Worksheet: Radioactive Decay

In this worksheet, we will practice calculating the change in the activity of a radioactive sample after a given amount of time has passed.

Q1:

If a radioactive isotope has a decay constant of 0.308 s−1, what is the mean lifetime of an atom of that isotope? Give your answer to 3 significant figures.

Q2:

Carbon-11 has a half-life of 20.3 minutes. The activity of a sample of pure carbon-11 is found to be 7,200 Bq. What will the activity of the sample be 4 hours later? Give your answer to 3 significant figures.

Q3:

What is the average amount of time it takes for an atom of a radioactive isotope to decay, as a ratio of the half-life of the isotope?

Q4:

Zinc-65 has a half-life of 244 days. What is its decay constant? Give your answer in units of s−1 to 3 significant figures.

  • A 3 . 2 9 × 1 0 s−1
  • B 6 . 8 4 × 1 0 s−1
  • C 2 . 8 4 × 1 0 s−1
  • D 4 . 7 4 × 1 0 s−1
  • E 1 . 4 3 × 1 0 s−1

Q5:

A sample of pure cobalt-57 is left in a sealed container for 100 days. At the end of the 100 days, the cobalt is taken out of the container. Its activity is measured and found to be 540 Bq. Cobalt-57 has a half-life of 272 days. What was the activity of the sample at the start of the 100 days? Give your answer to 3 significant figures.

Q6:

Isotope Gold-195 Gold-196 Gold-198 Gold-199
Half-life 186 days 6.18 days 2.70 days 3.17 days

The table lists the half-lives of several isotopes of gold. The activity of a pure sample of an isotope of gold is measured and found to be 2,500 Bq. Five days later, the activity is measured again and found to be 838 Bq. Which isotope of gold is the sample made of?

  • AGold-196
  • BGold-198
  • CGold-199
  • DGold-195

Q7:

The mean lifetime of carbon-10 is 27.8s. What is its decay constant? Give your answer to 3 significant figures.

Q8:

Time (Hours) 1 2 3 4 5
Activity (Bq) 5,240 5,000 4,770 4,540 4,330

The activity of a radioactive isotope is measured at intervals of 1 hour. The results are recorded in the table. What is the decay constant of the isotope? Give your answer in units of hours−1 to 3 significant figures.

Q9:

A sample of pure gold-196 initially contains 25,000 atoms. Fifty days later, only 92 atoms of gold-196 remain in the sample. What is the decay constant of gold-196? Give your answer in units of days−1 to 3 significant figures.

  • A 0.162 days−1
  • B 0.0408 days−1
  • C 0.0777 days−1
  • D 0.432 days−1
  • E 0.112 days−1

Q10:

A radioactive isotope has a half-life of 1,380 years. What proportion of a sample of the isotope would remain after 4,000 years? Give your answer to 3 significant figures.

Q11:

A sample of pure thorium-229 initially contains 20,000 atoms. Five years later, only 19,991 atoms of thorium-229 remain in the sample. Find the half-life of thorium-229. Round your answer to 3 significant figures.

Q12:

A sample of pure titanium-44 is produced in a laboratory. The half-life of titanium-44 is 63 years. After 5 years, the number of atoms of titanium-44 remaining in the sample is found to be 8,000. How many atoms of titanium-44 were there in the original sample? Round your answer to the nearest atom.

Q13:

The decay constant of silver-108 is 1 . 6 6 × 1 0 years−1. What is the half-life of silver-108? Give your answer in years to 3 significant figures.

Q14:

Gold-199 has a half-life of 3.17 days. What is its decay constant? Give your answer in units of days−1 to 3 significant figures.

Q15:

A sample of pure sodium-24 initially contains 2,000 atoms. The half-life of sodium-24 is 15.0 hours. How many atoms of sodium-24 remain in the sample after 2 days? Round your answer to the nearest atom.

Q16:

Which of the following formulas correctly relates the mean lifetime, 𝜏 , of a radioactive isotope to its decay constant, 𝜆 ?

  • A 𝜏 = ( 2 ) 𝜆 l o g
  • B 𝜏 = ( 2 ) 𝜆 l n
  • C 𝜏 = 𝜆 ( 2 ) l n
  • D 𝜏 = ( 2 ) 𝜆 l n
  • E 𝜏 = 1 𝜆

Q17:

Niobium-91 has a mean lifetime of 981 years. What is the half-life of niobium-91? Give your answer in years to 3 significant figures.

Q18:

Which of the following formulas correctly relates the half-life of a radioactive isotope to its decay constant, 𝜆 ?

  • A 𝑡 = ( 2 ) 𝜆 l n
  • B 𝑡 = 𝜆 ( 2 ) l n
  • C 𝑡 = 𝜆 ( 2 ) l n
  • D 𝑡 = 1 𝜆
  • E 𝑡 = 𝜆

Q19:

Cesium-134 has a half-life of 2.07 years. What is the mean lifetime of a cesium-134 atom? Give your answer in years to 3 significant figures.

Q20:

Which of the following formulas correctly relates the half-life of a radioactive isotope to its mean lifetime, 𝜏 ?

  • A 𝑡 = 𝜏 ( 2 ) l o g
  • B 𝑡 = ( 2 ) 𝜏 l n
  • C 𝑡 = 𝜏 ( 2 ) l n
  • D 𝑡 = 𝜏 ( 2 ) l n
  • E 𝑡 = 𝜏

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