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