A mu-meson of charge 'e',mass 208 m_e moves i | vedclass

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(B) The radius of the $n$-th orbit in a hydrogen-like atom is given by $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$.For the first Bohr orbit of a hy

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$n \approx 25$

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(B) The radius of the $n$-th orbit in a hydrogen-like atom is given by $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$.For the first Bohr orbit of a hydrogen atom $(Z=1, m=m_e, n=1)$:$r_1 = \frac{h^2 \epsilon_0}{\pi m_e e^2}$.For the $\mu$-meson system $(Z=3, m=208 m_e)$:$r_n = \frac{n^2 h^2 \epsilon_0}{\pi (208 m_e) (3) e^2}$.Equating the two radii $(r_n = r_1)$:$\frac{n^2 h^2 \epsilon_0}{\pi (208 m_e) (3) e^2} = \frac{h^2 \epsilon_0}{\pi m_e e^2}$.Simplifying the equation:$\frac{n^2}{208 	imes 3} = 1$.$n^2 = 624$.$n = \sqrt{624} \approx 24.98 \approx 25$.

$A$ $\mu$-meson of charge '$e$',mass $208 m_e$ moves in a circular orbit around a heavy nucleus having charge $+3e$. The quantum state '$n$' for which the radius of the orbit is the same as that of the first Bohr orbit for a hydrogen atom is [approximately]:

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