Q. 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 the Rydberg constant and h Planck's constant)
A) 24m/(25hR)
B) 24hR/(25m)
C) 25hR/(24m)
D) 25m/(24hR)
Explanation
[Solution from source] The photon energy for n = 5 → 1 is E = hcR(1 − 1/25) = (24/25)hcR. Its momentum p = E/c = (24/25)hR, and the atom recoils with equal momentum, so v = p/m = 24hR/(25m). The inverted forms have wrong dimensions for velocity. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.