Concept: The 'first line' of a series is the lowest energy transition. For the Lyman series (ground state \( p=1 \)), the first line corresponds to an electron falling from the closest upper level, which is \( n=2 \).
Formula:$$ \frac{1}{\lambda} = R_H \left( \frac{1}{p^2} - \frac{1}{n^2} \right) $$
Solution:- Substitute \( p=1 \) and \( n=2 \).
- \( \frac{1}{\lambda} = R_H \left( \frac{1}{1^2} - \frac{1}{2^2} \right) \)
- \( \frac{1}{\lambda} = R_H \left( 1 - \frac{1}{4} \right) = R_H \left( \frac{3}{4} \right) \)
- To find \( \lambda \), invert the fraction: \( \lambda = \frac{4}{3R_H} \).
Why other options are incorrect:Option A is an incorrect inversion leaving \( R_H \) in the numerator. Options B and C represent random algebraic errors or incorrect \( n \) values.
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