Question

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius $0.5\dot{\text{A}}$. If the speed of electron is $2.2\times {10}^6\text{m/s}$, then the current associated with the electron will be _____$\times {10}^{-2}\text{mA}$.
[Take $\pi$ as $\frac{22}{7}$]

Answer 1

The current due to a unit charge $e$ is given by,

$I=\frac{e}{T}$

In the equation, substituting $T=\frac{2\pi }{\omega }$ and $\omega =\frac{v}{r}$ we get,

$I=\frac{e\omega }{2\pi }=\frac{ev}{2\pi r}$

$I=\frac{1.6\times {10}^{-19}\times 2.2\times {10}^6\times 7}{2\times 22\times 0.5\times {10}^{-10}}=1.12\text{mA}$

$I=112\times {10}^{-2}\text{mA}$

$\therefore \text{Correct answer}:112$