Worksheet: Radioactive Half-Lives

In this worksheet, we will practice using measurements of activity or isotope ratios to calculate the half-lives and decay constants of unstable nuclei.

Q1:

Radon-222 has a half-life of 3.823 days. If a sample of pure radon-222 has an initial mass of 0.750 g, how much time is needed for only 0.100 g of radon-222 to remain?

Q2:

Radon-222 decays by 𝛼 emission and is one of the largest sources of radiation exposure for many people.

Write a balanced equation for the decay of radon-222.

  • A222862208042RnHg+He
  • B222862208242RnPb+He
  • C222862188442RnPo+He
  • D222862188242RnPb+He
  • E222862188442RnBi+He

After 12.7 days, 90.0% of a sample of radon-222 has decayed. Calculate the half-life for the decay process.

Radon-222 is most hazardous if inhaled. Which properties of 𝛼 particles are responsible for this effect?

  • AIt is weakly penetrating and weakly oxidizing.
  • BIt is strongly penetrating and strongly reducing.
  • CIt is weakly penetrating but strongly ionizing.
  • DIt is strongly penetrating but weakly oxidizing.
  • EIt is strongly penetrating but weakly ionizing.

Q3:

What is the half-life of a radioactive material?

  • AHalf of the time taken for all of the nuclei to decay
  • BHalf of the average time taken for nuclei to decay
  • CThe average time taken for nuclei to decay
  • DThe inverse of the rate constant for the decay process
  • EThe time taken for half of the nuclei to decay

Q4:

The half-life of 239Pu is 24,000 years. What fraction of 239Pu present today will be present in 1,000 years, assuming no additional 239Pu is formed?

Q5:

The decay of 1.000 g of 226Ra at 1 bar and 298 K produces 1.00×10 mL of gaseous 222Ra over 24 hours. Calculate the half-life of 226Ra.

  • A7.6×10 years
  • B3.2×10 years
  • C2.1×10 years
  • D5.0×10 years
  • E1.7×10 years

Q6:

After 25.0 years, a 0.5000 g sample of 133Ba contains only 0.0961 g of 133Ba. Calculate the half-life of 133Ba.

Q7:

The half-life of 99Tc is 6.0 hours. Calculate the rate constant for the decay of 99Tc.

  • A6.7×10 s
  • B8.0×10 s
  • C4.6×10 s
  • D3.2×10 s
  • E1.4×10 s

Q8:

Technetium-99m has a half-life of 6.01 hours. How much time is needed for 85.0% of a sample of technetium-99m to decay?

Q9:

Cobalt-60 decays to nickel-60 with a half-life of 5.27 years.

Calculate the decay constant for this process.

Calculate the fraction of a sample of cobalt-60 remaining after 15.0 years.

How much time is needed for 98.0% of a sample of cobalt-60 to decay?

Q10:

A 1.00×10 g sample of 257Md has a half-life of 5.52 hours.

Calculate the mass of 257Md after 70.0 minutes.

  • A6.7×10 g
  • B8.6×10 g
  • C9.1×10 g
  • D7.5×10 g
  • E8.1×10 g

Calculate the percentage of 257Md remaining after 3.00 days.

How much time is needed for the sample mass to decrease to 1.00×10 g?

Q11:

The isotope 240Np undergoes 𝛽 decay with a half-life of 1.032 hours.

Which isotope is produced by the decay?

  • A240U
  • B241Pu
  • C240Pu
  • D239Pu
  • E241U

How much time is needed for 99.0% of pure 240Np to decay?

What percentage of a sample of pure 240Np remains after 4.30 hours?

Q12:

What is the half-life of a radioactive material in terms of the rate constant for the radioactive decay, 𝜆?

  • Aln2𝜆
  • Bln2𝜆
  • Cln𝜆2
  • D𝜆2ln
  • E2𝜆ln

Q13:

Which of the following samples would have the greatest activity?

  • A0.124 kg of neptunium-238 𝑡=2.117days
  • B9.70 g of potassium-43 𝑡=22.3hours
  • C0.610 metric tons of bismuth-207 𝑡=32.9years
  • D1,440 µg of calcium-51 𝑡=10.08seconds
  • E730 mg of thallium-193 𝑡=21.68minutes

Q14:

Iodine-131 decays with a rate constant of 0.138 d−1. Calculate the half-life for this decay.

Q15:

Phosphorus-32 decays by 𝛽 emission with a rate constant of 4.85×10 d−1: 32153216ePS+e+̄𝜈. Calculate, in hours, the half-life for this first-order decay.

Q16:

Hassium-269 decays by 𝛼 emission with a rate constant of 2.55×10 s−1: 26910826510642HsSg+He. Calculate the half-life for this first-order decay.

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