Discussion
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
Answer: D
The atom emits 6 spectral lines.
After absorbing 12.75 eV, the electron's energy is \(-13.6 + 12.75 = -0.85\) eV, which is \(-13.6/n^{2}\) with \(n = 4\). From n = 4 it can return to the ground state by any combination of downward jumps, giving
\[ \frac{n(n - 1)}{2} = \frac{4 \times 3}{2} = 6 \]
lines (4→3, 4→2, 4→1, 3→2, 3→1, 2→1). 3 lines would be for excitation to n = 3, and 4 counts only the jumps from n = 4.
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