Language; Python

Exercise E.16: Simulate radioactive decay The equation u = -au is a relevant model for radioactive decay, where u() is the fraction of particles that remains in the radioactive substance at time t. The parameter a is the inverse of the so-called mean lifetime of the substance. The initial condition is u(0) = 1. a) Introduce a class Decay to hold information about the physical problem: the parameter a and a __call method for computing the right-hand side -au of the ODE. b) Initialize an instance of class Decay with a = In (2)/5600 1/y. The unit 1/y means one divided by year, so time is here measured in years, and the particular value of a corresponds to the Carbon-14 radioactive isotope whose decay is used extensively in dating organic material that is tens of thousands of years old. c) Solve u = -au with a time step of 500 y, and simulate the radioactive decay for T = 20,000 y. Plot the solution. Write out the final u(T) value and compare it with the exact value e-T Exercise E.16: Simulate radioactive decay The equation u = -au is a relevant model for radioactive decay, where u() is the fraction of particles that remains in the radioactive substance at time t. The parameter a is the inverse of the so-called mean lifetime of the substance. The initial condition is u(0) = 1. a) Introduce a class Decay to hold information about the physical problem: the parameter a and a __call method for computing the right-hand side -au of the ODE. b) Initialize an instance of class Decay with a = In (2)/5600 1/y. The unit 1/y means one divided by year, so time is here measured in years, and the particular value of a corresponds to the Carbon-14 radioactive isotope whose decay is used extensively in dating organic material that is tens of thousands of years old. c) Solve u = -au with a time step of 500 y, and simulate the radioactive decay for T = 20,000 y. Plot the solution. Write out the final u(T) value and compare it with the exact value e-T