Ernest Rutherford (the first New Zealander to be awarded theNobel Prize in chemistry) demonstrated that nuclei were very smalland dense by scattering helium-4 nuclei (⁴He) fromgold-197 (¹⁹⁷Au). See the figure below. The energy ofthe incoming helium nucleus was 8.80  10^-13 J,and the masses of the helium and gold nuclei were6.68  10^-27 and3.29  10^-25 kg, respectively (note that theirmass ratio is 4 to 197). If a helium nucleus scatters to an angleof 120° during an elastic collision with a gold nucleus, calculatethe helium nucleus's final speed.

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

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

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