Solving for the speed of a recoiling H atom

In summary, the conversation is about a practice problem involving a hydrogen atom in the n=2 state that decays to the ground state by emitting a photon. The question is asking for the speed of the recoiling atom afterwards. One approach is to find the energy difference between the two states and use it in the equation E = (1/2)mv^2 to solve for v. However, this method is not giving the correct answer. Another person suggests using conservation of momentum, which ultimately solves the problem.
  • #1
silex
2
0
Hey everyone,
I have a practice problem that I can't figure out:

A hydrogen atom is initially at rest and in the n=2 state. Subsequently, it decays to the ground state by emitting a photon. What is the speed of the recoiling atom afterwards? (Mass of H atom = 1.67 * 10^-27 kg)

My approach is to find the difference in energy between the two states by using E = -13.6/n^2 for each state (n=1 and n=2), then finding the energy difference, and setting that equal to (1/2)mv^2 and solving for v, but I'm not getting the right answer. (The correct answer is 3.4 m/s)
Can someone help me with this?

Thanks in advance

-s
 
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  • #2
use 4 in work reverse?
 
  • #3
I would use conservation of momentum.
 
  • #4
Using conservation of momentum solved the problem, thanks.
 

1. How do you calculate the speed of a recoiling H atom?

The speed of a recoiling H atom can be calculated using the equation v = √(2E/m), where v is the speed, E is the kinetic energy of the atom, and m is the mass of the atom.

2. What is the kinetic energy of a recoiling H atom?

The kinetic energy of a recoiling H atom can be calculated using the equation E = 1/2 * m * v^2, where E is the kinetic energy, m is the mass of the atom, and v is the speed of the atom.

3. What is the mass of a recoiling H atom?

The mass of a recoiling H atom is approximately 1 atomic mass unit (amu).

4. How does the speed of a recoiling H atom affect its kinetic energy?

The speed of a recoiling H atom is directly proportional to its kinetic energy. This means that as the speed of the atom increases, its kinetic energy also increases.

5. Can the speed of a recoiling H atom be measured experimentally?

Yes, the speed of a recoiling H atom can be measured experimentally using various methods such as time-of-flight spectroscopy or velocity map imaging.

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