Question

`sqrt"d"_1` and `sqrt"d"_2` are the impact parameters corresponding to scattering angles 60° and 90° respectively, when an α particle is approaching a gold nucleus. For d₁ = xd₂, the value of x will be ______.

Options

• 1

• 2

• 3

• 4

Answer 1

`sqrt"d"_1` and `sqrt"d"_2` are the impact parameters corresponding to scattering angles 60° and 90° respectively, when an α particle is approaching a gold nucleus. For d₁ = xd₂, the value of x will be 3.

Explanation:

cot `theta/2` ∝ b

i.e., more the impact parameter lesser is the angle of scattering.

Given: `sqrt"d"_1` = impact parameter in 1^st case

θ₁ = 60°

 `sqrt"d"_2` = impact parameter in 2^nd case

θ₂ = 90°

Hence, `(cot  theta_1/2)/(cot  theta_2/2) = sqrt("d"_1/"d"_2)`

On squaring both sides, we get;

⇒  `(cot  theta_1/2)/(cot  theta_2/2) = "d"_1/"d"_2`

⇒ `(sqrt3)^2/1 =  "d"_1/"d"_2`

⇒ d₁ = 3d₂