Question

The electric current $I$ created by the electron in the ground state of $H$ atom using Bohr model in terms of Bohr radius $(a_0)$ and velocity of electron in first orbit $v_0$ is

• A. $\frac{ev_{0}}{2\pi a_{0}}$
• B. $\frac{2\pi a}{ev_{0}}$
• C. $\frac{2\pi a}{v_{0}}$
• D. $\frac{v_{0}}{2\pi a}$

Answer 1

Answer: (A)

In the ground state of hydrogen atom, suppose,
$a_0 =$ Bohr radius
$v_0 =$ velocity of electron in first orbit
$\therefore $ Time taken by electron to complete one revolution,
$T = \frac{2\pi a_0}{v_0}$
$\therefore $ Current created, $I = \frac{\text{charge(e)}}{\text{time(t)}}$
$\frac{ev_0}{2\pi a_0}$