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 first line of Lyman for H-atom ($n=2 \rightarrow 1$), $1/\lambda = R(1/1^2 - 1/2^2) = 3R/4$. For second line of Balmer for ion ($n=4 \rightarrow 2$), $1/\lambda = Z^2 R(1/2^2 - 1/4^2) = Z^2 R(3/16)$. Equating them gives $3R/4 = Z^2 R(3/16) \Rightarrow Z^2 = 4 \Rightarrow Z = 2$.