In a hypothetical Bohr hydrogen atom,the mass | vedclass

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(A) The radius of the $n$-th orbit in Bohr's model is given by $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m e^2}$. Since $r \propto 1/m$,if the mass $m$ is

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$E_0 = -27.2 	ext{ eV}; r_0 = a_0/2$

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(A) The radius of the $n$-th orbit in Bohr's model is given by $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m e^2}$. Since $r \propto 1/m$,if the mass $m$ is doubled,the new radius $r_0$ becomes $r_0 = a_0/2$.The energy of the $n$-th orbit is given by $E_n = -\frac{m e^4}{8 \epsilon_0^2 n^2 h^2}$. Since $E \propto m$,if the mass $m$ is doubled,the new energy $E_0$ becomes $E_0 = 2 	imes (-13.6 	ext{ eV}) = -27.2 	ext{ eV}$.Thus,the correct option is $A$.

In a hypothetical Bohr hydrogen atom,the mass of the electron is doubled. The energy $E_0$ and the radius $r_0$ of the first orbit will be ($a_0$ is the Bohr radius).

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