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:

Third excited state is $n=4$, second is $n=3$, first is $n=2$. For $4 \rightarrow 3$, $1/\lambda_1 = R(\frac{1}{9} - \frac{1}{16}) = \frac{7R}{144}$. For $3 \rightarrow 2$, $1/\lambda_2 = R(\frac{1}{4} - \frac{1}{9}) = \frac{5R}{36}$. Ratio $\lambda_1/\lambda_2 = (144/7R) / (36/5R) = 20/7$.