Give the expression for the velocity of electron in the first orbit of hydrogen atom for the radius in the ground state of hydrogen atom. Hence, derive the expression for the magnetic field (B) at the centre of the nucleus due to the circular motion of electron.

Explanation

To derive the expression for the velocity of an electron in the first orbit of a hydrogen atom and the magnetic field at the center of the nucleus due to the circular motion of the electron, we can follow these steps:

### Step 1: Understand the Forces Acting on the Electron
In a hydrogen atom, the electron moves in a circular orbit around the nucleus due to the electrostatic force of attraction between the positively charged nucleus and the negatively charged electron. The two main forces acting on the electron are:
- **Centripetal Force (Fc)**: This is required to keep the electron in circular motion, given by the formula:
\[ F_c = \frac{mv^2}{r} \]
...