Final answer:
The correctly balanced nuclear reaction for the artificial transmutation of Curium to produce Californium is (242₉₆Cm + 4₂He → 245₉₈Cf + 1₀n). This option properly conserves both mass and charge.
Step-by-step explanation:
When Califormium is produced by the artificial transmutation of Curium, the nuclear reaction needs to be balanced in regards to atomic numbers and mass numbers. Analyzing the given options, the correctly balanced nuclear reaction for the production of Californium by bombarding Curium (Cm) with a neutron (n) can be found by following the general principles of nuclear reactions, such as conservation of nucleons and charge.
To determine the right answer, we'd consider the fact that in a nuclear reaction, the total mass number and atomic number must be consistent on both the left and right sides of the equation. The sum of the mass numbers of the reactants should equal the sum of the mass numbers of the products; the same must hold true for the atomic numbers.
In this case, option (b) (242₉₆Cm + 4₂He → 245₉₈Cf + 1₀n) is correct as it follows the law of conservation of mass and charge - the sum of mass numbers on the left (242 + 4 = 246) is equal to the sum on the right (245 + 1 = 246), and the sum of atomic numbers on the left (96 + 2 = 98) is equal to the atomic number on the right (98).