(Solved): Q.1 dN(t) at which the nuclei of a dt To model the phenomena of radioactive decay, it is assumed t ...

Q.1 dN(t) at which the nuclei of a dt To model the phenomena of radioactive decay, it is assumed that the rate, radioactive substance decays is proportional to the amount (the number of nuclei) N(t) of the substance remaining at a time t: dN (t) dt · = kN(t), k<0 (a) Explain clearly with a graph, using the concept of the derivative, why dN(t) dt < 0. (b) Solve this equation for initial value, N(t = 0) = N(0) = No. (c) If N (2) = 100 and k = 0.5, find the initial quantity No of radioactive material. (d) Find the time taken for a quantity of radioactive material to decay to one third of its initial value.