Hα line of Paschen series is produced due to the transition from n=4 to n=3
Hβ line of Paschen series is produced due to the transition from n=5 to n=3
Therefore,
1λα=RH[132−142] ...(1)
1λβ=RH[132−152] ...(2)
Where RH is the Rydberg constant.
From the equation (1) and (2) we get,
λβλα=7×225144×16
λβ=7 × 225144 × 16×6912 oA
⇒λβ=4725 oA