exponential decay

Question

The​ half-life of a radioactive substance is 33.9 years.

a. Find the exponential decay model for this substance.

b. How much of the sample of 1000 grams will remain after

20 ​years?

c. How long will it take a sample of 1000 grams to decay to 700 ​grams?

Answer 1

The kinetics of radioactive decay is 1st order.

It can be described by: N = N₀e^-kt

N = concentration of the radioactive substance after time t.

N₀ = initial concentration of radioactive substance

k = rate (decay) constant

t = time

The half-life (t_1/2) is related to k by: t_1/2 = 0.693/k. The half-life time is the time at which the concentration of radioactive is reduced exactly by half.

a. to find the exponential decay mode:

find k from the half-life time: k = 0.693/t_1/2 , and then plug in k into the equation: N = N₀e^-kt.

b. use your equation from (a), and plug in 1000 gram for N₀, and 20 years for t.

C. use your equation from (a), and pug in 1000 grams for N₀ , and 700 grams for N. Then solve the equation to get t. The unit of t is in years, since the unit of k is per year.

I hope that will help you to solve the problem.