A. Americium-241 is used in some smoke detectors. It is an alpha emitter with a

Question

A. 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 45.0{ m \%} of an Am-241 sample to decay?

B. A fossil was analyzed and determined to have a carbon-14 level that is 40{ m \%} that of living organisms. The half-life of C-14 is 5730 years. How old is the fossil?

In part B, I got that I needed to use (.5)n and n being A sample over A initial. I'm really confused how to do all the steps correctly since I always seem to do it wrong when I try to do these mastering chemistry questions. Please include step by step, I would really like to be able to know how to solve these for future references. Thank you!

Explanation / Answer

A) THE GOVERNING EQUATION FOR FIRST ORDER REACTION IS :-

rate constant(k)*time taken(t) = ln{initial concentration/concentration left after time 't'}

Also, for first order reactions, rate constant = ln2/half life = 0.693/432 = 0.0016 year-1

Now, as per the question ; let the initial concentration = 100%

Thus, concentration left after time 't' years = 55% (as 45 % sample decays)

Thus, 0.0016*t = ln(100/55) = 372.68 years

Thus, time required for 45% of the sample to decay = 372.68 years

2) THE GOVERNING EQUATION FOR FIRST ORDER REACTION IS :-

rate constant(k)*time taken(t) = ln{initial concentration/concentration left after time 't'}

Also, for first order reactions, rate constant = ln2/half life = 0.693/5730 = 1.21*10-4 year-1

Now, as per the question ; let the initial concentration = 100%

Thus, concentration left after time 't' years = 40% (as 60 % sample decays)

Thus 1.21*10-4*t = ln(100/40) = years

Thus, time required for 60% of the sample to decay = 7572.65 years = age of the fossil

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