Question

Assuming the atom in the ground state, the expression for the magnetic field at a point (nucleus) in hydrogen atom due to circular motion of electron is \[ \mu_0 = \text{permeability of free space},\; \epsilon_0 = \text{permittivity of free space},\; m = \text{mass of electron},\; e = \text{electronic charge},\; h = \text{Planck’s constant} \]

• A. $\frac{\mu_0 e^7 \pi m^2}{8 \epsilon_0^3 h^5}$
• B. $\frac{\mu_0 \pi m^2 e^5}{8 \epsilon_0^3 h^3}$
• C. $\frac{\mu_0 \pi m e^4}{8 \epsilon_0^3 h^3}$
• D. $\frac{\mu_0 \pi m^3 e^4}{8 \epsilon_0^2 h^2}$

Hint:

The formula for magnetic field around an electron in a hydrogen atom involves various constants and the quantum mechanical nature of the electron.

Answer 1

The Correct Option is A

Step 1: Expression for magnetic field.
For the magnetic field at a point in hydrogen atom due to circular motion of the electron: \[ B = \frac{\mu_0 e^7 \pi m^2}{8 \epsilon_0^3 h^5} \] This is derived from the general expression for magnetic field due to circular current in an atom.
Step 2: Conclusion.
The correct expression is option (A).