In Hydrogen spectrum the shortest wavelength in Balmer series is λ . The shortest wavelength in the Brackett series will be

For shortest wavelength in Balmer series, n1=2, n2=∞1λ=R142−1∞⇒λ=4RFor shortest wavelength in Brackett series, n1=4, n2=∞∴1λ'=R142−1∞⇒λ'=16R=4λ