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 _____ .

Question

d 1 and d 2 are the impact parameters corresponding to scattering angles 60 &#176; and 90 &#176; respectively, when an &#945; particle is approaching a gold nucleus. For d 1 = x d 2 , the value of x will be _____ .

Aicharya · Accepted Answer

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

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

$\Rightarrow \sqrt{d_{1}} \propto \cot (\frac{60 °}{2})$

$\Rightarrow \sqrt{d_{2}} \propto \cot (\frac{90 °}{2})$

$\frac{\sqrt{d_{1}}}{\sqrt{d_{2}}} = \frac{\cot (\frac{60 °}{2})}{\cot (\frac{90 °}{2})} = \sqrt{3} \Rightarrow d_{1} = 3 d_{2} \Rightarrow x = 3$

d 1 and d 2 are the impact parameters corresponding to scattering angles 60 ° and 90 °…

Solution

d 1 and d 2 are the impact parameters corresponding to scattering angles 60 &#176; and 90 &#176;…

Solution

d 1 and d 2 are the impact parameters corresponding to scattering angles 60 ° and 90 °…