Question

The first three spectral lines of H-atom in the Balmer series are given λ₁, λ₂, λ₃ considering the Bohr atomic model, the wavelengths of the first and third spectral lines `(lambda_1/lambda_3)` are related by a factor of approximately 'x' × 10^–1. The value of x, to the nearest integer, is ______.

Options

• 20

• 25

• 15

• 10

Answer 1

The first three spectral lines of H-atom in the Balmer series are given λ₁, λ₂, λ₃ considering the Bohr atomic model, the wavelengths of the first and third spectral lines `(lambda_1/lambda_3)` are related by a factor of approximately 'x' × 10^–1. The value of x, to the nearest integer, is 15.

Explanation:

Using the expression for Balmer series for For 1^st line,

`1/lambda_1 = "Rz"^2(1/4 - 1/9) = 5/36`Rz²

For 3^rd line,

`1/lambda_3 = "Rz"^2(1/4 - 1/25) = 21/100`Rz²

`lambda_1/lambda_3 = 21/100xx36/5` ⇒ 15.12 × 10^-1

So, x = 15.