√(d₁) and √(d₂) are the impact parameters corresponding to scattering angles 60 ° and 90 ° respectively, when an α particle is approaching a gold nucleus. For d1 = x d2, the value of x will be ____________. Numerical answer type. Work it out, then open the answer.

Answer: 3. Impact parameter b ∝ cot (θ/2). (√(d₁))/(√(d₂)) = (cot 30°)/(cot 45°) = √(3) d₁ = 3d₂, so x = 3. Answer: 3.

√(d₁) and √(d₂) are the impact parameters corresponding to scattering… | JEE Main 2022 (29 Jun, Shift 1)

Q10JEE Main 2022 · 29 JUN · SHIFT 1Medium

Atomic Models & Alpha-Particle Scattering

$\sqrt{d_1}$ and $\sqrt{d_2}$ are the impact parameters corresponding to scattering angles 60 $^\circ$ and 90 $^\circ$ respectively, when an $\alpha$ particle is approaching a gold nucleus. For d1 = x d2, the value of x will be ____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 3

Impact parameter $b \propto \cot(\theta/2)$ .
$\dfrac{\sqrt{d_1}}{\sqrt{d_2}} = \dfrac{\cot 30^\circ}{\cot 45^\circ} = \sqrt{3}$
$d_1 = 3d_2$ , so $x = 3$ . Answer: 3.

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