Part B An unknown radioactive substance has a half-life of 3.20 hours . If 22.5

Question

Part B

An unknown radioactive substance has a half-life of 3.20 hours . If 22.5 g of the substance is currently present, what mass A0 was present 8.00 hours ago?

Part C

Americium-241 is used in some smoke detectors. It is an alpha emitter with a half-life of 432 years . How long will it take in years for 40.0 % of an Am-241 sample to decay?

Part D

A fossil was analyzed and determined to have a carbon-14 level that is 50 % that of living organisms. The half-life of C-14 is 5730 years. How old is the fossil?

Explanation / Answer

Part B

radioactive decay follows first order kinetics

The integratd rate law is

k = [2.303/t ] log a/a-x

0.693/3.2= (2.303/8 ) log a /22.5

solving for a , a= 127.17 g

Part B

Using the same relation

0.693/432 = (2.303/t) log 100/60

Thus time = 318.42 yrs

Part C

Given N (initial ) = 1 and N = 0.5 and thalf = 5730 yrs

Thus t = [2.303 x 5730/0.693] log 1/0.5

= 5730 Yrs

Alternatively to have 50% decayed , half life is taken thus time = half life = 5730 yrs.

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