Uranium-235 fissions when it absorbs a slow-moving neutron. The two fission fragments can be almost any two nuclei
whose charges Q1 and Q2 add up to 92e (where e is the charge on a proton, e = 1.6 × 10−19 coulomb), and whose nucleons
add up to 236 protons and neutrons (U-236; U-235 plus a neutron). One of the possible fission modes involves nearly equal
fragments, palladium nuclei with Q1 = Q2 = 46e. The rest masses of the two palladium nuclei add up to less than the rest
mass of the original nucleus. (In addition to the two main fission fragments there are typically one or more free neutrons in
the final state; in your analysis make the simplifying assumption that there are no free neutrons, just two palladium nuclei.)
The rest mass of the U-236 nucleus is 235.996 u (unified atomic mass units), and the rest mass of each Pd-118 nucleus is
117.894 u, where 1 u = 1.7 × 10−27 kg (approximately the mass of one nucleon).
(a) Calculate the final speed v, when the palladium nuclei have moved far apart (due to their mutual electric repulsion).
Is this speed small enough that p2/(2m) is an adequate approximation for the kinetic energy of one of the palladium
nuclei? (It is all right to go ahead and make the nonrelativistic assumption first, but you then must check that the
calculated v is indeed small compared to c.)
(b) Using energy considerations, calculate the distance between centers of the palladium nuclei just after fission, when
they are starting from rest.
(c) A proton or neutron has a radius of roughly 1 × 10−15 m, and a nucleus is a tightly packed collection of nucleons.
Experiments show that the radius of a nucleus containing N nucleons is approximately (1.3 × 10−15 m) × N1/3.
What is the approximate radius of a palladium nucleus? Draw a sketch of the two palladium nuclei in part (b), and
label the distances you calculated in parts (b) and (c).