Understanding Recoil Kinetic Energy in Atomic Emission: Fact or Fiction?

[MiCasilla]

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?

 

[russ_watters]

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.

 

[MiCasilla]

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?

 

[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