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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