Half-Life Problem Set

Many thanks to 6th year CBC students for devising these problems.

Screen Shot 2014-11-04 at 19.19.36


  • After how many half-lives will 200g of Proactinium-234 decay to 6.25g?
  • Starting with 100grams of Proactinium-234, how many grams are left after 4 hours?
  • The American government recovered 239 million tonnes of Bismuth-210 from a mine in 1962, how much radioactive Bismuth-210 is left in the sample today?
  • 4g of Lead-214 remain after 12 half-lives, what was the original mass of radioactive Lead-214 in the sample?
  • If you had 3.5g of Proactinium-234 at 1pm, how much radioactive Proactinimu-234 do you have at 1:06pm?
  • If we have 1gram of Bismuth-234 remaining after 4 hours, how many kilograms did we start with?
  • The code to unlock an iPhone is the amount of time, in days, for 120grams of Polonium-210 to decay to 7.5grams. What is the code?
  • A radioactive sample is delivered to a University Physics department on the 21st January, 2016. What fraction of Thorium-234 is remaining on the 9th March 2016, correct to 2 decimal places?
  • If 200 radioactive nuclei remain from a sample of 1000 nuclei, how many half-lives have passed?
  • If 300 nuclei remain from a sample of 2400 nuclei, how many half-lives have passed.



  • In a sample of radioactive materials Thorium-234 and Bismuth-210 are in the ratio of 3:2 respectively. After 120 days 5g of Thorium atoms remain.
    • What is the initial amount of Thorium-234?
    • What is the initial amount of Bismuth-210?
    • Find the decay constant for both atoms.
    • What is the activity of both radioactive isotopes?
    • If a radioactive sample contained 100g of Radium-226 in 9,200 BC, what year will it be when there is 0.78125 g left in the sample?
  • A rock sample had 6 moles of Thorium-234 in it originally. How many grams of Thorium-234 remain after 48 days?
  • 6 atoms of Bismuth-210 remain after 6 half-lives. How many moles of radioactive Bismuth-210 were present initially?
  • A sample of 1gram Polonium-214 is left in a container over the course of a day (24hrs). How much Polonium-214 is left at the end of the day? Give your answer in the form 2a.
  • Lead-210 loses 45grams of its original mass in 132 years. What was the original mass? Ignoring any other element/isotope in the sample
  • If it took 84 hours for the atomic bomb that was dropped on Hiroshima to be transported from America to Japan and it contained 10kg of Uranium-234 intially, how much Uranium-234 was left in the sample when it reached Japan?

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