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  • The time period of revolution of electron in its ground state orbit in a hydrogen atom is . The frequency of revolution of the electron

The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6\times10^{-16}s. The frequency of revolution of the electron in its first excited state (in s-1) is:-
Option: 1  5.6\times 10^{12}
Option: 2 1.6\times 10^{14}
Option: 3 7.8\times 10^{14}  
Option: 4 6.2\times 10^{15}
 

Answers (1)

best_answer

The velocity of the nth orbit

 V_n \ \alpha \ \frac{z}{n}

the radius of the nth orbit

r_n \ \alpha \ \frac{n^2}{z}

 T=\frac{2\pi r}{V}\\ \\ \Rightarrow T \ \propto \ \frac{n^2\times n}{z \times z}=\frac{n^3}{z^2}\\\\ \Rightarrow T \propto\frac{1}{f} \\ \Rightarrow f \ \propto \ \frac{z^2}{n^3}

f_1=\frac{1}{1.6\times 10^{-16}} \ s^{-1}

and 

\frac{f_1}{f_2}=(\frac{n_2}{n_1})^{3}=8\\ \Rightarrow f_2=\frac{f_1}{8}=7.8 \times 10^{14} \ s^{-1}

 

So, option (3) is correct. 

Posted by

Ritika Jonwal

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