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?

• 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 is 24,000 years. What fraction of present today will be present in 1,000 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?

• A0.124 kg of neptunium-238
• B9.70 g of potassium-43
• C0.610 metric tons of bismuth-207
• D1,440 µg of calcium-51
• E730 mg of thallium-193

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 emission with a rate constant of d−1: Calculate, in hours, the half-life for this first-order decay.

Q16:

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