Problem set for solving radioactive decay equations:

Due Nov. 6^th, 2000.

1) The radioactive decay equation is , where P_o is the initial concentration of the parent, P_t is the concentration at any time t, t is the time, and l is the decay constant. You are given the following information:

• The decay constant l for element x is 0.1/yr.
• The initial quantity of the element x is 5 grams.

a) Determine the amount of element x after 1 year and after 20 years.

b) How much daughter element (y) is produced in 10 years?

c) We can never measure the amount of the initial parent, but we know that for every parent atom that decays, there is one daughter that is produced. This means that

P_t + D_t = P_o

so that the above equation reduces to . This equation can be rewritten as

How old is the rock if we have 4 grams of daughter y and 1 gram of parent element x?

2) Derive the equation for half life. We start with . The half-life is defined as the time necessary for P_t to be equal to ½ P_o. (So we can substitute ½ P_o for P_t). In order to do this you must remember that ln(e^x) = x. Also, -ln(1/2) = ln(2). This latter equation isn’t necessary, but is helpful.