Question

The minimum wavelength of Lyman series lines is \( P \), then the maximum wavelength of these lines is

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

Hint:

Series extremes: \begin{itemize} \item Max wavelength = smallest transition. \item Min wavelength = series limit. \end{itemize}

Answer 1

The Correct Option is A

Concept: Lyman series: transitions to \( n=1 \). Step 1: {\color{red}Minimum wavelength.} Occurs at \( n=\infty \to 1 \): \[ \frac{1}{P} = R \] Step 2: {\color{red}Maximum wavelength.} Occurs at \( n=2 \to 1 \): \[ \frac{1}{\lambda_{\max}} = R\left(1 - \frac14\right) = \frac{3R}{4} \] Step 3: {\color{red}Relation.} \[ \lambda_{\max} = \frac{4}{3}P \]