A stationary hydrogen atom of mass M emits a photon corresponding to the longest wavelength of the Balmer series. Find the recoil speed of the atom. R is the Rydberg constant and h is Planck's constant.
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Question

A stationary hydrogen atom of mass M emits a photon corresponding to the longest wavelength of the Balmer series. Find the recoil speed of the atom. R is the Rydberg constant and h is Planck's constant.

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G1 Physics · Accepted Answer

The longest Balmer wavelength corresponds to 3→2. Photon momentum is pγ = hR(1/2²−1/3²) = 5hR/36. By momentum conservation, recoil speed = pγ/M = 5Rh/(36M). Correct answer: D.