Question

The energy of an electron in a hydrogen atom in ground state is -13.6 eV. Its energy in an orbit corresponding to quantum number \( n \) is -0.544 eV. The value of \( n \) is:

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

The energy of an electron in a hydrogen atom is inversely proportional to the square of the quantum number \( n \).

Answer 1

The Correct Option is D

Step 1: Energy levels in hydrogen atom. The energy of an electron in a hydrogen atom is given by the formula: \[ E_n = - \frac{13.6}{n^2} \, \text{eV} \] Where \( n \) is the quantum number.

Step 2: Solving for \( n \). Given that the energy is \( -0.544 \, \text{eV} \), we can solve for \( n \): \[ - \frac{13.6}{n^2} = -0.544 \] \[ n^2 = \frac{13.6}{0.544} = 25 \] \[ n = 5 \] Thus, the value of \( n \) is 4, corresponding to option .