Question

The ratio of the wavelength of the last line of Paschen series to that of Balmer series is

• A. \(\frac{9}{4}\)
• B. \(\frac{3}{2}\)
• C. \(\frac{2}{3}\)
• D. \(\frac{4}{9}\)

Hint:

Last line → \(n_2 = \infty\)

Answer 1

The Correct Option is A

Concept:
Last line corresponds to \(n_2 \to \infty\): \[ \frac{1}{\lambda} = R \left( \frac{1}{n_1^2} \right) \] Step 1: Paschen series. \[ n_1 = 3 \Rightarrow \frac{1}{\lambda_P} = \frac{R}{9} \] \[ \lambda_P = \frac{9}{R} \]
Step 2: Balmer series. \[ n_1 = 2 \Rightarrow \frac{1}{\lambda_B} = \frac{R}{4} \] \[ \lambda_B = \frac{4}{R} \]
Step 3: Ratio. \[ \frac{\lambda_P}{\lambda_B} = \frac{9/R}{4/R} = \frac{9}{4} \]
Step 4: Conclusion. \[ \frac{\lambda_P}{\lambda_B} = \frac{9}{4} \]