Question

The ratio of the energies of the hydrogen atom in its first to second excited states is:

• A. 1/4
• B. 4/9
• C. 9/16
• D. 4

Hint:

The energy levels of the hydrogen atom follow the formula \( E_n = - \frac{13.6}{n^2} \), with energy inversely proportional to the square of \( n \).

Answer 1

The Correct Option is B

The energy levels of the hydrogen atom are given by: \[ E_n = - \frac{13.6}{n^2} \, \text{eV} \] where \( n \) is the principal quantum number. The energy ratio for the first and second excited states is: \[ \frac{E_2}{E_3} = \frac{\left( -\frac{13.6}{2^2} \right)}{\left( -\frac{13.6}{3^2} \right)} = \frac{4}{9} \]
Final Answer: \[ \boxed{\frac{4}{9}} \]