A sample of a radioactive isotope is discovered in a geology lab
CHEMISTRY · Multi-part · US High School · Chemistry · Atomic Structure & Nuclear · Atomic Structure & Nuclear
Problem
A sample of a radioactive isotope is discovered in a geology lab. Three successive measurements of its radioactivity yield the following results:
• A(2)=4.58 kBq
• A(7)=3.12 kBq
• A(15)=1.56 kBq
Time t is measured in days from the moment the sample was sealed. Assume the activity A(t) obeys dtdA=kA with constant k<0.
(a) Use the first two measurements to solve exactly for the decay constant k.
(b) With your value of k, compute the initial activity A0=A(0). Give your answer to three significant figures.
(c) Verify whether the third measurement at t=15 days is consistent with the model obtained in parts (a) and (b). Show numerical evidence to support your conclusion and quantify any percent discrepancy.
(d) Discuss two possible sources of the discrepancy you found in part (c) and explain how each could affect the reliability of the estimated initial activity.