Americium-241 is used in smoke detectors. it has a first-order rate constant for radioactive decay of k = 1.6x10^−3yr−1. by contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day−1.
(a) what are the half-lives of these two isotopes?
(b) which one decays at a faster rate?
(c) how much of a 1.00-mg sample of each isotope remains after three half-lives?
(d) how much of a 1.00-mg sample of each isotope remains after 4 days?

A. 433 years and 63 days

B. Iodine

C. 0.125mg

D. 1.00mg

Explanation:

A. Americium

The formula of a radioactive decay constant half life is t = 0.693/k

Where k is the decay constant.

For americium, k = 0.0016

t = 0.693/0.0016 = 433.125 apprx 433 years

For iodine, k = 0.011

Half life = 0.693/0.011 = 63 days.

B. Iodine decays at a faster rate.

C. After three half lives

For both, first half life yields a mass of 0.5mg, next yields 0.25mg, next yield 0.125mg

D. 1.00mg still remains.

Half life is high for both so the decay after one day is insignificant.

air quality

poor drinking water

and heavy polution

can lead to poor health

your answer would be “dry”