# JEE Main & Advanced Physics Atomic Physics a-Scattering Experiment

a-Scattering Experiment

Category : JEE Main & Advanced

'Geiger and Marsden (students of Rutherford) studied the scattering of $\alpha -$particles by gold foil on the advice of Rutherford and made the following observations.

(1) Most of the $\alpha -$particles pass through the foil straight away undeflected.

(2) Some of them are deflected through small angles.

(3) A few $\alpha -$particles (1 in 1000) are deflected through the angle more than ${{90}^{o}}$.

(4) A few $\alpha -$particles (very few) returned back i.e. deflected by ${{180}^{o}}$.

(5) Number of scattered particles : $N\propto \frac{1}{{{\sin }^{4}}(\theta /2)}$

(6) If t is the thickness of the foil and N is the number of $\alpha -$particles scattered in a particular direction (i.e. $\theta =$constant), it was observed that $\frac{N}{t}=\text{constant}$$\Rightarrow$$\frac{{{N}_{1}}}{{{N}_{2}}}=\frac{{{t}_{1}}}{{{t}_{2}}}$

(7) Distance of closest approach (Nuclear dimension) : The minimum distance from the nucleus up to which the $\alpha -$particle approach, is called the distance of closest approach $({{r}_{0}})$. At this distance the entire initial kinetic energy has been converted into potential energy so $\frac{1}{2}m{{v}^{2}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\,\frac{(Ze)\,2e}{{{r}_{0}}}$$\Rightarrow$${{r}_{0}}=\frac{Z{{e}^{2}}}{m{{v}^{2}}\pi {{\varepsilon }_{0}}}$$=\frac{4kZ{{e}^{2}}}{m{{v}^{2}}}$

(8) Impact parameter (b) : The perpendicular distance of the velocity vector $(\vec{\upsilon })$ of the $\alpha -$particle from the centre of the nucleus when it is far away from the nucleus is known as impact parameter. It is given as

$b=\frac{Z{{e}^{2}}\cot (\theta /2)}{4\pi {{\varepsilon }_{0}}\left( \frac{1}{2}m{{v}^{2}} \right)}\,$$\Rightarrow$$b\propto \cot (\theta /2)$

For large b, $\alpha$particles will go undeviated and for small b the $\alpha -$particle will suffer large scattering.

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