Question

The energy required (in eV) to excite an electron in a hydrogen atom from the ground state to the third state is:

• A. \( +0.85 \, \text{eV} \)
• B. \( -3.4 \, \text{eV} \)
• C. \( 12.1 \, \text{eV} \)
• D. \( -12.1 \, \text{eV} \)

Hint:

Use \( E_n = -13.6/n^2 \) to find energy levels. Excitation energy is difference between final and initial states.

Answer 1

The Correct Option is C

The energy levels in hydrogen atom are given by: \[ E_n = -13.6 \cdot \frac{1}{n^2} \, \text{eV} \] For ground state \( n = 1 \): \[ E_1 = -13.6 \, \text{eV} \] For third state \( n = 3 \): \[ E_3 = -13.6 \cdot \frac{1}{9} = -1.51 \, \text{eV} \] Energy required: \[ \Delta E = E_3 - E_1 = (-1.51) - (-13.6) = 12.09 \approx 12.1\, \text{eV} \]