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44. 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 from gold-197 nuclei. The energy of the

incoming helium nucleus was 8.00 x 10-13 J, and the masses of the helium and gold nuclei were

6.68 x 10-27 kg and 3.29 × 10-25 kg, respectively (note that their mass ratio is 4 to 197).

a. If a helium nucleus scatters to an angle of 120° 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.

He nucleus

V₁

120°

Gold nucleus

b. What is the final kinetic energy of the helium nucleus?

Fig: 1