Question

When a hydrogen atom emits a photon in going from $n=5ton=1$, its recoil speed is almost

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

Answer 1

Answer: (C)

$4m/s$

Energy of photon emitted $=13.6(\frac{1}{1}-\frac{1}{25})eV=13.056$ eV

Now, momentum of the photon $=\frac{13.056\times 1.6\times {10}^{19}}{3\times {10}^8}$----------(1)

Momentum of the hydrogen $=$ same as (1)

Let recoil speed be $V$.

$V(1841\times 9.1\times {10}^{-31})=\frac{13.056\times 1.6\times {10}^{19}}{3\times {10}^8}$

$\Rightarrow V\approx 4m/s$