Arrange the wavelengths of following transitions for an electron in hydrogen atom in increasing order.
(A) \( n=2 \) to \( n=1 \)
(B) \( n=3 \) to \( n=2 \)
(C) \( n=4 \) to \( n=3 \)
(D) \( n=3 \) to \( n=1 \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (D), (A), (B), (C)
For a transition in hydrogen, the Rydberg formula gives \( \frac{1}{\lambda} = R\left(\frac{1}{n_f^{2}} - \frac{1}{n_i^{2}}\right) \). The larger the bracket (the larger the energy difference), the shorter the wavelength.
\( \displaystyle \text{(A) } n=2 \text{ to } n=1:\;\; \frac{1}{1^{2}} - \frac{1}{2^{2}} = \frac{3}{4} = 0.75 \)
\( \displaystyle \text{(B) } n=3 \text{ to } n=2:\;\; \frac{1}{2^{2}} - \frac{1}{3^{2}} = \frac{5}{36} \approx 0.139 \)
\( \displaystyle \text{(C) } n=4 \text{ to } n=3:\;\; \frac{1}{3^{2}} - \frac{1}{4^{2}} = \frac{7}{144} \approx 0.049 \)
\( \displaystyle \text{(D) } n=3 \text{ to } n=1:\;\; \frac{1}{1^{2}} - \frac{1}{3^{2}} = \frac{8}{9} \approx 0.889 \)
Wavelength is inversely proportional to these values, so the order of increasing wavelength is the order of decreasing value: (D), (A), (B), (C).