Let P, Q, and R denote the amounts of three radioactive substance at time t. Sup

Question

Let P, Q, and R denote the amounts of three radioactive substance at time t. Suppose P->Q->R, in the sense that the product of P is Q and the decay product of Q is R-- this is called a radioactive chain. the half-life of substance P is 1 day, the half-life of substance Q is 2 day, and 3 days for substance R. The process starts with an amount Po of substance P and none of the others. Give the system of DE's for the amount of each substance along with inital conditions, then solve for R(t) and sketch R(t) vs t.

Explanation / Answer

dP/dt = -ln(2)P ------------------- 1 dQ/dt = ln(2)P - ln(2)Q/2 ----------------- 2 dR/dt = ln(2)Q/2 - ln(2)R/3 --------------------- 3 initial conditions : P(0) = Po , Q(0) = R(0) = 0

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