Question

An excited hydrogen atom initially at rest in n=3 state, emits a photon by making a transition to ground state . Then the momentum of the hydrogen atom will be (in N.s)-

• A. $6.45\times {10}^{-27}$
• B. $6.63\times {10}^{-34}$
• C. $2.15\times {10}^{-27}$
• D. none of the above

Answer 1

The correct option is A $6.45\times {10}^{-27}$

$\frac{1}{\lambda }=1.01\times {10}^7(\frac{1}{n_1^2}\times \frac{1}{n_2^2})⟶\left(i\right)$

$p=\frac{h}{\lambda }⟶\left(ii\right)$

$\text{momentum= p, planck's constant=}h$

$\begin{array}{ccc}\Rightarrow p& =h\times 1.01\times {10}^7(\frac{1}{n_1^2}-\frac{1}{n_2^2})& \\ \Rightarrow p& =6.6\times {10}^{34}\times 1.01\times {10}^7& \times \left(\frac{1-1}{12}\right)\\ & =6.45\times {10}^{-27}{Ns}^{}& \end{array}$