Atomic Structure: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Atomic Structure. Understanding the underlying formula is key to arriving at the correct answer below:

Longest wavelength in Lyman is $\lambda_L = \frac{4}{3R}$. Longest wavelength in Balmer is $\lambda_B = \frac{36}{5R}$. Their ratio is $\lambda_L / \lambda_B = \frac{4}{3R} \times \frac{5R}{36} = \frac{20}{108} = \frac{5}{27}$.