Chapter 8, Problem 49PE

Professional Application

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 (⁴He) from gold-197 nuclei (¹⁹⁷Au). The energy of the incoming helium nucleus was $8.00\times {10}^{-13}$ J, and the masses of the helium and gold nuclei were $6.68\times {10}^{-27}$ kg and $3.29\times {10}^{-25}$ 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. (b) What is the final kinetic energy of the helium nucleus?