Question

Energy of H atom in ground state is 13.6 eV. No of spectral lines emitted by 'H' atom when a photon of energy 12.75 eV is received?

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

When a hydrogen atom absorbs a photon of energy, the electron moves to a higher energy level. The number of spectral lines corresponds to the number of possible transitions.

Answer 1

The Correct Option is B

The energy levels of the hydrogen atom are quantized, and the energy required to excite the electron from one level to another is given by the difference in the energy of the levels. - The ground state energy of the hydrogen atom is \(13.6 \, \text{eV}\). - When the atom absorbs a photon of energy \(12.75 \, \text{eV}\), the electron will move to an excited state. The possible energy levels of the hydrogen atom are: \[ E_n = \frac{-13.6}{n^2} \, \text{eV} \] Where \(n\) is the principal quantum number. Since the electron is initially at \(n = 1\), it will be excited to a higher level. The energy difference between the levels will give the number of spectral lines. After absorbing \(12.75 \, \text{eV}\), the electron will be in the \(n = 3\) state. The possible transitions are: - \(n = 3 \to n = 2\) - \(n = 3 \to n = 1\) Thus, the number of spectral lines emitted is 3.