Question

Muon $\left({\mu }^{-1}\right)$ is negatively charged $(\left|q\right|=\left|e\right|)$ with a mass $m_{\mu }=200m_e$, where $m_e$ is the mass of the electron and $e$ is the electronic charge. If ${\mu }^{-1}$ is bound to a proton to form a hydrogen like atom, identify the correct statements
(A) Radius of the muonic orbit is $200$ times smaller than that of the electron
(B) the speed of the ${\mu }^{-1}$ in the nth orbit is $\frac{1}{200}$ times that of the electron in the nth orbit
(C) The ionization energy of muonic atom is $200$ times more than that of an hydrogen atom
(D) The momentum of the muon in the nth orbit is $200$ times more than that of the electron

• A. (A), (B), (D)
• B. (B), (D)
• C. (C), (D)
• D. (A), (C), (D)

Answer 1

Answer: (D)

(A), (C), (D)

(A) Radius of muon $=\frac{\text{Radius of hydrogen}}{200}$

Radius of H atom $=r=\frac{{\in }_o{n}^2{h}^2}{\pi m{e}^2}$

Radius of muon $=r_{\mu }=\frac{{\in }_o{n}^2{h}^2}{\pi \times 200m{e}^2}$

$r_{\mu }=\frac{r}{200}$

(B) Velocity relation given is wrong

(C) Ionization energy in $e^{-}$ H atom

$E=\frac{+m{e}^4}{8{\in }_o^2{n}^2{h}^2}$

$E_{\mu }=\frac{200m{e}^4}{8{\in }_o^2{n}^2{h}^2}=200E$

(D) Momentum of H-atom

$mvr=\frac{nh}{2\pi }$

momentum of muon is $200\times mvr$

hence (A), (C) & (D) are correct