Open Question
A fossil is found to have a 14C level of 76.0% compared to living organisms. How old is the fossil?
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21. Nuclear Chemistry
Radioactive Half-Life
Multiple Choice
A 2.00 mg sample of the radioisotope phosphorus-32 is found to contain 0.400 mg of phosphorus-32 after 33.3 days. Calculate the half-life (in days).
A
22.2 days
B
11.1 days
C
33.3 days
D
16.7 days
Verified step by step guidance1
Identify the initial mass (m₀) and the remaining mass (m) of the radioisotope phosphorus-32. Here, m₀ = 2.00 mg and m = 0.400 mg.
Use the formula for radioactive decay: m = m₀ * (1/2)^(t/T), where t is the time elapsed (33.3 days) and T is the half-life. Rearrange the formula to solve for T: T = t / (log(m/m₀) / log(1/2)).
Substitute the known values into the rearranged formula: T = 33.3 / (log(0.400/2.00) / log(1/2)).
Calculate the logarithm of the ratio of the remaining mass to the initial mass: log(0.400/2.00).
Calculate the half-life T using the values obtained in the previous steps.
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