d 1 and d 2 are the impact parameters corresponding to scattering angles 6 0 ∘ and 9 0 ∘ respectively, when an α particle is approaching a gold nucleus. For d 1 = x d 2 , the value of x wi

Question

d 1 ​ ​ and d 2 ​ ​ are the impact parameters corresponding to scattering angles 6 0 ∘ and 9 0 ∘ respectively, when an α particle is approaching a gold nucleus. For d 1 ​ = x d 2 ​ , the value of x will be _____ .

TestHub · Accepted Answer

The relation between impact parameter and scattering angle is $b = \frac{k z e ^{2}}{E} cot (\frac{θ}{2})$

$\Rightarrow b \propto cot (\frac{θ}{2})$

$\Rightarrow d_{1} \propto cot (\frac{6 0 ^{\circ}}{2})$

$\Rightarrow d_{2} \propto cot (\frac{9 0 ^{\circ}}{2})$

$\frac{d _{1}}{d _{2}} = \frac{c o t ( \frac{6 0 ^{\circ}}{2} )}{c o t ( \frac{9 0 ^{\circ}}{2} )} = 3 \Rightarrow d_{1} = 3 d_{2} \Rightarrow x = 3$

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