(a) In Geiger-Marsden experiment, calculate the distance of closest approach for an alpha particle with energy 2.56 × 10^-12 J. Consider that the…

a) For $\displaystyle \alpha$ particles, distance of closest approach $$\begin{aligned} r_{\alpha} & =\frac{1}{4 \pi \varepsilon_{0}} \frac{2 Z e^{2}}{E_{k}} \\ r_{\alpha} & =\frac{9 \times 10^{9} \times 2 \times 79 \times\left(1.6 \times 10^{-19}\right)^{2}}{2.56 \times 10^{-12}} \\ & =14.22 \times 10^{-15} \mathrm{~m} \\ & =14.22 \mathrm{fm} \end{aligned} $$

b) For proton, distance of closest approach $$\begin{aligned} r_{p} & =\frac{1}{4 \pi \varepsilon_{0}} \frac{Z e^{2}}{E_{k}} \\ r_{p} & =\frac{r_{\alpha}}{2} \\ & =7 \cdot 11 \times 10^{-15} \mathrm{~m} \end{aligned} $$