Final answer:
To balance the nuclear equation, we must find a nucleus whose addition will make the mass and atomic numbers equal on both sides. The missing nucleus is an oxygen isotope, 18/8 O, which balances the equation to 249/98 Cf + 18/8 O → 263/106 Sg + 4 1/0 n.
Step-by-step explanation:
The student's question is asking to balance a nuclear reaction by supplying the missing nucleus in the given reaction. After analyzing the reaction 249/98 Cf +__ → 263/106 Sg + 4 1/0 n, we can see that the mass numbers (top numbers) and atomic numbers (bottom numbers) need to be balanced on both sides of the equation. In order to balance the equation, we need to add the missing mass number and atomic number from the left side to match the total on the right side.
To balance this equation, note that the sum of the mass numbers on the right side (seaborgium-263 plus four neutrons) is 263 + (4 × 1) = 267, while the mass number on the left side of the equation is 249 for the californium (Cf) nucleus. The missing mass number is therefore 267 - 249 = 18. Similarly, the sum of the atomic numbers on the right side (seaborgium-106 plus zero from the neutrons) is 106, and the atomic number on the left is 98 for the californium nucleus. The missing atomic number is 106 - 98 = 8.
Therefore, the missing nucleus must have a mass number of 18 and an atomic number of 8, which corresponds to an oxygen nucleus, 18/8 O. The balanced nuclear equation is 249/98 Cf + 18/8 O → 263/106 Sg + 4 1/0 n.