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Homework Help: Recoil velocity of atom interms of mass and energy

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data
    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 absorbtion.

    2. Relevant 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.

    3. The attempt at a solution
    Please see relevant equations above
  2. jcsd
  3. Apr 27, 2010 #2
    I will tell you in small steps, so you can get the solution.
    1)First find recoil energy (ER). It is just kinetic energy (KE). Use mass m and velocity v.
    2)Now relate the equation in (1) to atom's momentum pa. a for atom.
    3)What is the momentum of photon pp (subscript p for photon) with energy E (remember photon travels with speed of light c)?
    4)Apply conservation of momentum, i.e. pp=pa.
    5)When you apply and solve for ER you get ER in terms of energy E, m and c.
    good luck.
  4. Apr 29, 2010 #3
    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.
  5. Apr 29, 2010 #4
    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?
    Last edited: Apr 29, 2010
  6. Aug 6, 2010 #5
    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.
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