Calculate Speed of Recoiling Hydrogen Atom After Transition to Ground State

In summary, a hydrogen atom in the n = 4 quantum state transitions to the ground state and emits a photon. The speed of the recoiling hydrogen atom can be calculated by finding the energy difference and potential energy, but the mass of the atom is needed. The mass of a hydrogen atom is equivalent to that of 1 proton. Conservation of energy is the key concept in solving this problem.
  • #1
the armed pacifist
2
0
A hydrogen atom, initially at rest in the n = 4 quantum state, undergoes a transition to the ground state, emitting a photon in the process. What is the speed (in terms of m/s) of the recoiling hydrogen atom?

anyone knows what to do? i calculated the energy difference and got 12.75 eV and i calculated the potential energy as well, but i don't know which mass to assign the atom...

any help is appreciated...
 
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  • #2
(1) What's conserved during the emission?
(2) You can look up the mass of a hydrogen atom!
 
  • #3
reply

well, that's the thing- the problem doesn't state anything more than I put on there... the mass of a hydrogen atom will be that of 1 proton, but I'm not sure if that's what i should look for...

any thoughts?
 
  • #4
You don't need any more information to solve the problem. What's the answer to my first question? (Hint: In any kind of "explosion", what's conserved?)
 

FAQ: Calculate Speed of Recoiling Hydrogen Atom After Transition to Ground State

What is the formula for calculating the speed of a recoiling hydrogen atom?

The formula for calculating the speed of a recoiling hydrogen atom is given by v = (E1 - E2) / m, where E1 is the energy of the initial state, E2 is the energy of the final state, and m is the mass of the hydrogen atom.

How do you determine the energy of a hydrogen atom in its ground state?

The energy of a hydrogen atom in its ground state is determined by the Rydberg formula, which is given by E = -13.6 eV / n^2, where n is the principal quantum number. For the ground state, n = 1, so the energy would be -13.6 eV.

What is the mass of a hydrogen atom?

The mass of a hydrogen atom is approximately 1.0079 atomic mass units (amu) or 1.673 x 10^-27 kilograms.

How does the speed of a recoiling hydrogen atom change with different energy levels?

The speed of a recoiling hydrogen atom will increase as the energy levels increase. This is because a higher energy level corresponds to a larger difference in energy between the initial and final states, which results in a greater velocity according to the formula v = (E1 - E2) / m.

Can the speed of a recoiling hydrogen atom be faster than the speed of light?

No, the speed of a recoiling hydrogen atom cannot exceed the speed of light. This is because the speed of light is the maximum speed limit in the universe according to the theory of relativity.

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