Question

The shortest wavelength in the Lyman series of hydrogen \([R_H = 1.097 \times 10^7~\text{m}^{-1}]\) is:

• A. 91.2 nm
• B. 364.6 nm
• C. 820.4 nm
• D. 2278.9 nm

Hint:

For Lyman series, shortest wavelength occurs for transition from \(n = \infty\) to \(n = 1\). Use \(\lambda_\text{min} = 1/R_H\).

Answer 1

The Correct Option is A

Step 1: Lyman series formula.
1/λ = R_H (1 - 1/n²) for n>1. The shortest wavelength corresponds to n → ∞.

Step 2: Limiting case.
1/λ_min = R_H (1 - 0) = R_H.

Step 3: Numerical evaluation.
λ_min = 1/R_H = 1/(1.097×10⁷) ≈ 9.12×10⁻⁸ m = 91.2 nm.

Step 4: Conclusion.
The shortest Lyman wavelength is 91.2 nm.