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 . 4 0 × 1 0 2 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 . 7 0 × 1 0 2 mol
  • B 1 . 8 0 × 1 0 2 mol
  • C 1 . 0 0 × 1 0 2 mol
  • D 1 . 2 0 × 1 0 2 mol
  • E 8 . 4 9 × 1 0 3 mol

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

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

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

  • A 4 . 5 0 × 1 0 4 mol
  • B 1 . 0 0 × 1 0 3 mol
  • C 3 . 7 5 × 1 0 4 mol
  • D 9 . 0 0 × 1 0 4 mol
  • E 6 . 0 0 × 1 0 4 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 . 0 0 × 1 0 s−1. What is the half-life of this material?

  • A 3 0 2 × 1 0 years
  • B 1 6 3 × 1 0 years
  • C 4 4 6 × 1 0 years
  • D 6 9 3 × 1 0 years
  • E 8 1 5 × 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 = 1 0 decay/min g. What is the age of the wood? Use a value of 3 . 8 4 × 1 0 1 2 s−1 for the decay constant of carbon-14 and a value of 1 0 1 2 for the relative abundance of carbon-14.

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