Question

Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atom in the ground state initially is excited by monochromatic radiation of photon energy 12.75 eV. The number of spectral lines emitted by the hydrogen atom, according to Bohr’s theory will be

• A. 2
• B. 4
• C. 3
• D. 6
• E. 5

Hint:

Number of spectral lines = \(\frac{n(n-1)}{2}\).

Answer 1

The Correct Option is D

Concept: Energy levels: \[ E_n = -\frac{13.6}{n^2} \]

Step 1: Find excited level.
Energy required from \(n=1\) to \(n=4\) is approx 12.75 eV.

Step 2: Number of lines.
\[ \frac{n(n-1)}{2} = \frac{4 \times 3}{2} = 6 \]