In a Bohr atom the electron is replaced by a particle of mass 150 times the mass of the electron and the same charge. If $a_{0}$ is the radius of the Bohr orbit, then that of the new atom will be

150 a_{0}

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\sqrt{150} a_{0}

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\frac{a_{0}}{\sqrt{150}}

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\frac{a_{0}}{150}

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Solution

The correct option is D $\frac{a_{0}}{150}$
$r \propto \frac{1}{m}$ ; $\frac{r_{2}}{r_{1}} = \frac{m_{1}}{m_{2}}$
$r_{1} = a_{0}$ ; $m_{1} = m_{e}$ ; $m_{2} = 150 m_{e}$
$r_{2} = \frac{m_{e}}{150 m_{e}} a_{0} = \frac{a_{0}}{150}$

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