An unknown radioactive element decays into non-radioactive substances. In 420 days the radioactivity of a sample decreases by 62 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 80 mg?

time needed: 

Answer 1

420 days 62% decay

1.00-.62 = .38 = 38% left after 420 days

A= what's left P= starting amount, r= daily rate of decay, t = number of days

A=Pe^rt

.38 = e^420r

take natural logs of both sides

ln.38 = 420r

r = ln.38/420 = about -0.0023 = -0.23% per day decay rate

half life is when

1/2=e^-0.0023t

ln.5 = -0.0023t

t = ln.5/-0.0023 = about 301.37

= about 301 days

80 = 100e^rt

.8 = e^-.0023t

t = ln.8/-.0023 = about 97.02 days

= about 97 days

use a calculator with a natural log function, usually the key with "ln"