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  • The frequency of revolution of an electron in the nth orbit is fn. If the electron makes a transition from the nth orbit to (n-1) th orbit t

The frequency of revolution of an electron in the nth orbit is fn. If the electron makes a transition from the nth orbit to (n-1) th orbit t

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\begin{array}{l} m r \omega^{2}=\frac{k e^{2}}{r^{2}} \text { or } \omega^{2}=\frac{k e^{2}}{m r^{3}} \\ \text { or } 4 \pi^{2} f_{n}^{2}=\frac{k e^{2}}{m r^{3}} \text { or } f_{n}^{2}=\frac{k e^{2}}{4 \pi^{2} m r^{3}} \\ \text { But, } r=\frac{1}{k} \times \frac{n^{2} h^{2}}{4 \pi^{2} m e^{2}} \\ \therefore f_{n}^{2}=\frac{k e^{2}\left(k \times 4 \pi^{2} m e^{2}\right)^{2}}{4 \pi^{2} m\left(n^{2} h^{2}\right)^{3}} \\ \text { or } f_{n}^{2}=\frac{k^{4} e^{8}\left(4 \pi^{2}\right)^{2} m^{2}}{\left(n^{2} h^{2}\right)^{3}} \\ \text { or } f_{n}=\frac{4 \pi^{2} k^{2} m e^{4}}{n^{3} h^{3}} \end{array}

 

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Satyajeet Kumar

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