In hydrogen spectrum, the shortest wavelength in the Balmer series is \( \lambda \). The shortest wavelength in the Bracket series is :

For Balmer series, shortest wavelength \( \frac{1}{\lambda} = R(1/2^2 - 0) = \frac{R}{4} \Rightarrow \lambda = \frac{4}{R} \). For Brackett series, shortest wavelength \( \frac{1}{\lambda_B} = R(1/4^2 - 0) = \frac{R}{16} \Rightarrow \lambda_B = \frac{16}{R} = 4\lambda \).