A 5-kg quantity of radioactive isotope decays to 2 kg after 10 years. Find the decay constant of the isotope. k =

k = -0.09165 years^(-1)

Explanation:

The exponential decay model of a radioactive isotope is generally given as;

A(t) = A_o(e^(kt))

Where;

A_o is quantity of isotope before decay, k is decay constant and A(t) is quantity after t years

We are given;

A_o = 5 kg

A(10) = 2kg

t = 10 years

Thus;

A(10) = 2 = 5(e^(10k))

Thus;

2 = 5(e^(10k))

2/5 = (e^(10k))

0.4 = (e^(10k))

In 0.4 = 10k

-0.9164 = 10k

k = -0.9164/10

k = -0.09165 years^(-1)