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An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquired as a result of photon emission will be: (m is the mass of the electron, R is Rydberg constant and h is Planck’s constant)

1. 24hR
2. 25hR
3. 25m
4. 24m

Correct answer: 25hR

Solution

When the electron transitions from the fifth energy level to the ground state, the energy difference is emitted as a photon. By conservation of momentum, the atom recoils with momentum equal to the photon's momentum. Using the energy of the photon (E = hR(1/n1² - 1/n2²)) and the relation p = E/c, the velocity of the atom can be derived as v = (25hR)/m.

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