Q: If the decay constant of plutonium-244 is $$8.64 \times 10$$^{-7}$$\ \mathrm{yr}^{-1}$$, what is its half-life?

$$8.02 \times 10^5$\ \mathrm{yr}$$

Question 1

A radioactive isotope has a half-life of 8 days. If you start with 100 mg of the isotope, how much will remain after 24 days?

Accepted Answer

$$12.5\ \mathrm{mg}$$

Question 2

Which of the following best describes the concept of radioactive half-life ($$t_{1/2}$$)?

Accepted Answer

The time required for half of the radioactive nuclei in a sample to decay.

Question 3

The decay constant $$k$$ for a radioactive isotope is $$0.693\ \mathrm{yr}^{-1}. $$What is the half-life of this isotope?

Accepted Answer

$$1\ \mathrm{yr}$$

Question 4

A sample of radon-222 has an initial activity of $$8.5 	imes 10^4$ disintegrations per minute. After 7.3 days, its activity is 4.7$$ 	imes $$10^4$$ dpm. What is the half-life of radon-222?

Accepted Answer

$$6.1\ \mathrm{days}$$

Question 5

If the decay constant of plutonium-244 is $$8.64 	imes 10$$^{-7}$$\ \mathrm{yr}^{-1}$$, what is its half-life?

Accepted Answer

$$8.02 	imes 10^5$\ \mathrm{yr}$$

Question 6

A sample initially contains $$5.1 	imes 10^3$ mg of arsenic-74 (t$$_{1/2} = 18$$ days). How much arsenic-74 remains after 60 days?

Accepted Answer

$$775.52\ \mathrm{mg}$$

Question 7

What percentage of carbon-14 ($$t_{1/2} = 5715$$ years) remains in a sample estimated to be 16,115 years old?

Accepted Answer

$$12.47\%$$

Question 8

Which equation correctly relates the half-life ($$t_{1/2}) $$and the decay constant ($$k) $$for a first-order radioactive decay?

Accepted Answer

$$t_{1/2} = \frac{0.693}{k}$$

Question 9

If a radioactive sample has a half-life of 10 years, what fraction of the original sample remains after 30 years?

Accepted Answer

$$\frac{1}{8}$$

Question 10

A scientist is studying a radioactive isotope with a half-life of 5 days. If the scientist wants only 10% of the original sample to remain, approximately how many days should they wait?

Accepted Answer

$$16.6\ \mathrm{days}$$

Question 11

Which of the following statements about radioactive decay is TRUE?

Accepted Answer

The half-life of a radioactive isotope is independent of the initial concentration.

Question 12

A radioactive sample decays according to first-order kinetics. If the initial amount is $$A_0$$ and the amount remaining after time $$t is$$ $$A$$, which equation correctly describes this relationship?

Accepted Answer

$$A = A_0$ e$$^{-kt}$$

Question 13

The half-life of iodine-131 is 8.05 days. What fraction of iodine-131 remains after 24.15 days?

Accepted Answer

$$\frac{1}{8}$$

Question 14

A radioactive sample has a half-life of 15 years. How many years will it take for the sample to decay to 25% of its original amount?

Accepted Answer

$$30\ \mathrm{years}$$

Question 15

Which of the following is a correct real-life application of radioactive half-life?

Accepted Answer

Carbon-14 dating is used to estimate the age of archaeological artifacts.

Radioactive Half-Life: Concepts, Calculations, and Applications

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