Hydrogen Spectrum & Spectral Series question from MHT CET 2023 (10 May, Shift 1)

Answer: (a)

1. For a hydrogen-like atom $\frac{1}{\lambda} = RZ^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$; shortest wavelength means $n_2 = \infty$.
2. Balmer (H, $Z=1$): $\frac{1}{\lambda} = \frac{R}{4}$
3. Brackett ($n_1=4$): $\frac{1}{\lambda} = \frac{RZ^2}{16}$
4. $\frac{Z^2}{16} = \frac{1}{4} \Rightarrow Z^2 = 4 \Rightarrow Z = 2$
5. So the answer is (a) 2.