One of the waste products of a nuclear reactor is plutonium-239. This nucleus is radioactive and decays by splitting into a helium-4 nucleus and a uranium-235 nucleus. The latter of which is also radioactive and will itself decay some time later. The energy emitted in the plutonium decay is 8.40 ×10⁻²⁷ J and is entirely converted into the kinetic energy of the helium and uranium nuclei. The mass of the helium nucleus is 6.68 ×10⁻²⁷ kg, while that of the uranium is 3.92 ×10⁻²⁵ kg (note that the ratio of the masses is 4 to 235).

a. Calculate the speed of the He in meters per second, assuming the plutonium nucleus is originally at rest.