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(D) The Bohr magneton $(\mu_B)$ is defined as the magnetic moment of an electron orbiting in the first Bohr orbit of a hydrogen atom.According to Bohr

Vedclass · Accepted Answer

$\frac{e h}{4 \pi m_e}$

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(D) The Bohr magneton $(\mu_B)$ is defined as the magnetic moment of an electron orbiting in the first Bohr orbit of a hydrogen atom.According to Bohr's quantization condition, the angular momentum $L$ is given by $L = m_e v r = \frac{n h}{2 \pi}$.For the first orbit $(n = 1)$, $L = \frac{h}{2 \pi}$.The magnetic moment $\mu$ of a current loop is given by $\mu = I A$, where $I = \frac{e}{T}$ and $T = \frac{2 \pi r}{v}$.Thus, $\mu = \frac{e v}{2 \pi r} 	imes (\pi r^2) = \frac{e v r}{2}$.Substituting $L = m_e v r$, we get $\mu = \frac{e L}{2 m_e}$.Substituting $L = \frac{h}{2 \pi}$, we get $\mu_B = \frac{e}{2 m_e} 	imes \frac{h}{2 \pi} = \frac{e h}{4 \pi m_e}$.

Bohr magneton is given by (symbols have their usual meanings)

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