Question

The energy of an electron revolving in the nth orbit in Bohr model of hydrogen atom is proportional to:

• A. \(n^2\)
• B. \(n\)
• C. \(\frac{1}{n}\)
• D. \(\frac{1}{n^2}\)

Hint:

While Energy is proportional to \(1/n^2\), remember that the Radius of the orbit is proportional to \(n^2\) and Velocity is proportional to \(1/n\).

Answer 1

The Correct Option is D

To solve this problem, we need to understand the relation between the energy of an electron in the Bohr model of a hydrogen atom and its orbit number, \( n \).

1. According to the Bohr model, the energy \( E_n \) of an electron in the nth orbit of a hydrogen atom is given by the formula: \(E_n = -\frac{13.6 \, \text{eV}}{n^2}\). This formula shows that the energy is inversely proportional to the square of the orbit number \( n \).
2. From the formula, it is clear that as \( n \) increases, the energy becomes less negative (i.e., closer to zero), which means that the electron is at a higher energy level. Conversely, the lower the \( n \), the more negative the energy, indicating a lower energy level for the electron.
3. The options provided are:
   • \( n^2 \)
   • \( n \)
   • \( \frac{1}{n} \)
   • \( \frac{1}{n^2} \)
4. Therefore, the correct answer is that the energy of an electron in the nth orbit in the Bohr model of the hydrogen atom is proportional to \(\frac{1}{n^2}\).

In conclusion, the energy of an electron in the Bohr model decreases with increasing \( n \) because it is inversely proportional to the square of the orbit number \( n \).