Radioactive Isotopes, Exponential Decay

Question

The radioactive isotope 239Pu has a half-life of approximately 24100 years. After 1200 years, there are 3g of 239Pu.

(1) What was the initial quantity? ____ g

(2) How much of it remains after 12000years? ____ g

Answer 1

A(t) = Amount after t years

 

      = A₀e^kt, where A₀ is the initial amount and k is a constant

 

A(24100) = A₀e^24100k = (1/2)A₀

 

                    e^24100k = 0.5

 

                      24100k = ln(0.5)

 

                              k = -0.0000288

 

A(t) = A₀e^-0.0000288t

 

A(1200) = A₀e^{-0.0000288(1200)} = 3

 

               A₀e^_-0.03456 = 3

 

                          A₀ = 3.1054924 g

 

A(12000) = 3.1054924e^{-0.0000288(12000)} = 2.198 g