When a photon is absorbed by an atom counter-propagating to the light source, its velocity is decreased by momentum conservation. When the absorbed photon is spontaneously emitted by the excited atom, the atom receives a momentum kick in a random direction. The spontaneous emissions are isotropic and therefore these momentum kicks average to zero for the mean velocity. On the other hand, the mean squared velocity, ⟨ ⟨ v 2 ⟩ ⟩ , is not zero in the random process, and thus heat is supplied to the atom. At equilibrium, the heating and cooling rates are equal, which sets a limit on the amount by which the atom can be cooled. As the transitions used for Doppler cooling have broad natural linewidths γ γ (measured in radians per second), this sets the lower limit to the temperature of the atoms after cooling to be