and watch that, otherwise give this video a thumbs up, subscribe if you haven't and if you want more videos including daily live videos, why not become a patron, the link also in the description, see you later.


We are learning about hybridization and we have shown you the contours of SP hybrid orbital. Well contours of other hybrid orbitals also look qualitatively the same. Quantitatively of course they are different SP hybrid means as you know we have taken linear combination of a 2s orbital and a 2p orbital. Notionally we always take 2pz orbital because generally if there is one bond we like to do it along z axis but have a closer look at the contour diagram. So, what I did not discuss in the previous module is just have a look at these numbers here of course it is 0 right this is the nodal surface. Then if you let us start with the major loop this one is 0.1 these are all relative numbers 0.2, 0.3, 0.4 and so here is the peak this should not be difficult for you to understand because we have actually plotted in real time those hydrogen atom orbitals earlier and you have seen how these 3D shapes come and what contour lines are and in the minor loop here I have shown the minor loop to have a negative sign of a function here also see it is minus 0.4 outside and slowly it comes in minus 0.1 minus 0.3 so sorry what am I saying minus 0.1 outside minus 0.2 minus 0.3 minus 0.4 is in the middle right. So, again it builds up on the other side and the nucleus is engulfed by the minor loop and we talked about this and then we said that we look at the shape of 2S orbital 3D shape and 2P orbital 3D plot takes sections it becomes clear that in the immediate vicinity of the nucleus it is a sign of the 2S orbital that takes precedence and the interesting thing about 2S and 2P orbitals is that 2S orbital decays to 0 after a while with maximum at nucleus 2PZ is the other way round it is 0 at nucleus rises to a maximum later on. So, well later on in terms of R at a longer values of R is more accurate. So, that is why in the immediate vicinity of the nucleus it is a sign of the 2S orbital that predominates and that sign does not predominate far away because it is more than offset by the 2PZ orbital sign at long distances from the nucleus. On one side you have constructive interference that is where you get the major loop on the other side you get destructive interference that is where the loop becomes small. So, you can think that as a process of hybridization what happens is so what have we drawn these orbitals these are sort of this tell you where the probability is more. If you think of a P orbital if you think of an S orbital it is it has no directionality. If you think of P orbital equal probability this side equal as that side because this side is minus that side is plus in wave function psi psi square d r or well let us say it is the same. So, same probability but we do not want that we want the electron density to be on one side so that the bond is highly directional then we will get a strong bond. So, by formation of this major loop and minor loop what we can effectively do is we effectively ensure that we have a situation where the majority the most of the electron cloud is on one side or rather we have prepared highly directional orbitals. Now when I talk like this of course I do not mean that we take acetylene and push the electron cloud we do not. In acetylene the electron cloud gets rearranged because it has to form what each carbon has to form a bond with another carbon and hydrogen atom. So, this is the driving force that ensures this rearrangement of new of electron cloud that in a very qualitative manner you can say is hybridization. If you want to think of it without even the little bit of math that we are doing. Everything if you remember the discussion we made of Pauling's introduction to this it is a field that determines what kind of hybridization there will be here the presence of other atoms that is the driving force how many bonds are to be formed that leads to a redistribution of electron clouds which in other words is formation of hybrid orbitals. Okay. So, we have talked about S pure vitals now it is time to talk about some other geometry S pure vitals are good for linear geometry. Now we want to talk about the next step linear geometry means AB2 kind of molecules triatomic molecules of course acetylene is not triatomic but let us keep things simple. Next I want to talk about AB3 kind of molecules that is trigonal geometry since I need 3 hybrid orbitals like this and they have to be at 120 degrees with each other I need 3 atomic orbitals to participate in the process of hybridization. Now the orbitals that I use are S and P orbitals 3 orbitals 1 has to be S always you cannot really mix only 3 P orbitals and get what you want. You mix 3 P orbitals you will never get 3 orbitals in a plane hybrid orbitals that is why S is required. So, S and 2 P orbitals. So, let us work with for now P X and P Y orbitals and let us say that this hybrid orbitals are in some orientation. So, the angle with X of hybrid 1 is theta 1 the angle with X for hybrid 2 is theta 2 and for hybrid 3 the angle with X is theta 3. Please remember I have only defined angles with X axis. So, now if I want to write an expression of these orbitals what will the wave functions be? The wave functions will be something like so let us say I want to write I will write psi 1 for hybrid 1 I am writing psi 1 and please do not worry if you cannot read my handwriting in any case everything is written nicely down below that is equal to say some coefficient C 1 multiply by psi 2 S plus some coefficient multiplied by psi 2 P X plus some coefficient let us say multiplied by psi 2 P Y I do not need psi 2 P Z because I am working in the X Y plane. So, P X and P Y are the orbitals that I should use. So, I have held the molecule in the X Y plane for my convenience. In ideal case scenario it should be held with any orientation in space but I want to simplify the problems I am putting it like this and we will come back to this several times in our discussion. So, now see can I not write something like this C 1 is fine instead of C 2 I can write C 2 dashed multiplied by in place of C 2 will you disagree if I write C 2 dash multiplied by cos theta 1 psi P X and this will be not C 3. C 3 is going to be the same C 2 dashed sin theta 1 psi P X that way we have a little bit of a control over the system because what these cos and sin tell us is sort of the components we are working out components these are like vectors these arrows that have drawn these are the hybrid orbitals you can think of this arrow as one hybrid orbital you can think of an arrow here as P X and arrow here as P Y. So, like we resolve vectors into the components I can write like this then it becomes a little easier because you know what this has to be normalized also. So, the C 1 dash can go out in the normalization constant what about C 1 we will see. So, we will write like this here I am not even trying to normalize yet actually there should be a normalization constant multiplying this these C 1's see what we have written we have written same C 1 for psi S everywhere why because the contribution of S to all the orbitals has to be same we are working with the with equivalent orbitals. So, S character is same also there is only one 2 S orbital in the atom. So, there is I hope it is not very difficult for you if I write 3 C 1 square is equal to 1 because C C 1 square is contribution of this S orbital in the first wave function C 2 square is a contribution of psi 2 S in the second wave function second hybrid wave function this is well again this is C 1 C 1 square is a contribution of psi 2 S in the third hybrid wave function. So, the total contribution has to be 1 because there is 1 2 S orbital. So, 3 C 1 square equal to 1 so C 1 is equal to 1 by root 3 this is something we are going to use later also. So, already without much hassle I have found out C 1 and what I can also do is if I know what theta is actually I do not have to do anything I just write the value of cos theta 1 I will write the value of sin theta 1 theta 2 sin theta 2 sin theta 3 cos theta 3 and I have got the hybrid wave functions then if required I can normalize. So, this is the most general strategy of writing expressions for your hybrid orbitals. But what we will do is see we have simplified the problem here by holding it in x y plane. So, since we are willing to do that why not simplify it even further by holding one of the hybrid orbitals along one of the axes that will make life even simpler. So, this is how we are going to work it work out the actual coefficients for this problem you might get up a little baffled here and you might think what is going on who has told you that one of the hybrid orbitals is along y axis nobody has told me but nobody has told me where y axis is it is in my hand we are working in free space we are pretending as if you have this one molecule and nothing else so I can set my axis in whichever way I want if you have objections to me playing around with the molecule then I will play around with the axis right. If Muhammad does not go to the mountain the mountain will go to Muhammad it is not so difficult it is relative motion. So, let us say that we work in a situation where the first hybrid orbital is aligned with the y axis the advantage of doing this is that your coefficient of this P y is going to become 0 for the first hybrid orbital. So, C 3 will be 0 first of all I have written a general expression for the hybrid orbital. So, what I am doing here is that I am writing phi for hybrid orbital wave functions I am writing sorry I am writing phi for hybrid wave functions I am writing psi for the pure atomic orbitals. So, for H 1 I have written C 1 psi s plus C 2 psi px plus C 3 psi p y for the second hybrid I have written C 4 psi s plus C 5 psi px plus C 6 psi p y for third one I have written C 7 psi s plus C 8 psi px plus C 9 psi p y just given numbers to coefficients you are free to use different notations you can write C 1 1, C 1 2, C 1 3 or you want to write C 1 s, C 1 p x, C 1 p y different books use different notations please write whatever you want I have used a simple notation in which we give the simple tags to the coefficients. Now what more how more how can we simplify this but before that let us look at the picture once I have held the molecule in x 5 plane I have held H 1 along y axis. So, naturally the second hybrid is going to be like this let us say the second hybrid is towards the positive side of x and negative side of y the angle between y axis and H 2 is 120 degrees angle between y and x is 90 degrees. So, this angle between x and H 2 is 30 degrees. Similarly, the angle between x and H 3 is 30 degrees and H 3 has to be on the other side. So, minus x and minus y I hope that is not difficult to understand now let me try to write the coefficients one by one. So, we have written psi H 1 sorry phi H 1 S P 2 to be detained C 1 from here C 1 psi s plus as we have said earlier there is no contribution from P x here because the orbital is aligned with H 1 is there a contribution from psi s definitely otherwise the shape will not change. So, no contribution from P x and a contribution from C 3. So, one S orbital and one P orbital is are contributing does that make it an S P orbital no it does not it is still S P 2 orbital please hold on to this thought and we will come back to it. Now, do we know what the C 1 is actually we do remember this C 1 must be equal to C 4 must be equal to C 7 remember because S orbital has to make equal contribution to the all the hybrid orbitals. So, C 1 must be equal to C 4 equal to C 7. So, 3 C 1 square must be equal to 1 as we have discussed earlier C 1 is actually 1 by root 3. So, you already know 2 of the coefficients C 1 is 1 by root 3 C 2 is 0 can we figure out C 3 well I have done it in a particular way on the slides but let us just go by whatever we are discussing. So, this is 1 by root 3 C 1 C 2 equal to 0 and we know that for normalization C 1 square plus C 2 square plus C 3 square must be equal to 0. So, 1 by 3 plus C 3 square is equal to 0 what am I doing I am as usual making a mess with 0 then there is the end of it is not it physical chemists are sometimes obsessed with 0s but they are also obsessed with 1 we are talking about normalization condition remember right we are talking about normalization condition which means your integral phi h 1 sp 2 phi h 1 sp 2 that has to be equal to 1 which means I will write it here and then I will erase integral C 1 psi s I put a bracket here plus I will not even write this because you are already convinced that this is 0 plus C 3 psi p y in the same thing C 1 psi s plus C 3 psi p y that is equal to 1 if you expand this what do you get you get C 1 square integral psi s into psi s over all space what is this this is equal to 1 because psi s is normalized similarly I can get C 3 square again I will get psi p y into psi p y integral whole square plus I write C 1 C 3 integral psi s psi p y that is going to be equal to 0 right because this s and p are orthogonal to each other similarly the last term will also be equal to 0 so C 1 square plus C 3 square will be equal to 1 so 1 third plus C 3 square equal to 1 so C 3 is equal to 1 minus 1 third is 2 third root over 2 by 3 not very difficult to figure in fact it is very easy to figure out I do not even have to do the rest you can I think figure out the rest by yourself it is very very simple fun like this is like solving Sudoku or something and it gives you some very interesting insight hold on to the thought the question that we had raised that in the first orbital we are mixing your 1 s orbital and 1 p orbital so is that sp hybridization and we said no the hybridization is still sp 2 how did that happen actually I have answered the question already but I have not told you that we will come to the answer but by then see if you can figure it out yourself see if you can convince yourself that it is really sp 2 and not sp sp sp okay meanwhile we will go ahead and we will write the expression for psi h 2 2 so psi h 2 I can write as we will keep C 4 well no need I already know that it is 1 by root 3 plus C 5 here I will explicitly write minus C 6 because I know very well that psi 2 is on the negative side of y so the value of p y the value of coefficient of p y has to be negative so what I will do is I will keep the coefficients the C is not coefficients the C is C 1, C 2, C 3 I will keep them to be either 0 or positive so I will write the sign explicitly that will be minus and if I want to write an expression for psi h 3 will you agree with me that it has to be C 7 psi s with C 7 equal to C 1 equal to C 4 equal to 1 by root 3 C 7 psi s minus C 8 psi p x minus C 9 psi p y will you agree with me because this h 3 is towards minus x as well as minus y so both the coefficients should have explicit minus sign okay now how do we go about it how do we work this out now we remember the angle the angle is 120 degrees so this angle between x and h 2 is 30 degrees this angle between minus x and h 3 is also 30 degrees this we have done already this is total x contribution is 1 see what happens is when we prepare the slide we have some particular kind of chain of thought whether I may come and I speak here in front of you or in front of the camera the chain of thought sometimes evolves so I might not be saying things exactly in the same sequence but everything is there so we have already figured this out okay this is important this is something I have not said see mod C 5 is equal to mod C 8 do you agree mod C 6 equal to mod C 9 6 mod C 8 equal to mod C 9 do you agree here I have already written C 5 unfortunately so what I am saying is modulus of the coefficient so well there is no need to write modulus also because I made the coefficients this if the C is I made them positive already so mod of coefficient of psi p x has to be the same for h 2 as well as h 3 because the angle is 30 degrees right so what will this component be they should be the same in magnitude so I will write this as C 5 I will write this as minus C 5 similarly this will be minus C 6 this will be minus C 6 what else can we write we can write all these things C 1 square plus 0 plus C 3 square equals to 0 we already did that C 1 square plus C 3 square C 5 square plus C 6 square equal to 1 that is again from normalization condition you will get the same equation from h 2 as well as h 3 so for p x and p y coefficient 0 plus C 5 square plus C 5 square equal to 1 this is C 5 this is C 5 this is 0 okay now we are almost done right because once again how many p x orbitals are there this is one p x orbital right that is why we are saying that this C 5 where is it gone 0 plus C 5 square plus C 5 square equal to 1 0 C 5 C 5 and when I take square this minus minus square of minus becomes plus also so I do not remember where the white space is I will write here so what do I get here 2 C 5 square equal to 1 so C 5 is equal to 1 by root 2 I hope you have your pen and paper with you please write these values down because I have everything written down in the next slide but if you write down you can check so 1 by root 2 that is what I have got so how many coefficients are left now out of the 9 coefficients we have figured out all these we have figured out these we have figured out this we have figured out C 5 also we have figured out C 3 the only thing that we now want to find out would be C 6 okay how do I find C 6 is it difficult it is not difficult it is very easy right because now you can use anything you can use normalization condition by taking C 1 square plus C 5 square plus C 6 square equal to 1 or you can use orthogonality also you can say the C 1 square plus 0 plus C 3 into C 6 equal to 0 so you already know C 3 so only unknown will be C 6 and you can find it out right so when you do that this is what you get I hope the coefficients we worked out are all matching 1 by root 3 root over 2 by 3 1 by root 2 this we worked out this come out to be 1 by root 6 okay so very nicely we have been able to figure out the coefficients of the atomic orbitals in the hybrid orbitals hybrid sp2 orbitals when we hold the molecule in xy plane with one of the hybrid orbitals along the y axis we found the coefficients and we have written the expressions and first thing we see is they are all orthogonal to each other they are normalized we have used the normalization condition are they orthogonal it is easy to see h1 and h2 or h1 and h3 1 by root 3 into 1 by root 3 is 1 by 3 then root 2 by 3 into minus 1 by root 6 is equal to what root 2 by 3 by root 3 is equal to again 1 by 3 so plus 1 by 3 and here we are multiplying plus by minus is minus 1 by 3 that is equal to 0 so please satisfy yourself that how many pairs can you take 3 C 2 right factorial 3 by factorial 2 3 pairs all the 3 pairs of these h orbitals hybrid orbitals they are orthogonal to each other please convince yourselves please work them out please also convince yourselves that they are normalized but it is not even required because we have used normalization condition to be even construct them now we come back to that question the first one is it sp2 or is it sp well to answer the question we need to remember that the mod square of any coefficient gives us the contribution so in the first orbital contribution of psi s is one third or you can write 0.33 if you want I like one third better contribution of P y is square of root 2 by 3 well to third what is the ratio of how do I write it s character I write like this is to p character oh man such bad handwriting the ratio of s character to p character is 1 by 3 is 2 by 3 is 1 by 2 so sp2 sp2 means contribution of s in that orbital is one third total contribution of p is 2 third I should not have said that now because that has a little bit of spoiler for what I am going to say after this well it is okay so contribution from p orbital has to be twice the contribution of s orbital that is the meaning of sp2 it does not mean that exactly one s orbital has to mix with exactly 2 p orbital we are dealing with wave functions here okay so scaling remember scaling the scaling and all can be done let us look at h2 what is the contribution of s orbital that is a foolish question now because contribution is same one third what is the contribution of psi px it is actually half what is the contribution of p y is actually one sixth so what we see is that px contributes to a lesser extent to h2 then does p y and that is not so surprising right not so surprising also sorry what am I saying px contributes to greater extent than p y this is half and this is 1 by 6 that is not so surprising just look at this figure this angle is 30 degrees this angle is 60 degrees it is no wonder that the contribution of the of px is going to be 3 times more than contribution of p y right look at the components you will get it but what is the total contribution of p orbitals half plus one sixth is equal to since it is easy I will actually do it in detail is equal to 4 by 6 is equal to 2 by 3 total contribution of p orbitals is 2 by 3 same as what it was in h1 right so total contribution is the same and it is not very difficult to see that total contribution of p once again here is 2 by 3 as compared to 1 by 3 for s so all are sp2 hybrid orbitals all are equivalent and meaning of sp2 then is what is the contribution that contribution of s is one third total contribution of p total p character is double of that two third 0.33 and 0.67 if you will right so this is what we have worked out from square of coefficients we have established that contribution of s is 0.33 contribution of p I should write 0.67 in all the orbitals they are all equivalent and using them you can now perform bonding in the familiar way for these molecules that are familiar to all of us okay so much for your sp2 orbitals well we started in a way that the angle is 120 degrees but our time is running out so we will stop now but little bit of this discussion of sp2 orbitals is left for the next class we will do back calculation like what we did earlier remember when we were testing our approximate methods we worked with systems for which exact solution was known and we tried to see whether we get the result we are going to calculate the angle and see whether we get 120 degrees that is going to be very useful for us when we talk about sp3 orbitals later on but let us take that along with sp3 orbitals in the next class