# Recoil Kinetic Energy

I'm reading in a book that the recoil kinetic energy of an atom after the emission of a photon is:

Kr = (E1 - E2)^2 / 2Mc^2

Where M is the mass of the atom and E1 is the initial level from where the electron jumped back to E2, producing the photon.

Is this true? where does it come from?

Mentor
Originally posted by MiCasilla
Is this true? where does it come from?
Where does the recoil come from? Newton's First Law. Every action has an equal and opposite reaction.

Thank you Russ,

I am not too familiar with this. What I'm trying to find out is where this formula comes from. It is not so obvious to me. In fact I am not even sure if it is right.

When the photon is emitted from the atom I can understand that it recoils, just like a gun does if you shoot...

I assume that the formula came from conservation of energy and momentum, but I do not see how to get there.

Does it make sense to you?

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dhris
Hello,

If the electron jumps from E1 to E2, the photon has energy (E1-E2), by conservation of energy. A photon's momentum and energy satisfy the relation E=cp (this is probably your missing ingredient). Therefore, the photon has p = (E1-E2)/c. The atom now has momentum -p by conservation of momentum and its kinetic energy is given by Kr = (1/2)M v^2 = (1/(2M)) p^2. Substituting the expression for p from above leads to the answer you seek.

dhris