Question

An electron can remain in excited state for about ${10}^{-8}$ seconds. If in a Hydrogen atom an electron is in first excited state then select the correct statement(s).

• A. Radius of circular path in 1st excited state is 212 pm
• B. Speed of electron in 1st excited state is $1.1\times {10}^{6}m/s$
• C. Before transition to ground state electron will make around $8.2\times {10}^6$ revolutions
• D. Speed of electron decreases as it moves to ground state from excited state

Answer 1

Answer: (A), (B), (C)

The correct options are
A Radius of circular path in 1st excited state is 212 pm
B Speed of electron in 1st excited state is $1.1\times {10}^{6}m/s$
C Before transition to ground state electron will make around $8.2\times {10}^6$ revolutions

$n=2r=\frac{{ϵ}_0{h}^2}{\pi m{e}^2}\left(\frac{n^2}{Z}\right)=53\left(\frac{n^2}{Z}\right)\Rightarrow r_2=53\times 4=212pmv=\frac{e^2}{2{ϵ}_{0}h}\left(\frac{Z}{n}\right)=2.2\times {10}^6\left(\frac{Z}{n}\right)m/s\Rightarrow v_2=1.1\times {10}^{6}m/s$

$w=2\pi f\Rightarrow f=\frac{v}{r\times 2\pi }=\frac{2.2\times {10}^6\left(\frac{Z}{n}\right)}{53\times {10}^{-12}\frac{n^2}{Z}2\pi }$

No. of revolutions is, $N=f\times {10}^{-8}=8.2\times {10}^6$