Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering197helium-4 nuclei (“He) from gold-197 nuclei (19 Au). The energy of the incoming helium nucleus was 7.91 x 1013 J, and the masses of the helium and gold-25nuclei were 6.68 x 10-27 kg and 3.29 × 10¯kg, respectively (note that their mass ratio is 4 to 197. Assume that the helium nucleus travels in the +x-directionbefore the collision.)(a) If a helium nucleus scatters to an angle of 108° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and thefinal velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus.120°He nucleusGold nucleus4He speedm/s197,Au velocitym/s197Au direction° counterclockwise from the +x-axis(b) What is the final kinetic energy (in J) of the helium nucleus?

Given, Initial KE of the He nucleus: Ei=7.91×10-13 J Mass of He nucleus: mHe=6.68×10-27 kg Mass of…

Answered: Ernest Rutherford (the first New…

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