Question

A hydrogen atom emits a photon corresponding to an electron transition from n =5 to n=1. The recoil speed of hydrogen atom is almost (mass of proton = $1.6\times {10}^{-27}kg$)

• A. $10m{s}^{-1}$
• B. $2\times {10}^{-2}m{s}^{-1}$
• C. $4ms-1$
• D. $8\times {10}^{2}m{s}^{-1}$

Answer 1

The correct option is C $4ms-1$

$P_{H-atom}=P_{photon}=\frac{E_{radiated}}{c}$

$=\frac{13.6[\frac{1}{n_1^2}-\frac{1}{n_2^2}]eV}{C}$

$1.6\times {10}^{-27}\times v=\frac{13.6[\frac{1}{12}-\frac{1}{5^2}]\times 1.6\times {10}^{-14}}{3\times {10}^6}$

$v\approx 4m{s}^{-1}$