Question

The longest wavelength associated with Paschen series is ______.

(Given: R_H = 1.097 × 10⁷ SI unit)

Options

• 1.094 × 10⁻⁶ m

• 2.973 × 10⁻⁶ m

• 3.646 × 10⁻⁶ m

• 1.876 × 10⁻⁶ m

Answer 1

The longest wavelength associated with Paschen series is 1.876 × 10⁻⁶ m.

Explanation:

Given: R_H = 1.097 × 10⁷ SI unit

For the Paschen series, the electron falls to n₁ = 3.

The longest wavelength corresponds to the smallest energy difference, i.e., transition n₂ = 4

Using the Rydberg formula:

`1/lambda = R_H (1/3^2 - 1/4^2)`

= `R_H (1/9 - 1/16)`

`1/lambda = R_H * 7/144`

⇒ λ = `144/(7 R_H)`

= `144/(7 xx 1.097 xx 10^7)`

= 1.876 × 10⁻⁶ m