A radioactive substance R1 having decay rate k1 disinteg
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A radioactive substance R1 having decay rate k1 disintegrates into a second radioactive substance R2 having decay rate k
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A radioactive substance R1 having decay rate k1 disintegrates into a second radioactive substance R2 having decay rate k2. Substance R2 disintegrates into R3, which is stable. If mi (t) represents the mass of substance Ri at time t, i = 1, 2, 3, the applicable equations are m? 1 = ?k1m1 m? 2 = k1m1 ? k2m2 m? 3 = k2m2. Draw a block diagram of a compartment model of the overall reaction. Label the directed arrows that represent the mass flows between compartments with the appropriate radioactive decay rate constants. Use the eigenvalue method to solve the above system under the conditions m1(0) = m0, m2(0) = 0, m3(0) = 0. For each of the matrices in Problems 18 through 23, use a computer to assist in finding a fundamental set of solutions to the system x? = Ax
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