Smallest wavelength of lyman
λ1=R(121−∞21)
R=λ1=911 nm−1
λmax for balmer series
n1=2→n2=3
λB1=R(41−91)
λB1=911(365)
λB=(591×36)=655.2 nm
λmax paschen
n1=3→n2=4
λp1=911(321−421)=911×1447
λp=(791×144)=1872 nm
Δλ=λP−λB=1872−655.2
Δλ=1216.8
Δλ≈1217