Friday, July 9, 2010  More Quantum Mechanics: Electron Spin  So
far, we've seen three different quantum numbers: n (principal),
l (angular momentum), and m_l (magnetic). We now examine how the
fourth quantum number (m_s) or electron spin came about.  By the
early 1920s, quantum mechanics had developed to the point that
theorists realized an electron magnetic moment ought to exist.
In any external magnetic field B, the magnetic moment ought to
experience a force similar to what a magnetic compass needle
experiences in Earth's magnetic field. According to quantum
mechanics, the assumed values should be quantized, so the
magnetic moment can assume only certain values, given by:  2l +
1  Thus, the orientation number will depend on the second
quantum number, l. The angular momentum (L) would therefore be:
L = h/2 pi[l(l +1)]^1/2  In 1922, the German physicists Otto
Stern and Walther Gerlach passed a beam of electrons through a
non-uniform magnetic field B as shown in the top sketch of the
diagram (C denotes colli