Step 1: Understanding the Concept:
According to Bohr's model, the velocity and orbital radius of an electron depend on the principal quantum number $n$.
The frequency of revolution is the inverse of the time period, which depends on radius and velocity. Step 2: Key Formula or Approach:
Radius of $n^{\text{th}}$ orbit: $r_n \propto n^2$.
Velocity of electron in $n^{\text{th}}$ orbit: $v_n \propto \frac{1}{n}$.
Time period $T_n = \frac{2\pi r_n}{v_n}$.
Frequency $f_n = \frac{1}{T_n} = \frac{v_n}{2\pi r_n}$. Step 3: Detailed Explanation:
Using the proportionalities:
\[ f_n \propto \frac{v_n}{r_n} \]
Substitute the dependencies on $n$:
\[ f_n \propto \frac{1/n}{n^2} \]
\[ f_n \propto \frac{1}{n \cdot n^2} \]
\[ f_n \propto \frac{1}{n^3} \]
This means the frequency is inversely proportional to the cube of the principal quantum number $n^3$. Step 4: Final Answer:
The frequency is inversely proportional to $n^3$.