Q83 / 89 · KVPY 2017 (5 Nov SB/SX) · Physics

The magnitude of acceleration of the electron in the $\mathrm{n}^{\mathrm{th}}$ orbit of hydrogen atom is $\mathrm{a}_{\mathrm{H}}$ and that of singly ionized helium atom is $a_{\mathrm{He}}$. The ratio $\mathrm{a}_{\mathrm{H}}: \mathrm{a}_{\mathrm{He}}$ is

  • Correct answer
    A
    $1: 8$
  • B
    $1: 4$
  • C
    $1: 2$
  • D
    dependent on $\mathrm{n}$

Solution

$r \propto \frac{1}{z} \& v \propto z$ $\therefore$ according $\left(\frac{v^{2}}{r}\right) \propto z^{2} \times \frac{1}{(1 / z)}=z^{3}$ $\frac{a_{H}}{a_{H e}}=\left(\frac{z_{H}}{z_{\mathrm{He}}}\right)^{3}=\left(\frac{1}{2}\right)^{3}=\frac{1}{8}$

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

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