Question
Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei $\left( ^4\textrm{He} \right)$ from gold-197 nuclei $\left( ^{197}\textrm{Au} \right)$. The energy of the incoming helium nucleus was $8.00 \times 10^{-13} \textrm{ J}$, and the masses of the helium and gold nuclei were $6.68 \times 10^{-27} \textrm{ kg}$ and $3.29 \times 10^{-25} \textrm{ kg}$, respectively (note that their mass ratio is 4 to 197). (a) If a helium nucleus scatters to an angle of $120^\circ$ during an elastic collision with a gold nucleus, calculate the helium nucleus’s final speed and the final velocity (magnitude and direction) of the gold nucleus. (b) What is the final kinetic energy of the helium nucleus?

a) $v_{He}' = 1.49 \times 10^7 \textrm{ m/s}$

$v_{Au}' = 6.16 \times 10^5 \textrm{ m/s, } 29.3^\circ \textrm{ below positive x-axis}$

b) $7.38 \times 10^{-13} \textrm{ J}$

Solution Video