Question

The frequency of revolution of the electron in Bohr's orbit varies with \(n\), the principal quantum number as

• A. \(\dfrac{1}{n}\)
• B. \(\dfrac{1}{n^3}\)
• C. \(\dfrac{1}{n^4}\)
• D. \(\dfrac{1}{n^2}\)

Hint:

\[ r_n \propto n^2 \] \[ v_n \propto \frac{1}{n} \] \[ f_n \propto \frac{1}{n^3} \]

Answer 1

The Correct Option is B

Step 1: Write the expression for frequency of revolution.
\[ f=\frac{v_n}{2\pi r_n} \] where: \[ v_n=\text{velocity in }n^{th}\text{ orbit} \] and \[ r_n=\text{radius of }n^{th}\text{ orbit} \]

Step 2: Use Bohr model relations.
For Bohr orbits: \[ v_n \propto \frac{1}{n} \] and \[ r_n \propto n^2 \]

Step 3: Substitute into frequency formula.
\[ f \propto \frac{\frac{1}{n}}{n^2} \] \[ f \propto \frac{1}{n^3} \]

Step 4: Identify the correct option.
Therefore: \[ \boxed{f \propto \frac{1}{n^3}} \] Hence, the correct answer is: \[ \boxed{\mathrm{(2)}} \]