Question

Calculate the longest wavelength in the Paschen series.

(Given R_H =1.097 ×10⁷ m^-1)  

Answer 1

Given: n = 3, m = 4

To find: Longest wavelength in Paschen series (λ_L)

Formula: `1/lambda_"L" = "R"[1/"n"^2 - 1/"m"^2]`

Calculation: 

From formula,

`1/lambda_"L" = "R"[1/3^2 - 1/4^2]`

∴ `1/lambda_"L" = "R"[1/9 - 1/16]`

= `"R"[(16 - 9)/(9 xx 16)] = (1.097 xx 10^7 xx 7)/(9 xx 16)`

∴ `lambda_"L" = (9 xx 16)/(1.097 xx 7) xx 10^-7`

= antilog {log(9) + log(16) − log(1.097) − log(7)} × 10⁻⁷

= antilog{0.9542 + 1.2041 − 0.0402 − 0.8451} × 10⁻⁷ 

= antilog{1.2730} × 10⁻⁷

= 18.75 × 10⁻⁷ m

∴ λ_L = 18750 Å

The longest wavelength in the Paschen series is 18750 Å.