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As the electron in Bohr's orbit of hydrogen atom passes from state $n=2$ to, $n=1$, the $\mathrm{KE}(\mathrm{K})$ and the potential energy (U) changes as
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$K$ four fold, $U$ also four fold
$\mathrm{KE}$ of an electron in nth orbit : $\mathrm{K}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}^{2}}$ and PE of an electron in nth orbit :
$\mathrm{U}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}^{2}}$
$\therefore$ When an electron passes from state $\mathrm{n}=2$ to $\mathrm{n}=1$ $\frac{\mathrm{K}_{2}}{\mathrm{~K}_{1}}=\frac{1^{2}}{2^{2}}=\frac{1}{4}$
$\begin{array}{l}
\text { or } \mathrm{K}_{1}=4 \mathrm{~K}_{2} \\
\frac{\mathrm{U}_{2}}{\mathrm{U}_{1}}=\frac{\mathrm{l}^{2}}{2^{2}}=\frac{1}{4} \\
\text { or } \mathrm{U}_{1}=4 \mathrm{U}_{2}
\end{array}$
$\mathrm{U}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}^{2}}$
$\therefore$ When an electron passes from state $\mathrm{n}=2$ to $\mathrm{n}=1$ $\frac{\mathrm{K}_{2}}{\mathrm{~K}_{1}}=\frac{1^{2}}{2^{2}}=\frac{1}{4}$
$\begin{array}{l}
\text { or } \mathrm{K}_{1}=4 \mathrm{~K}_{2} \\
\frac{\mathrm{U}_{2}}{\mathrm{U}_{1}}=\frac{\mathrm{l}^{2}}{2^{2}}=\frac{1}{4} \\
\text { or } \mathrm{U}_{1}=4 \mathrm{U}_{2}
\end{array}$
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