Half-Life

Half-life is the time it takes for a radioactive material to lose half of its radioactivity. Isotopes can have very different half-lives. E.g. Uranium-235 (used in nuclear power stations) has a half-life of 700 million years, while the half-life of flourine-18 (used in hospitals) is less than 2 hours.

• Do things remain radioactive forever? [2]

  • No - Each time a decay happens and an alpha, beta or gamma is given out, it means more radioactive nucleus has disappeared.
  • As the unstable nuclei all steadily disappear, the activity as a whole will decrease (So the older a sample becomes, the less radiation it will emit)
  • How quickly the activity drops off varies a lot. (For some isotopes it takes just a few hours before nearly all the unstable nuclei have decayed, whilst others last for millions of years)

• What is Half-life? [1]

  • Half-life is "the time taken for half of the radioactive atoms now present to decay", or "The time taken for the activity (or count rate) to fall by half"
    • Why can't we use the whole-life instead of the half-life? [1]
      • The problem with trying to measure the whole life is that the activity never reaches zero - and so it's life never seems to end!
      • (which is why we have to use the idea of half-life to measure how quickly the activity drops off)
    • Two radioactive sources are placed in a box. One with a short half-life, the other with a very long half-life. Which radioactive source would have a greater activity and which would remain radioactive for longer? [2]
      • The source with a short half-life would have the greater activity because lots of nuclei are decaying quickly.
      • The source with a very long half-life would remain radioactive longer because most of the nuclei don't decay for a long time - they just sit there, unstable, biding their time

• What does "Bq" mean? [1]

  • Radioactivity is usually measured in counts per minute (cpm) or becquerels (Bq)
    • What is the difference between cpm and Bq? [2]
      • 1 cpm = 1 decay per minute. 
      • 1 Bq = 1 decay per second.

• What is the Half-life of a sample if the activity of a radioisotope is 640 cpm and two hours later it has fallen to 40 cpm? [4]

  • Initial Count = 640 cpm
    • after 1 half-life = ½ of 640 cpm = 320 cpm
      • after 2 half-lives = ½ of 320 cpm = 160 cpm
        • after 3 half-lives = ½ of 160 cpm = 80 cpm
          • after 4 half-lives = ½ of 80 cpm = 40 cpm
  • It takes 4 half-lives (for the activity to fall from 640 cpm --> 40 cpm)
    • 4 half-lives = 2 hours
      • 1 half-life = ¼ of 2 hours
        • 1 half-life = ½ hour (30 mins).

• How do you find the Half-life on a graph? [3]

  • When the half-life of a sample is plotted as a graph it will always be shaped like the one below.
  • locate half of the initial activity (on the vertical axis) and find what time interval it corresponds to (on the bottom axis).
  • Repeat this two or three times & you should find the time interval is always the same (this is the half-life).

• How can you use half-life to work out the age of rocks, fossils and other specimens (radioactive dating)? [3]

  • E.g. Igneous rocks contain radioactive uranium which has a ridiculously long half-life. It eventually decays to become a stable isotope of lead.
  • Step 1) By measuring the amount of radioactive isotope (i.e. uranium-238) left in a sample, the relative proportions of uranium : lead can be found. 
  • Step 2) This proportion will tell you how many half-lives have occured (providing the original sample had no traces of lead already in it)
  • Step 3) By multiplying the half-life (i.e. half-life of Uranium-238 = 4,500 million years ), with the number of half-lives past, an approximate age can be found.

• How does Carbon Dating work? [3]

  • Carbon-14 makes up about 1 / 10,000,000 (1 ten-millionth) of the Carbon found in the air. This level stays fairly constant in the air and living things.
  • When something dies, no new Carbon-14 enters the dead body, or dead wood, or dead whatever.
  • The Carbon-14 that is trapped inside gradually decays
  • By measuring the proportion of Carbon-14 remaining in the dead specimen you can calculate how many half-lives have occured since it died
  • Since the Half-life of Carbon-14 = 5,730 years, you can work out how long ago the specimen died.
    • E.g. An axe handle was found to contain 1 part in 40,000,000 Carbon-14. How old is the axe? [2]
      • When alive, Carbon-14 = 1 / 10 million
        • After 1 half-life = ½ of 1 / 10 million = 1 / 20 million
          • After 2 half-lives = ½ of 1 / 20 million = 1 / 40 million
      • ...Hence, the axe handle is 2 half-lives old
        • = 2 x (5,730 years)
          • = 11,460 years old

• What are the assumptions Carbon Dating is based upon? [3]

  • The level of Carbon-14 in the atmosphere has always been constant
    • The level of Carbon-14 hasn't always been constant - what may have caused the changes in levels of Carbon? [3]
      • Cosmic radiation
      • Climate change
      • Human activity
    • How do scientists using Carbon Dating account for this? [1]
      • They adjust their results using calibration tables
  • All living things take in the same proportion of their carbon as Carbon-14
    • Not all living things act as we expect. For example, some plants take up less Carbon-14 than expected. How would this affect the results of the age obtained through carbon dating? [1]
      • They may seem older than they really are
  • Substances haven't ben contaminated by a more recent source of carbon (after they've died)

• Classwork

  • 1) What is the half-life of an isotope?
  • 2) Calculate the half-life of a sample of copper-64 with an activity at the start of the experiment of 400 Bq, and an activity 1 day later of 100 Bq.
  • 3) This data shows the count rate for a radioactive source at various times. Plot a graph of this data and use it to find the half-life of the substance (0 mins = 750 counts; 20 mins = 568 counts; 40 mins = 431 counts; 60 mins = 327 counts; 80 mins = 247 counts; 100 mins = 188 counts; 120 mins = 142 counts)
  • 4) An old bit of cloth was found to have 1 atom of Carbon-14 to 80,000,000 atoms of Carbon-12. If Carbon-14 decays with a half-life of 5,730 years, and the proportion of Carbon-14 to Carbon-12 in living material is 1 to 10,000,000, find the age of the cloth.
  • 5) The graph shows how the count rate of a radioactive isotope decreases with time.
    • What is the half-life of this isotope?
    • What was the count rate after 3 half-lives?
    • What fraction of the original radioactive nuclei will still be unstable after 5 half-lives?
    • After how long was the count rate down to 100?
  • 6) Uranium-238 decays with a half-life of 4.5 billion years into a stable form of lead. A meteorite was found to contain some uranium-238 and some lead in the ratio of 1:1. If there was no lead in the meteorite when it was created, how old is the meteorite?

•  Homework

  • 1) A Radioactive isotope has a half-life of 40 seconds
    • What fraction of the unstable nuclei will still be radioactive after 6 minutes
      • (hint: you'll need to change 6 minutes into seconds)
    • If the initial count rate of the sample was 8000 counts per minute, what would be the approximate count rate after 6 minutes?
    • After how many whole minutes would the count rate have fallen below 10 counts per minute?
  • 2) Carbon-14 makes up approximately 1 part in 10,000,000 of the carbon in living things
    • What happens to the proportion of carbon-14 in a plant or animal when it dies?
    • The half-life of carbon-14 is 5,730 years. Explain what this means in terms of the number of carbon-14 atoms in a sample
  • 3) A leather strap from an archaeological dig was found to have 1 part in 80,000,000 carbon-14
    • Use the data given in Q2 to help you estimate the age of the strap.
    • Suggest two reasons why your answer might be inaccurate
  • 4) Some egyptian leather sandals are known to be from 3700 BCE.
    • Approximately what fraction of the carbon in the sandals would you expect to be carbon-14?
  • 5) A Website is advertising "Wooly mammoth tusks" for sale. An investigator buys one and carries out a radiocarbon test. The test shows that the tusk contains 1 part in 15,000,000 carbon-14.
    • Given that wooly mammoths are believed to have become extinct 10,000 years ago, is the tusk likely tobe genuine? Explain your answer.