In an atom, electron of charge (-e) performs U.C.M. around a stationary positively charged nucleus, with…
In an atom, electron of charge (-e) performs U.C.M. around a stationary positively charged nucleus, with period of revolution 'T'. If 'r' is the radius of the orbit of the electron and ' $\mathrm{v}^{\prime}$ is the orbital velocity, then the circulating current (I) is proportional to
$\mathrm{e}^{1} \mathrm{r}^{-1} \mathrm{v}^{-1}$
$\mathrm{e}^{1} \mathrm{r}^{1} \mathrm{~V}^{-1}$
$\mathrm{e}^{1} \mathrm{~V}^{1} \mathrm{r}^{-1}$
$\mathrm{v}^{1} \mathrm{r}^{1} \mathrm{e}^{-1}$
Solution
In an atom, electron of charge $(-e)$ perform U.C.M. around a stationary positively charged nucleus, with period of revolution $\mathrm{'T'}$.
If $' r^{\prime}$ is the radius of the orbit of the electron and ' $v$ ' is the orbital velocity, then the circulating current $\mathrm{(I)}$ is proportional to $\underline{\mathbf{e}}^{\mathbf{1}}$ $\underline{\mathbf{v}}^{\mathbf{1}}$ $\underline{\mathbf{r}}^{\mathbf{-1}}$.
$\frac{2 \pi r}{\mathrm{T}}=v$
$\mathrm{I}=\frac{\mathrm{e}}{\mathrm{T}}=\frac{\mathrm{ev}}{2 \pi \mathrm{r}}=\mathrm{e}^{1} \mathrm{v}^{1} \mathrm{r}^{-1} \frac{1}{2} \pi$
$\mathrm{I} \propto e^{1} v^{1} r^{-1}$
$\frac{2 \pi r}{\mathrm{T}}=v$
$\mathrm{I}=\frac{\mathrm{e}}{\mathrm{T}}=\frac{\mathrm{ev}}{2 \pi \mathrm{r}}=\mathrm{e}^{1} \mathrm{v}^{1} \mathrm{r}^{-1} \frac{1}{2} \pi$
$\mathrm{I} \propto e^{1} v^{1} r^{-1}$