An unknown radioactive element decays into non-radioactive substances. In 680 days the radioactivity of a sample decreases by 64 percent.

Question

(a) What is the half-life of the element?

half-life:    (days)

(b) How long will it take for a sample of 100 mg to decay to 75 mg?

time needed:    (days)

Answer 1

680 days decays 64%

.64 = e^680r were r = daily decay rate

ln.64 = 680r

r = ln.64/680

half life is > 680 days, and when

1/2 = e^(ln.64/680)t

solve for t

ln.5 = t(ln.64/680)

t = ln.5/(ln.64)/680)

100 to 75 is less than 680 days and when

75/100 = e^(ln.64/680)t

solve for t

t = ln.75/((ln.64)/680)

use a calculator with a natural log function