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Q.

In a hypothetical Bohr’s hydrogen atom the mass of the electron is doubled. The energy $E_{0}$ and radius $r_{0}$ of the first orbit will be ( $a_{0}$ is the Bohr radius for the first orbit)

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a

$E_{0} = - 27.2 e V, r_{0} = a_{0}$

b

$E_{0} = - 13.6 e V, r_{0} = a_{0} / 2$

c

$E_{0} = - 27.2 e V, r_{0} = a_{0} / 2$

d

$E_{0} = - 13.6 e V, r_{0} = a_{0}$

answer is C.

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Detailed Solution

$E \propto m_{e}$ and $r \propto \frac{1}{m_{e}}$ when mass of electron is doubled, then $E \to 2 E_{0}$ and $r \to \frac{a_{0}}{2}$

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In a hypothetical Bohr’s hydrogen atom the mass of the electron is doubled. The energy E0 and radius r0 of the first orbit will be ( a0 is the Bohr radius for the first orbit)