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.

  • A 2 2 2 8 6 2 1 8 8 2 4 2 R n P b + H e
  • B 2 2 2 8 6 2 1 8 8 4 4 2 R n B i + H e
  • C 2 2 2 8 6 2 1 8 8 4 4 2 R n P o + H e
  • D 2 2 2 8 6 2 2 0 8 2 4 2 R n P b + H e
  • E 2 2 2 8 6 2 2 0 8 0 4 2 R n H g + H e

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 strongly penetrating and strongly reducing.
  • BIt is weakly penetrating and weakly oxidizing.
  • 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
  • BThe inverse of the rate constant for the decay process
  • CThe time taken for half of the nuclei to decay
  • DThe average time taken for nuclei to decay
  • EHalf of the average time taken for nuclei to decay

Q4:

The half-life of 2 3 9 P u is 2 4 0 0 0 years. What fraction of 2 3 9 P u present today will be present in 1 0 0 0 years, assuming no additional 2 3 9 P u is formed?

Q5:

The decay of 1.000 g of 2 2 6 R a at 1 bar and 298 K produces 1 . 0 0 × 1 0 mL of gaseous 2 2 2 R a over 24 hours. Calculate the half-life of 2 2 6 R a .

  • A 2 . 1 × 1 0 years
  • B 5 . 0 × 1 0 years
  • C 7 . 6 × 1 0 years
  • D 3 . 2 × 1 0 years
  • E 1 . 7 × 1 0 years

Q6:

After 25.0 years, a 0.5000 g sample of 1 3 3 B a contains only 0.0961 g of 1 3 3 B a . Calculate the half-life of 1 3 3 B a .

Q7:

The half-life of 9 9 T c is 6.0 hours. Calculate the rate constant for the decay of 9 9 T c .

  • A 6 . 7 × 1 0 s
  • B 8 . 0 × 1 0 s
  • C 1 . 4 × 1 0 s
  • D 4 . 6 × 1 0 s
  • E 3 . 2 × 1 0 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 . 0 0 × 1 0 g sample of 2 5 7 M d has a half-life of 5.52 hours.

Calculate the mass of 2 5 7 M d after 70.0 minutes.

  • A 8 . 6 × 1 0 g
  • B 6 . 7 × 1 0 g
  • C 9 . 1 × 1 0 g
  • D 8 . 1 × 1 0 g
  • E 7 . 5 × 1 0 g

Calculate the percentage of 2 5 7 M d remaining after 3.00 days.

How much time is needed for the sample mass to decrease to 1 . 0 0 × 1 0 g?

Q11:

The isotope 2 4 0 N p undergoes 𝛽 decay with a half-life of 1.032 hours.

Which isotope is produced by the decay?

  • A 2 4 0 P u
  • B 2 4 0 U
  • C 2 4 1 P u
  • D 2 4 1 U
  • E 2 3 9 P u

How much time is needed for 99.0% of pure 2 4 0 N p to decay?

What percentage of a sample of pure 2 4 0 N p 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 ?

  • A 𝜆 2 l n
  • B l n 2 𝜆
  • C 2 𝜆 l n
  • D l n 𝜆 2
  • E l n 2 𝜆

Q13:

Which of the following samples would have the greatest activity?

  • A 0.124 kg of neptunium-238 𝑡 = 2 . 1 1 7 d a y s
  • B 0.610 metric tons of bismuth-207 𝑡 = 3 2 . 9 y e a r s
  • C 9.70 g of potassium-43 𝑡 = 2 2 . 3 h o u r s
  • D 730 mg of thallium-193 𝑡 = 2 1 . 6 8 m i n u t e s
  • E 1,440 µg of calcium-51 𝑡 = 1 0 . 0 8 s e c o n d s

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 . 8 5 × 1 0 d−1: Calculate, in hours, the half-life for this first-order decay.

Q16:

Hassium-269 decays by 𝛼 emission with a rate constant of 2 . 5 5 × 1 0 s−1: Calculate the half-life for this first-order decay.

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