Q148 / 180 · KCET 2018 · Physics

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

  • A
    2T
  • B
    4T
  • C
    1T
  • Correct answer
    D
    \( 8 \mathrm{~T} \)

Solution

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, $\frac{T}{T}=8$ $\Rightarrow T_{1}=8 T$

Hence, the correct answer is option: 'D'.

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