This assignment is due at the beginning of lecture on Monday, 9 Feb.

1. For our model of nuclear decay (N >> 1) we have N(t) = N_oe^-t/τ, where τ is the e-folding time of our decay or the mean lifetime. Derive an expression for the half-life (λ) of an isotope in terms of τ.

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For the following problems, use the Euler method ode solver you developed in Lab #1. Be sure to include the following with your homework solution:

• brief discussion (your approach, assumptions, observations);
• complete code listings (with comments);
• graphical results (comparison of analytic results with your numerical simulation);
• a discussion of errors.
2. Select a radioactive isotope (other than ²³⁵U or ²³¹Th). Find it's theoretical τ and λ. Simulate it's decay beginning with a suitable N_o. Verify that the half-life is indeed λ.
3. G-N §§1.1
4. G-N §§1.3 (For this problem, consider the errors in terms of the terminal velocity, v_t = a/b.)

Extra Credit. Consider the case of exponential growth, where τ < 0. This is just the more general case of exponential change where τ ∈ ℜ, for which our original solution and numerical approach are valid. Compare the performance of the Euler method for long times using a simulation of ±τ. Pay particular attention to the errors.