Question

Calculate the impact parameter of a $5MeV\alpha$ -particle scattered by $10^{\circ }$ when it approaches a gold nucleus.

• A. $3\times 10^{-13}m$
• B. $4\times 10^{-12}m$
• C. $2.6\times 10^{-13}m$
• D. $10^{-13}m$

Answer 1

Answer: (C)

$b=\frac{Z{e}^2\cot \theta /2}{4\pi {\epsilon }_0\left(\frac{1}{2}m{v}^2\right)}$
$=\frac{9\times 10^9\times 79\times {\left(1.6\times 10^{-19}\right)}^2\cot 5^{\circ }}{5\times 1.6\times 10^{-13}}$
$b=\frac{9\times 79\times 1.6\times 1.6\times 10^{-16}}{8\times 0.0875}$
(tan $5^{\circ }=0.0875$)
$b=2.6\times 10^{-13}m$