Question

According to Bohr atom model, in which of the following transitions will the frequency be maximum ?

• A. n = 2 to n = 1
• B. n = 3 to n = 2
• C. n = 4 to n = 3
• D. n = 5 to n = 4

Hint:

The first transition of any series (e.g., $n=2$ to $n=1$ in Lyman) always has much higher energy than any transition between higher adjacent levels.

Answer 1

The Correct Option is A

Step 1: Frequency $f \propto \Delta E$. The energy difference $\Delta E = 13.6 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)\ \text{eV}$.
Step 2: In the hydrogen spectrum, energy levels get closer as $n$ increases.
Step 3: $\Delta E_{2 \to 1} = 13.6(1 - 1/4) = 10.2\ \text{eV}$.
Step 4: $\Delta E_{3 \to 2} = 13.6(1/4 - 1/9) \approx 1.89\ \text{eV}$. The $2 \to 1$ transition has the largest energy gap, thus the highest frequency.