How long will it take for 87% of the original radioisotope to decay?

Question

I dont understand how to do this problem.

I know to use N=N.e^-λt and ln2=λT1/2, but i dont know how to solve for the 87% part.

Thank you all for helping me. =)

Answer 1

N = N` e^(-kt),         k = lambda

N/N` = e^(-kt)

In your problem, N/N` = 1.0 - 0.87 = 0.13

0.13 = e^(-kt)

ln(0.13) = ln (e^(-kt)) = -kt

-2.0402 = -kt

t = (2.0402) / k

Since k = ln (2) / T 1/2,    k = 0.693 / T 1/2

T 1/2 is half life

t = (2.0402 / 0.693)  x  (T 1/2)

t = 2.944 x  T 1/2