Demiurge42

The following question was asked on Y! Answers by Ben O.

"A hydrogen atom is initially at rest (approximately), in an excited state of unknown quantum number n. The electron drops to the next lower energy level emitting a photon. Estimate the largest possible recoil velocity of the atom."

My first thought was that there couldn't be any recoil because of conservation of energy. When the photon is emitted, energy is converted from the energy stored in the electron orbital to a photon. Therefore, the atom can't recoil since this would add kinetic energy that comes from nowhere.

But what about momentum. A photon has momentum. Therefore the atom must recoil to conserve momentum.

Does the atom actually recoil? How are the issues of conservation of momentum and energy resolved? If the atom does recoil, what is used to determine its recoil?

There's no need to actually solve the problem. I am just trying to get a better understanding of what happens.

I learned in Physics class that the force from a magnetic field on a charged particle is: F = q v x B. Where v and B are the velocity and magnetic field vectors, q is the charge and x means cross product. But, the velocity depends on my frame of reference. For instance I could be moving at the same velocity as the particle so that the particle appears to be stationary in my frame of reference. The force on the particle can't change just because my velocity changes. If it did then different observers would see something different. I'm obviously missing something here.