Question

Calculate the shortest wavelength of the Paschen series for the H atom.

Answer 1

Formula: `1/λ =  R_H(1/n^2 - 1/m^2)` Here n < m

where, λ is the wavelength,

R → Rydberg’s constant = 1.097 × 10⁷ m⁻¹

For the shortest wavelength of Paschen series,

n = 3, m = ∞

∴ `1/λ_s = 1.097 xx 10^7(1/3^2 - 1/∞^2)`

∴ `1/λ_s = 1.097 xx 10^7(1/9 -0)`

∴ `1/λ_s = 0.12188 xx 10^7`

∴ `λ_s = 1/(0.12188 xx 10^7)`

∴ λ_s = 8.204 × 10⁻⁷

∴ λ_s = 8204 Å