3. (18 points) The transuranic element, californium-252, is a strong neutron emitter used in starting nuclear reactors, weapons detection (at airports), surveying oil wells, and in medical therapy for treating brain tumors and cancer of the esophagus. It is produced in nuclear reactors by a series of fission reactions and has a half-life of 2.646 years. Californium-252 undergoes two reactions as shown in the equations below: (1) radioactive decay to curium-248 with emission of an alpha particle (He nucleus), and (2) spontaneous fission to Ce143 and Ru105 with emission of neutrons (n) and beta particles (e) 96.9%:98252Cf96248Cm+243.1%:98252Cf58143Ce+44105Ru+xn+x For a given amount of Cf-252, 96.9% undergoes radioactive decay, and 3.1% undergoes spontaneous fission. Spontaneous fission of Cf-252 involves a variety of reactions, one of which is written above, and produces an average of 3.9 neutrons per fission event. (a) Find the value of x in reaction (2) that balances the equation. Note that a neutron is composed of a proton plus an electron. (b) With the atomic masses listed in the table below, determine the reaction energies, in units of MeV, for both reactions. (c) A medical neutron source consists of a pellet (1.4mm in diameter and 5mm long) that contains 500 micrograms of Cf-252. Determine the radiation, in units of Becquerels (Bq), for each reaction at time zero and 10 years later. Note: 1 Becquerel =1Bq= the number of decay events per second that produce ionizing radiation. Ionizing radiation includes alpha particles, beta particles, and neutrons. Nuclear masses of selected isotones