A muon is an unstable particle with a mass of | vedclass

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(A) The reduced mass $\mu_{red}$ of the system is given by $\mu_{red} = \frac{m_p m_{\mu}}{m_p + m_{\mu}}$.Given $m_p \approx 1836 \, m_e$ and $m_{\mu

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$2.53$

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(A) The reduced mass $\mu_{red}$ of the system is given by $\mu_{red} = \frac{m_p m_{\mu}}{m_p + m_{\mu}}$.Given $m_p \approx 1836 \, m_e$ and $m_{\mu} = 207 \, m_e$, we have $\mu_{red} = \frac{1836 	imes 207}{1836 + 207} \, m_e \approx 186 \, m_e$.The energy levels of a hydrogen-like atom are given by $E_n = -\frac{\mu_{red}}{m_e} 	imes \frac{13.6 \, eV}{n^2}$.For the ground state $(n=1)$, the energy is $E_1 = -186 	imes 13.6 \, eV = -2529.6 \, eV$.The ionization energy is the energy required to remove the muon from the ground state to infinity, which is $-E_1 = 2529.6 \, eV \approx 2.53 \, keV$.

$A$ muon is an unstable particle with a mass of $207 \, m_e$ and a charge of either $+e$ or $-e$. $A$ muon $(\mu^-)$ is captured by a hydrogen nucleus to form a muonic atom. If the proton captures the $\mu^-$, find the ionization energy of this atom in $keV$.

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