b
For \(H : \frac{1}{\lambda}= R _{ H } \times 1^2\left(\frac{1}{1^2}-\frac{1}{\infty^2}\right)\)

\(\frac{1}{\lambda_{ He ^{+}}}= R _{ H } \times 2^2 \times\left(\frac{1}{4}-\frac{1}{9}\right)\)

From \((1)\) and \((2)\) \(\frac{\lambda_{ He ^{+}}}{\lambda}=\frac{9}{5}\)

\(\lambda_{ He ^{+}}=\lambda \times \frac{9}{5}\)

\(\lambda_{ He ^{+}}=\frac{9 \lambda}{5}\)