Question

What is the magnetic field at the centre of the nucleus when an electron is revolving in the first orbit of the hydrogen atom?

Answer 1

12.5 T

Answer 2

The magnetic field at the center of the nucleus due to the revolving electron is calculated using the formula for the magnetic field at the center of a current loop, $B = \frac{\mu_0 I}{2r}$. The current $I$ is the charge of the electron divided by its time period of revolution, $I = \frac{e}{T} = \frac{ev}{2\pi r}$. Substituting this gives $B = \frac{\mu_0 ev}{4\pi r^2}$. Using the standard values for the radius ($r_1 = 0.529 \times 10^{-10}$ m) and velocity ($v_1 = 2.188 \times 10^6$ m/s) of the electron in the first Bohr orbit of hydrogen, along with the values of $e$ and $\mu_0$, the magnetic field is calculated to be approximately 12.5 T.