Question

In hydrogen atom spectrum, (R → Rydberg's constant)
A. the maximum wavelength of the radiation of Lyman series is 4/3R
B. the Balmer series lies in the visible region of the spectrum
C. the minimum wavelength of the radiation of Paschen series is 9/R
D. the minimum wavelength of Lyman series is 5/4R
Choose the correct answer from the options given below :

• A. A, B and C Only
• B. A, B and D Only
• C. A, B Only
• D. B, D Only

Hint:

Minimum wavelength corresponds to the "series limit," which is always calculated by setting $n_2 = \infty$.

Answer 1

The Correct Option is A

To solve the problem related to the hydrogen atom spectrum, we need to analyze each statement given in the options. The Rydberg formula for the wavelength of the spectral lines is given by:

\[\frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)\]

where \( R \) is the Rydberg constant, \( n_1 \) is the lower energy level, and \( n_2 \) is the higher energy level.

• Lyman Series: Involves transitions from higher energy levels to the \( n_1 = 1 \) level.
• Balmer Series: Involves transitions from higher energy levels to the \( n_1 = 2 \) level.
• Paschen Series: Involves transitions from higher energy levels to the \( n_1 = 3 \) level.

1. Statement A: The maximum wavelength of the radiation of the Lyman series is calculated for the transition from \( n_2 = 2 \) to \( n_1 = 1 \).

   \[\frac{1}{\lambda_{\text{max}}} = R\left(1 - \frac{1}{4}\right) = \frac{3R}{4}\]

   Thus, the maximum wavelength \(\lambda_{\text{max}} = \frac{4}{3R}\), so Statement A is correct.

2. Statement B: The Balmer series lies in the visible region, which is historically confirmed by experimental observations. Hence, Statement B is correct.
3. Statement C: The minimum wavelength of the Paschen series corresponds to the transition from \( n_2 = \infty \) to \( n_1 = 3 \).

   \[\frac{1}{\lambda_{\text{min}}} = R\left(\frac{1}{3^2}\right) = \frac{R}{9}\]

   Thus, \(\lambda_{\text{min}} = \frac{9}{R}\), so Statement C is correct.

4. Statement D: The minimum wavelength of the Lyman series corresponds to the transition from \( n_2 = \infty \) to \( n_1 = 1 \), giving:

   \[\frac{1}{\lambda_{\text{min}}} = R\left(1\right) = R\]

   Thus, \(\lambda_{\text{min}} = \frac{1}{R}\), making Statement D incorrect as it states \(\frac{5}{4R}\).

Considering the above explanations, the correct answer is A, B and C Only.