(Solved): 6. ( 10 pts.) Consider the following radioactive decay chain of fission products, where nuclide D i ...

6. ( 10 pts.) Consider the following radioactive decay chain of fission products, where nuclide $D$ is stable. ${\mathrm{A}}_0,{\mathrm{B}}_0$, and ${\mathrm{D}}_0$ are the constant fission rates of production (nuclides/s), and ${?}_{?},{?}_{\mathrm{B}}$ and ${?}_{\mathrm{C}}$ are the decay constants. Write the set of four differential equations describing the radioactive decay chain in terms of the above parameters, and the number of nuclei ${\mathrm{N}}_{?},{\mathrm{N}}_{\mathrm{B}},{\mathrm{N}}_{\mathrm{C}}$ and ${\mathrm{N}}_{\mathrm{D}}$ at time $t$. (Do not solve the differential equations.) [ Ans. Radioisotope A: $\frac{d{N}_A}{dt}=A_0?{?}_{?}{N}_A(t)$ ]