1. Use Bohr radius relation for hydrogen

For hydrogen atom, $r_n = n^2 a_0$ where $a_0 = 52.9\,\text{pm}$

2. Given radius

The electron falls to an orbit of radius $r_n = 211.6\,\text{pm}$

So, $n^2 a_0 = 211.6$ $n^2 = \frac{211.6}{52.9} = 4$ $n=2$

Thus, the transition ends at the orbit with principal quantum number $n_f = 2$

3. Identify the spectral series

In hydrogen spectrum:

• Lyman series: transitions ending at $n=1$
• Balmer series: transitions ending at $n=2$
• Paschen series: transitions ending at $n=3$
• Brackett series: transitions ending at $n=4$

Since the transition ends at $n_f=2$ it belongs to the Balmer series.

4. Check options

• A: Lyman series $\to$ ends at $n=1$, incorrect
• B: Balmer series $\to$ ends at $n=2$, correct
• C: Paschen series $\to$ ends at $n=3$, incorrect
• D: Brackett series $\to$ ends at $n=4$, incorrect

Therefore, the correct answer is B.