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The radius of the first permitted Bohr orbit, for the electron, in a hydrogen atom equals $0.51 \AA$ and its ground state energy equals $-13.6 \mathrm{eV}$. If the electron in the hydrogen atom is replaced by muon $\left(\mu^{-}\right)$[charge same as electron and mass $\left.207 \mathrm{~m}_{\mathrm{e}}\right]$, the first Bohr radius and ground state energy will be, (1) $2.56 \times 10^{-13} \mathrm{~m},-13.6 \mathrm{eV}$ (2) $0.53 \times 10^{-13} \mathrm{~m},-3.6 \mathrm{eV}$ (3) $25.6 \times 10^{-13} \mathrm{~m},-2.8 \mathrm{eV}$ (4) $2.56 \times 10^{-13} \mathrm{~m},-2.8 \mathrm{keV}$
The radius of the first permitted Bohr orbit, for the electron, in a hydrogen atom equals $0.51 \AA$ and its ground state energy equals $-13.6 \mathrm{eV}$. If the electron in the hydrogen atom is replaced by muon $\left(\mu^{-}\right)$[charge same as electron and mass $\left.207 \mathrm{~m}_{\mathrm{e}}\right]$, the first Bohr radius and ground state energy will be, (1) $2.56 \times 10^{-13} \mathrm{~m},-13.6 \mathrm{eV}$ (2) $0.53 \times 10^{-13} \mathrm{~m},-3.6 \mathrm{eV}$ (3) $25.6 \times 10^{-13} \mathrm{~m},-2.8 \mathrm{eV}$ (4) $2.56 \times 10^{-13} \mathrm{~m},-2.8 \mathrm{keV}$
Physics | Physics
The radius of the first permitted Bohr orbit, for the electron, in a hydrogen atom equals $0.51 \AA$ and its ground state energy equals $-13.6 \mathrm{eV}$. If the electron in the hydrogen atom is replaced by muon $\left(\mu^{-}\right)$[charge same as electron and mass $\left.207 \mathrm{~m}_{\mathrm{e}}\right]$, the first Bohr radius and ground state energy will be, (1) $2.56 \times 10^{-13} \mathrm{~m},-13.6 \mathrm{eV}$ (2) $0.53 \times 10^{-13} \mathrm{~m},-3.6 \mathrm{eV}$ (3) $25.6 \times 10^{-13} \mathrm{~m},-2.8 \mathrm{eV}$ (4) $2.56 \times 10^{-13} \mathrm{~m},-2.8 \mathrm{keV}$

The correct answer is (4)

Sol. $r_{n} \propto \frac{1}{m}$
$
\begin{array}{l}
\mathrm{r}_{\mu}=\frac{0.51}{207}=2.56 \times 10^{-13} \mathrm{~m} \\
\mathrm{E} \propto \mathrm{m}_{\mathrm{e}} \\
\begin{array}{l}
(E)_{\mu} & =-13.6 \times 207 \\
& =-2.8 \mathrm{keV}
\end{array}
\end{array}
$

i

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