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:

For longest wavelength in Lyman series ($n_2=2$ to $n_1=1$), $1/\lambda_L = R(1 - 1/4) = 3R/4$. For longest wavelength in Balmer series ($n_2=3$ to $n_1=2$), $1/\lambda_B = R(1/4 - 1/9) = 5R/36$. Ratio $\lambda_L/\lambda_B = (4/3R) / (36/5R) = 20/108 = 5/27$.