A muon (mu^-) is a negatively charged particl | vedclass

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(D) The radius of an orbit is given by $r_n = \frac{\epsilon_0 n^2 h^2}{\pi m Z e^2}$. Since $r \propto \frac{1}{m}$,the radius of the muonic orbit $r

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$(A), (C), (D)$

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(D) The radius of an orbit is given by $r_n = \frac{\epsilon_0 n^2 h^2}{\pi m Z e^2}$. Since $r \propto \frac{1}{m}$,the radius of the muonic orbit $r_{\mu} = \frac{r_e}{200}$. Thus,$(A)$ is correct.The velocity of an electron in the $n^{th}$ orbit is $v_n = \frac{Z e^2}{2 \epsilon_0 n h}$. Since $v$ is independent of mass $m$,the speed of the muon is the same as that of the electron. Thus,$(B)$ is incorrect.The ionization energy is $E_n = \frac{m Z^2 e^4}{8 \epsilon_0^2 n^2 h^2}$. Since $E \propto m$,the ionization energy of the muonic atom $E_{\mu} = 200 E_H$. Thus,$(C)$ is correct.The momentum is $p = m v$. Since the velocity $v$ is the same for both and $m_{\mu} = 200 m_e$,the momentum of the muon is $200$ times that of the electron. Thus,$(D)$ is correct.Therefore,statements $(A), (C),$ and $(D)$ are correct.

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