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 (⁴He) from gold-197 (¹⁹⁷Au). See the figure below. The energy of the incoming helium nucleus was 8.80  10^-13 J, and the masses of the helium and gold nuclei were 6.68  10^-27 and 3.29  10^-25 kg, respectively (note that their mass ratio is 4 to 197). 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.

Put the origin of the coordinate system at the site of the stationary gold nucleus and the +x direction in the direction in which the incoming helium nucleus travels. Write a statement of conservation of energy, momentum in the x direction, and momentum in the y direction to obtain three equations and three unknowns. See if you can solve the three equations simultaneously for the three unknowns. m/s

Calculate the final velocity (magnitude and direction) of the gold nucleus. (Assume the positive x direction is the direction in which the helium nucleus is initially traveling, and that it scatters 120° clockwise from the +x-axis.)

magnitude	? m/s
direction	? ° (counterclockwise from the +x-axis)

Answer 1