Question

The energy of a photon in a hydrogen atom is \( -13.6 \, \text{eV} \). What are the possible energies of the electron in other levels of the hydrogen atom?

• A. \( -13.6 \, \text{eV}, +27.2 \, \text{eV} \)
• B. \( -27.2 \, \text{eV}, +13.6 \, \text{eV} \)
• C. \( -27.2 \, \text{eV}, -13.6 \, \text{eV} \)
• D. \( -13.6 \, \text{eV}, -27.2 \, \text{eV} \)

Hint:

The energy of an electron in a hydrogen atom decreases with increasing quantum number and follows the formula \( E_n = - \frac{13.6}{n^2} \).

Answer 1

The Correct Option is B

Step 1: Understanding the energy levels of hydrogen atom.
In a hydrogen atom, the energy of the electron in a given level \( n \) is given by the equation: \[ E_n = - \frac{13.6}{n^2} \, \text{eV} \] where \( n \) is the principal quantum number.
Step 2: Calculating the energy for other levels.
For the first excited state (n=2), the energy is \( E_2 = - \frac{13.6}{2^2} = - 3.4 \, \text{eV} \). Similarly, for higher levels, the energy can be calculated.
Step 3: Conclusion.
The possible energies for the electron in different levels are \( -27.2 \, \text{eV} \) and \( +13.6 \, \text{eV} \), which makes option (B) correct.