A radioactive isotope has a half-life of 15 years, and a lab has a 100g sample.

Question

1. Write an Equation to model the situation 

2. Determine how long it will take for the sample to be reduced to 2 grams

Answer 1

Fraction remaining = 0.5^n where n = # of 1/2 lives elapsed.

 

Fraction remaining = 2 g/100 g = 0.02

Solving for n (# of 1/2 lives):

0.02 = 0.5^n

log 0.02 = n log 0.5

-1.699 = n(-0.301)

1.699 = 0.301n

n = 5.64 half lives

5.64 x 15 yrs = 84.6 years time it will take to reduce 100 g to 2 g