d 1 and d 2 are the impact parameters corresponding to scattering angles 60 ° and 90 ° respectively, when an α particle is approaching a gold nucleus. For d 1 = x d 2 , the value of x will be _____ .

Step-by-step solution

The relation between impact parameter and scattering angle is b = k z e 2 E cot θ 2 ⇒ b ∝ cot θ 2 ⇒ d 1 ∝ cot 60 ° 2 ⇒ d 2 ∝ cot 90 ° 2 d 1 d 2 = cot 60 ° 2 cot 90 ° 2 = 3 ⇒ d 1 = 3 d 2 ⇒ x = 3