An electron is revolving in a circular orbit of radius $r$ in a hydrogen atom. The angular momentum of the electron is $L$. The relation between the magnetic dipole moment $(m)$ associated with it,the gyromagnetic ratio $(R)$,and $L$ is:
- A$m = -\frac{L}{R}$
- B$m = -RL$
- C$m = -RL^2$
- D$m = \frac{R}{L}$
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$A$. Speed of revolution of electron $i$. $\frac{1}{4 \pi \varepsilon_0} \frac{2 \pi Z e^2}{n h}$ $B$. Kinetic energy $ii$. $-\left(\frac{1}{4 \pi \varepsilon_0}\right)^2 \frac{2 \pi^2 m e^4 Z^2}{n^2 h^2}$ $C$. Total energy $iii$. $\left(\frac{1}{4 \pi \varepsilon_0}\right)^2 \frac{2 \pi^2 m e^4 Z^2}{n^2 h^2}$ $D$. Frequency $iv$. $\left(\frac{1}{4 \pi \varepsilon_0}\right)^2 \frac{4 \pi^2 Z^2 e^4 m}{n^3 h^3}$
| $A$. Speed of revolution of electron | $i$. $\frac{1}{4 \pi \varepsilon_0} \frac{2 \pi Z e^2}{n h}$ |
| $B$. Kinetic energy | $ii$. $-\left(\frac{1}{4 \pi \varepsilon_0}\right)^2 \frac{2 \pi^2 m e^4 Z^2}{n^2 h^2}$ |
| $C$. Total energy | $iii$. $\left(\frac{1}{4 \pi \varepsilon_0}\right)^2 \frac{2 \pi^2 m e^4 Z^2}{n^2 h^2}$ |
| $D$. Frequency | $iv$. $\left(\frac{1}{4 \pi \varepsilon_0}\right)^2 \frac{4 \pi^2 Z^2 e^4 m}{n^3 h^3}$ |
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