Answer: The isotope produced after the transmutation process of Cf-249 and C-12 is
![_(104)^(257)\textrm{Rf}](https://img.qammunity.org/2020/formulas/chemistry/college/d6pr4mlhs5ihrh7fjzsezsn6slt85ttmlz.png)
Step-by-step explanation:
Transmutation is defined as the process where one chemical isotope gets converted to another chemical isotope. The number of protons or neutrons in the isotope gets changed.
The chemical equation for the reaction of Californium-249 nucleus with Carbon-12 nucleus follows:
![_(98)^(249)\textrm{Cf}+_6^(12)\textrm{C}\rightarrow _(Z)^(A)\textrm{X}+4_0^1\textrm{n}](https://img.qammunity.org/2020/formulas/chemistry/college/uddoyobtlzmcg78cx4qkxv2goaja5bvgak.png)
In a nuclear reaction, the total mass and total atomic number remains the same.
To calculate A:
Total mass on reactant side = total mass on product side
249 + 12 = A + 4
A = 257
To calculate Z:
Total atomic number on reactant side = total atomic number on product side
98 + 6 = Z + 0
Z = 104
Hence, the isotope produced after the transmutation process of Cf-249 and C-12 is
![_(104)^(257)\textrm{Rf}](https://img.qammunity.org/2020/formulas/chemistry/college/d6pr4mlhs5ihrh7fjzsezsn6slt85ttmlz.png)