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\sqrt{\mathrm{d}_{1}}$ and $\sqrt{\mathrm{d}_{2}} are the impact parameters corresponding to scattering angles 60^{\circ}$ and $90^{\circ} respectively, when an \alpha particle is approaching a gold nucleus. For \mathrm{d}_{1}=x \mathrm{~d}_{2}, the value of \mathrm{x} will be______________.

Option: 1

3


Option: 2

5


Option: 3

8


Option: 4

6


Answers (1)

best_answer

\mathrm{Impact \: parameter \: \alpha \cot \left(\frac{\theta}{2}\right)}

\mathrm{\begin{aligned} & \sqrt{\frac{d_{1}}{d_{2}}}=\frac{\sqrt{3}}{1} \\ \end{aligned} }

\mathrm{d_{1}=3 d_{2} }

\mathrm{\Rightarrow x=3 }

Hence correct answer is 3

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