The smallest wavelength of Lyman series is 91 nm. Find the difference between the largest wavelengths of Paschen and Balmer series.

Solution:

Smallest wavelength of Lyman series:

λ = 91 nm

Rydberg relation:

1/λ = R

Largest wavelength of Balmer series:

λ_B = 4/R

Largest wavelength of Paschen series:

λ_P = 9/R

Difference:

Δλ = (9/R) - (4/R) = 5/R

Since:

1/R = 91 nm

Δλ = 5 × 91 = 455 nm

Answer: 455 nm