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Home » The radius of the first permitted Bohr orbit, for the electron, in a hydrogen atom equals and its ground state energy equals . If the electron in the hydrogen atom is replaced by muon [charge same as electron and mass , the first Bohr radius and ground state energy will be, (1) (2) (3) (4)
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}

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