## Nuclear Decay System Solver

Variable =   Value =   Rate =

Equation # =

1. Press Add after you enter the values for each equation.
2. Press Create System after all equations have been entered.
3. Press Run to plot the variables used to define the first two rate equations.
4. Press Clear System to erase current system.
5. Press Show System to see what equations have been entered into JavaScript.

For example, enter the following rows of information which represent rate equations for radioactive decay:

Variable Initial Value Rate
t 0 1
N 100 -0.1*N

The time variable will usually have a rate of unity since dt/dt=1 wtih a starting time of t=0.  The second row describes the decay as dN/dt = -0.1N , with the initial number of nuclei set to 100.  Ten percent of these particles will decay during every time unit.  Time, since it is the first variable entered will appear on the horizontal axis and n will appear on the vertical axis.

Section 2 Exercises:

Use the above physlet to solve the following problems.  Clear the system each time you begin a new exercise. The half-lives can be found in an appendix of the text.

1. A mole of pure 231Th is created.  What percentage of nuclei is left after an hour, a day, and a week?
2. The activity of a 210Po source is 10mCi.  After three years, what is the activity?
3. A nuclear reactor creates a certain isotope at a constant rate, P [nuclei/sec].  If the isotope has a lifetime of t = 1/R, the rate equation is given by

dN/dt = P - RN

If the initial number of the new nuclei is zero, what is the expression for the equilibrium number of new nuclei?

1. The probability of a 13C nucleus absorbing a proton in a (p,n) reaction is 0.001.   What nucleus is being produce?  What is its lifetime?

2. A beam of 1013 protons/sec is incident upon a sample of 13C. After 10 minutes, how many of the new nuclei have been produced?  After an hour?