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The period of revolution of an electron in the ground state of hydrogen atom is \( T \). The period of
revolution of the electron in the first excited state is
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revolution of the electron in the first excited state is
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\( 8 \mathrm{~T} \)
Time period of revolution of electron is given as
$T=\frac{2 \pi r}{v}$
We know $r \propto n^{2}$ and $v \propto \frac{1}{n}$
$\Rightarrow T \propto n^{3}$
Time period of revolution in ground state $=\mathrm{T}$
Time period of revolution in first excited state $=T_{1} \propto 2^{3}=8$
Therefore, $\frac{T}{T}=8$
$\Rightarrow T_{1}=8 T$
$T=\frac{2 \pi r}{v}$
We know $r \propto n^{2}$ and $v \propto \frac{1}{n}$
$\Rightarrow T \propto n^{3}$
Time period of revolution in ground state $=\mathrm{T}$
Time period of revolution in first excited state $=T_{1} \propto 2^{3}=8$
Therefore, $\frac{T}{T}=8$
$\Rightarrow T_{1}=8 T$
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