# 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 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
- B
- C
- D
- 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 particles are responsible for this effect?

- AStrongly penetrating but weakly ionizing
- BStrongly penetrating but weakly oxidizing
- CWeakly penetrating but strongly ionizing
- DStrongly penetrating and strongly reducing
- EWeakly penetrating and weakly oxidizing

**Q3: **

What is the half-life of a radioactive material?

- AThe average time taken for nuclei to decay.
- BHalf of the time taken for all of the nuclei to decay.
- CHalf of the average time taken for nuclei to decay.
- DThe time taken for half of the nuclei to decay.
- EThe inverse of the rate constant for the decay process.

**Q4: **

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

**Q5: **

The decay of 1.000 g of at 1 bar and 298 K produces mL of gaseous over 24 hours. Calculate the half-life of .

- A years
- B years
- C years
- D years
- E years

**Q6: **

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

**Q7: **

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

- A s
- B s
- C s
- D s
- E 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 g sample of has a half-life of 5.52 hours.

Calculate the mass of after 70.0 minutes.

- A g
- B g
- C g
- D g
- E g

Calculate the percentage of remaining after 3.00 days.

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

**Q11: **

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

Which isotope is produced by the decay?

- A
- B
- C
- D
- E

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

What percentage of a sample of pure 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, ?

- A
- B
- C
- D
- E

**Q13: **

Which of the following samples would have the greatest activity?

- A µg of calcium-51
- B 9.70 g of potassium-43
- C 0.124 kg of neptunium-238
- D 730 mg of thallium-193
- E 0.610 tonnes of bismuth-207

**Q14: **

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