Recoil velocity of atom interms of mass and energy

[NUFC]

Homework Statement

I have a question to answer but am struggling to even start it. The question is basically an atom absorbs a photon (energy E), rest mass of atom is m, find recoil velocity in terms of E and m after absorption.

Homework Equations

i think i need th emomentum of the photon which i believe is p = m(rel) * c and rest mass of atom m = E/c^2 but that is as far as i get.

The Attempt at a Solution

S
Please see relevant equations above

 

[Rajini]

Hi,
I will tell you in small steps, so you can get the solution.
1)First find recoil energy (E_R). It is just kinetic energy (KE). Use mass m and velocity v.
2)Now relate the equation in (1) to atom's momentum p_a. a for atom.
3)What is the momentum of photon p_p (subscript p for photon) with energy E (remember photon travels with speed of light c)?
4)Apply conservation of momentum, i.e. p_p=p_a.
5)When you apply and solve for E_R you get E_R in terms of energy E, m and c.
good luck.

 

[NUFC]

Hi Rajini, I have tried to follow your simple steps but unfortunately am still baffled, I find it dificult to get my head around this type of problem!. What I have is
1) Er = 1/2mv^2
2) Pa = (M(atom) + M(photon))v(atom) - now not sure how to relate this with 1
3) Pp = gammaM(photon)V(photon)

Unfortunately that is it at the moment, my mind is blank!

I will keep plugging away but thanks for your help anyway.

 

[Rajini]

Hi,
I have given you more details.
You can related step 2 to 1.
What is the formula for momentum ? and formula for momentum of photon ?
TIP: find momentum for atom and photon separately (dont add)
also 3. is wrong (photon has no mass) !
Please write what all you did?

 

[Cruikshank]

Hello, I am stuck on the same problem! But the answer given above does not work. Momentum is conserved, but mechanical energy is *not*, because the atom absorbs the energy and an electron jumps to a higher orbit in response. I assumed the Doppler effect for light was involved, and I got exactly double the result the book did (Bransden and Joachain, Chapter 1, problem 21.) I can't find the factor of two anywhere. I used an expansion of the square root and approximated.