Atoms - Result Question 9
10. 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 $-13.6 eV$. If the electron in the hydrogen atom is replaced by muon $(\mu^{-})$[charge same as electron and mass $207 m_e$ ], the first Bohr radius and ground state energy will be,
(a) $2.56 \times 10^{-13} m,-13.6 eV$
[NEET Odisha 2019]
(b) $0.53 \times 10^{-13} m,-3.6 eV$
(c) $25.6 \times 10^{-13} m,-2.8 eV$
(d) $2.56 \times 10^{-13} m,-2.8 eV$
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Answer:
Correct Answer: 10. (d)
Solution:
(d) $r \propto \frac{1}{m}$
$R=\frac{0.51}{207} \therefore 2.56 \times 10^{-13} m$
$E \propto m$
$\therefore \quad(E) _{\mu}=-13.6 \times 207=-2.8 keV$
