Question

Calculate the impact parameter of a $5 MeV \alpha$ -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)

$b=\frac{Z e^{2} \cot \theta / 2}{4 \pi \varepsilon_{0}\left(\frac{1}{2} m v^{2}\right)}$
$=\frac{9 \times 10^{9} \times 79 \times\left(1.6 \times 10^{-19}\right)^{2} \cot 5^{\circ}}{5 \times 1.6 \times 10^{-13}}$
$b =\frac{9 \times 79 \times 1.6 \times 1.6 \times 10^{-16}}{8 \times 0.0875}$
(tan $5^{\circ}=0.0875$)
$b=2.6 \times 10^{-13} m$