Worksheet: Radioactive Decay

In this worksheet, we will practice calculating the activity of a radioactive sample after a given amount of time using the half-life of the isotope.

Q1:

A radioactive sample initially contains 2.40×10 mol of a radioactive material which has a half-life of 6.00 hours.

Approximately how many moles of the radioactive material remain after 6.00 h?

  • A 1 . 2 0 × 1 0 mol
  • B 8 . 4 9 × 1 0 mol
  • C 1 . 0 0 × 1 0 mol
  • D 1 . 7 0 × 1 0 mol
  • E 1 . 8 0 × 1 0 mol

Approximately how many moles of the radioactive material remain after 12.00 h?

  • A 6 . 0 0 × 1 0 mol
  • B 1 . 2 0 × 1 0 mol
  • C 9 . 0 0 × 1 0 mol
  • D 6 . 6 7 × 1 0 mol
  • E 3 . 3 3 × 1 0 mol

Approximately how many moles of the radioactive material remain after 36.00 h?

  • A 1 . 0 0 × 1 0 mol
  • B 3 . 7 5 × 1 0 mol
  • C 9 . 0 0 × 1 0 mol
  • D 4 . 5 0 × 1 0 mol
  • E 6 . 0 0 × 1 0 mol

Q2:

A sample of radioactive material is obtained from a very old rock. A plot of the natural logarithm of the sample’s activity versus time yields a slope value of 1.00×10 s−1. What is the half-life of this material?

  • A 6 9 3 × 1 0 years
  • B 4 4 6 × 1 0 years
  • C 8 1 5 × 1 0 years
  • D 3 0 2 × 1 0 years
  • E 1 6 3 × 1 0 years

Q3:

A piece of wood from an ancient Egyptian tomb is tested for its carbon-14 activity. It is found to have an activity per gram 𝐴=10 decay/ming. What is the age of the wood? Use a value of 3.84×1012 s−1 for the decay constant of carbon-14 and a value of 1012 for the relative abundance of carbon-14.

Q4:

An old campfire is uncovered during an archaeological dig. Charcoal from the fire is found to contain less than 12,000 times the normal amount of carbon-14. Find the minimum age of the charcoal, to the nearest year. Use a value of 5,730 years for the half-life of carbon-14.

Q5:

The 𝛽 particles emitted in the decay of tritium interact with matter to create light in a glow-in-the-dark exit sign. At the time of manufacture, such a sign has an activity of 25.0 Ci. The half-life of the tritium is 12.3 years.

Find the mass of the tritium in the sign. Use a value of 3.016 u for the mass of a tritium atom.

What is the activity of the tritium in the sign exactly four years after the sign’s manufacture?

Q6:

Consider a block of uranium-238 with a mass of 2,000 kg.

Using a value of 4.468 billion years for the half-life of uranium-238, find the activity of the block. Give your answer to three significant figures.

Q7:

A large power reactor that has been in operation for some months is turned off, but residual activity in the core still produces 180 MW of power. If the average energy per decay of the fission products is 1.50 MeV, what is the activity of the core?

  • A 7 . 5 0 × 1 0 Ci
  • B 2 . 0 3 × 1 0 Ci
  • C 2 . 5 9 × 1 0 Ci
  • D 5 . 3 6 × 1 0 Ci
  • E 6 . 7 3 × 1 0 Ci

Q8:

Gallium has two stable isotopes. The atomic mass of 6931Ga is 68.925581 u and this isotope has an abundance of 60.108%. The atomic mass of 7131Ga is 70.924705 u and this isotope has an abundance of 39.892%. Calculate the atomic mass of the element gallium.

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