explain and show all work please and write clearly please answer all parts A to C or I will give you a thumbs down and report you

Problem 2. A radioactive isotope decays at a rate proportional to its concentration (i.e., first-order reaction). If concentration of an isotope is C(mg/L), then its rate of decay may be expressed as rd[mg/(Ls)]=kC where k is a reaction rate constant. (a) A solution of a radioisotope whose volume and concentration are V(L) and C0(mg/L) respectively is placed in a closed vessel. Write a balance equation on the isotope in the vessel and an initial condition. (b) Half-life is defined as the time required for the isotope concertation to decrease to half of its initial value. Using the balance equation in part (a), prove the half-life t1/2=(ln2)/k. (c) The half-life of 222Rd is 3.8 days. A batch of 222Rd solution that was used in a radio-tracing experiment has been collected in a holding tank. The activity of this isotope must decay to 1% of its present value before the solution can be discarded. How long will it take