Question

Calculate the wavelength for the first three lines in the Paschen series. 
(Given R_H =1.097 ×10⁷ m^-1)  

Answer 1

Given:

R_H = 1.097 × 10⁷ m⁻¹,

For Paschen series, n = 3, 

To find: Wavelength of first three lines of Paschen series

Formula:

For the Paschen series, `1/lambda = "R"_"H"(1/3^2 - 1/"m"^2)`

Calculation:

For the first line of the Paschen series, 

From the formula, 

`1/lambda = 1.097 xx 10^7 (1/3^2 - 1/4^2)`

= `1.097 × 10^7 × (7/(9 xx 16))`

= 0.05333 × 10⁷ m⁻¹ 

Using the reciprocal table,

λ₁ = 1.876 × 10⁻⁶ m 

For the second line of the Paschen series,

From formula, 

`1/lambda_2 = 1.097 xx 10^7 (1/3^2 - 1/5^2)`

`= 1.097 × 10^7 × (16/(9 xx 25))`

= 0.075 × 10⁷ m⁻¹

Using the reciprocal table,

λ₂ = 1.282 × 10⁻⁶ m

For the third line of the Paschen series,

From formula,

`1/lambda_3 = 1.097 xx 10^7 (1/3^2 - 1/6^2)`

= `1.097 xx 10^7 xx (27/(9 xx 36))`

= 0.0914 × 10⁷ m⁻¹ 

Using the reciprocal table,

`lambda_3` = 1.094 × 10^-6 m 

The wavelength of the first three lines of the Paschen series is 1.876 × 10⁻⁶ m, 1.282 × 10⁻⁶ m, 1.094 × 10^-6 m, respectively.