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 ๐›ผ 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 2 0 8 2 4 2 R n P b + H e
  • B 2 2 2 8 6 2 1 8 8 2 4 2 R n P b + H e
  • C 2 2 2 8 6 2 1 8 8 4 4 2 R n B i + H e
  • D 2 2 2 8 6 2 1 8 8 4 4 2 R n P o + 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 ๐›ผ 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 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 โˆ’ 4 mL of gaseous 2 2 2 R a over 24 hours. Calculate the half-life of 2 2 6 R a .

  • A 3 . 2 ร— 1 0 4 years
  • B 5 . 0 ร— 1 0 4 years
  • C 7 . 6 ร— 1 0 5 years
  • D 2 . 1 ร— 1 0 3 years
  • E 1 . 7 ร— 1 0 3 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 4 . 6 ร— 1 0 โˆ’ 5 s
  • B 8 . 0 ร— 1 0 โˆ’ 5 s
  • C 6 . 7 ร— 1 0 โˆ’ 5 s
  • D 3 . 2 ร— 1 0 โˆ’ 5 s
  • E 1 . 4 ร— 1 0 โˆ’ 5 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 ร— 1 0 โˆ’ 6 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 7 . 5 ร— 1 0 โˆ’ 7 g
  • B 6 . 7 ร— 1 0 โˆ’ 7 g
  • C 8 . 1 ร— 1 0 โˆ’ 7 g
  • D 8 . 6 ร— 1 0 โˆ’ 7 g
  • E 9 . 1 ร— 1 0 โˆ’ 7 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 ร— 1 0 โˆ’ 7 g?

Q11:

The isotope 2 4 0 N p undergoes ๐›ฝ โˆ’ decay with a half-life of 1.032 hours.

Which isotope is produced by the decay?

  • A 2 3 9 P u
  • B 2 4 0 U
  • C 2 4 1 P u
  • D 2 4 0 P u
  • E 2 4 1 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, ๐œ† ?

  • A l n ๐œ† 2
  • B l n 2 ๐œ†
  • C ๐œ† 2 l n
  • D l n 2 ๐œ†
  • E 2 ๐œ† l n

Q13:

Which of the following samples would have the greatest activity?

  • A ยตg 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 dโˆ’1. Calculate the half-life for this decay.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.