Question

A hydrogen atom moving at a speed $v$ absorbs a photon of wavelength $122\text{nm}$ and stops. The value of $v$ is (mass of hydrogen atom $=1.67\times {10}^{-27}\text{kg}$)

• A. $3.25\text{m/sec}$
• B. $6.25\text{m/sec}$
• C. $9.25\text{m/sec}$
• D. $12.25\text{m/sec}$

Answer 1

The correct option is A $3.25\text{m/sec}$

From conservation of momentum,

$\overrightarrow{p_i}=\overrightarrow{p_f}$

Initial momentum of the system, ${\overrightarrow{p}}_i=mv-\frac{h}{\lambda }$

Final momentum of the system, $\overrightarrow{p_f}=0$

$\Rightarrow mv-\frac{h}{\lambda }=0$

$\Rightarrow v=\frac{h}{\lambda m}=\frac{6.63\times {10}^{-34}}{1.67\times {10}^{-27}\times 122\times {10}^{-9}}=3.25\text{m/sec}$

Hence, $\left(A\right)$ is the correct answer.