Recoil velocity of atom interms of mass and energy

In summary: Here is what I got: 1)ER = (1/2mv^2)2)Pa = (M(atom) + M(photon))v(atom)3)Pp = M(photon)v(photon)4)ER-2*Pa = E(photon)5)E(photon) = M(atom) + 2*M(photon)v(photon)Can you help me understand this?Hi,In summary, you calculated the recoil energy of an atom after absorbing a photon.
  • #1
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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 absorbtion.


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
 
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  • #2
Hi,
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.
 
  • #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.
 
  • #4
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?
 
Last edited:
  • #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.
 

Related to Recoil velocity of atom interms of mass and energy

1. What is the equation for calculating recoil velocity of an atom?

The equation for calculating recoil velocity of an atom is v = √(2E/m), where v is the recoil velocity, E is the energy of the atom, and m is the mass of the atom.

2. How does the mass of an atom affect its recoil velocity?

The mass of an atom directly affects its recoil velocity. As the mass of the atom increases, its recoil velocity decreases. This is because the equation for recoil velocity is inversely proportional to the mass of the atom.

3. Is recoil velocity affected by the type of energy an atom possesses?

Yes, the type of energy an atom possesses can affect its recoil velocity. For example, if the atom has thermal energy, its recoil velocity will be different compared to if it has kinetic energy. This is because different types of energy have different equations for calculating recoil velocity.

4. How is recoil velocity related to the conservation of momentum?

Recoil velocity is related to the conservation of momentum, which states that the total momentum of a system remains constant in the absence of external forces. In the case of an atom, when it experiences a recoil velocity, it is due to a transfer of momentum from one atom to another, while the total momentum of the system remains constant.

5. What is the significance of understanding recoil velocity for scientists?

Understanding recoil velocity is important for scientists as it helps them understand the behavior of atoms and their interactions with other atoms. It is also essential for various fields of study, such as nuclear physics, atomic and molecular spectroscopy, and laser technology. Knowledge of recoil velocity also allows scientists to make accurate calculations and predictions in experiments and technological applications.

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