In hydrogen spectrum, if the shortest wavelength in Balmer series is , the shortest wavelength in Brackett series is

Step-by-step solution

For Balmer series, 1 _ Balmer =R ( 1 2^2 - 1 n^2 ) , where n=3,4,5 For shortest wavelength, n= array rlrl & 1 & =R ( 1 2^2 )= R 4 or & = 4 R array For Brackett series, 1 _ Brackett =R ( 1 4^2 - 1 n^2 ) , where n=5,6,7, Again, for shortest wavelength, n= aligned & 1 _ Brackett =R ( 1 4^2 )= R 16 & or _ Brackett = 16 R =4 ( 4 R )=4 aligned [From Eq. (i)]