Question

A radioactive substance has a half-life of 17.33 years. Use the formula n(t) = n0e^

−kt which tells
you how much is left at time t > 0 to find how much of a 20-gm sample would remain one hundred
years after it is collected. Round your answer to the nearest two decimal places.

Answer 1

t 1/2 = 17.33 yrs ,

k = ln 2 / t1/2 = ( 0.693) / ( 17.33 yrs) = 0.04 yr-1

now no = 20 g , t = 100 yrs , we will find n(t)

n(t) = 20g exp ( - 0.04 yr-1 x 100 yrs)

= 20g exp ( -4)

= 0.37 g