Concept: Wavelength of emitted radiation is mathematically derived from the Rydberg formula based on initial and final principal quantum numbers.
Formula:$$ \frac{1}{\lambda} = R_H \left( \frac{1}{p^2} - \frac{1}{n^2} \right) $$
Solution:- The electron transitions from the second orbit (\( n = 2 \)) to the first orbit (\( p = 1 \)).
- Substitute the values: \( \frac{1}{\lambda} = R_H \left( \frac{1}{1^2} - \frac{1}{2^2} \right) \).
- Simplify the parentheses: \( \frac{1}{\lambda} = R_H \left( 1 - \frac{1}{4} \right) = R_H \left( \frac{3}{4} \right) \).
- To find \( \lambda \), invert the equation: \( \lambda = \frac{4}{3R_H} \).
Why other options are incorrect:Option B (\( \frac{3}{4}R_H \)) is the un-inverted wave number (\( 1/\lambda \)) rather than wavelength. Options C and D involve incorrect algebraic simplifications.
Note: The source text formats the fraction exactly as 4/3RH.
Quality & Fidelity Assurance:
Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.