Arrange the following transitions of electron in hydrogen atom in the increasing order of the wavelengths associated with them.
(A) \( n = 2 \) to \( 1 \)
(B) \( n = 3 \) to \( 2 \)
(C) \( n = 3 \) to \( 1 \)
(D) \( n = 4 \) to \( 2 \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (C), (A), (D), (B)
The wavelength of the emitted photon is set by the energy difference between the two levels: the larger the energy gap, the shorter the wavelength. By the Rydberg formula,
\( \displaystyle \frac{1}{\lambda} = R\left(\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}\right) \)
\( \displaystyle \text{(A) } n = 2 \text{ to } 1: \ \frac{1}{\lambda} = R\left(1 - \frac{1}{4}\right) = 0.75\,R \)
\( \displaystyle \text{(B) } n = 3 \text{ to } 2: \ \frac{1}{\lambda} = R\left(\frac{1}{4} - \frac{1}{9}\right) \approx 0.139\,R \)
\( \displaystyle \text{(C) } n = 3 \text{ to } 1: \ \frac{1}{\lambda} = R\left(1 - \frac{1}{9}\right) \approx 0.889\,R \)
\( \displaystyle \text{(D) } n = 4 \text{ to } 2: \ \frac{1}{\lambda} = R\left(\frac{1}{4} - \frac{1}{16}\right) = 0.1875\,R \)
Increasing wavelength means decreasing \( 1/\lambda \): (C), (A), (D), (B).