part a. You are using a Geiger counter to measure the activity of a radioactive

Question

part a. You are using a Geiger counter to measure the activity of a radioactive substance over the course of several minutes. If the reading of 400. counts has diminished to 100. counts after 79.2 minutes , what is the half-life of this substance?

Part B An unknown radioactive substance has a half-life of 3.20 hours . If 48.6 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 45.0 % of an Am-241 sample to decay?

Part D A fossil was analyzed and determined to have a carbon-14 level that is 70 % that of living organisms. The half-life of C-14 is 5730 years. How old is the fossil?

Explanation / Answer

A) The governing equation for 1st order kinetic is :-

k*t = ln([A0]/[A]) ; where k = rate constant ; [A0] & [A] are initial and concentration after time 't' respectively.

Thus, k*79.2 = ln(400/100)

or, rate constnt, k = 0.0175 min-1

Now, half life = ln2/k = 39.59 minutes

B) rate constant, k = ln2/half life = 0.216 hr-1

Now, 0.216*8 = ln(A0/48.6)

or, A0 = 274.82 g

C) decay constant = ln2/half life = 0.693/432 = 0.0016 yr-1

Now, 0.0016*t = ln(100/55)

or, t = 373.64 years

D) decay constant = ln2/half life = 0.693/5730 = 1.21*10-4 yr-1

Now, 1.21*10-4*t = ln(100/70)

or, t = 2947.7 years

Thus, fossil is 2947.7 years old.

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