Chapter 27, Problem 26Q

To determine

Why photons have slightly less energy than that predicted by equation

hf= E_u-E_l.

Answer to Problem 26Q

Solution:

Due to some energy spent in the motion of hydrogen atom opposite to photon motion.

Explanation of Solution

The light is emitted only when an electron jumps from a higher state to lower energy (state), a single photon is emitted in a transition whose energy and momentum are taken away. Most of the energy goes into the photon, but not all of it, because of conservation of momentum.

Virtually there is a small spring that pushes hydrogen atom in the opposite direction of photon motion (to keep the total momentum=0). This energy has to come from the energy released by the electron transition, so that the resultant photon has a slightly less total energy and momentum that predict from the formula hf= E_u-E_l..