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The radius of the first permitted Bohr orbit for the electron in a hydrogen atom equals 0.51 Å and its ground state energy -13.6 eV. If the electron in the hydrogen is replaced by muon ($\mu^-$) [charge same as electron and mass $207m_e$], the first Bohr radius and ground state energy will be:
Detailed Solution
Reduced mass $\mu=\frac{m_\mu m_p}{m_\mu+m_p}=\frac{207\times1836}{207+1836}m_e\approx186m_e$. Radius $\propto\frac{1}{\mu}$ and energy $\propto\mu$: $r_1'=\frac{m_e}{\mu}r_1$ (of the order of $10^{-13}$ m) and $E'=\frac{\mu}{m_e}E=186\times(-13.6$ eV$)\approx-2.5$ keV. The source key gives option (3).