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Half-Life

Key Concepts

  • The half-life of a radioisotope is the time required for half the atoms
        in a given sample to undergo radioactive, or nuclear, decay.

  • Half-life is given the symbol t½

  • Different radioisotopes have different half-lives.

  • The amount of radioactive isotope remaining can be calculated:

        Nt = No x (0.5)number of half-lives

        Where:
        Nt = amount of radioisotope remaining
        No = original amount of radioisotope
        number of half-lives = time ÷ half-life

Examples

  1. Consider strontium-90 which has a half-life of approximately 28 years.

    • Initially, at time t=0, the sample is 100% strontium-90

    • After 28 years, only half the original amount of strontium will remain:
          ½ x 100% = 50%

    • After another 28 years, only half of this amount of strontium-90 will remain:
          ½ x 50% = 25%

    • After another 28 years, only half of this amount of strontium will remain:
          ½ x 25% = 12.5%

    • and so on.

    • At any given time,
          the amount of strontium-90 that has undergone decay can be calculated:

          amount of strontium-90 decayed = the original amount - the amount remaining.

    Number of Half-lives Time (years) % Strontium-90 remaining % Strontium-90 that has decayed
    0 0 100 0
    1 28 50 50
    2 56 25 75
    3 84 12.5 87.5
    4 112 6.25 93.75
    5 140 3.125 96.875
    6 168 1.5625 98.4375

  2. Calculate the percentage of strontium-90 remaining after 280 years.

    Nt = No x (0.5)number of half-lives

    Nt = ? %
    No = 100%
    number of half-lives = time ÷ half-life = 280 ÷ 28 =10

    Nt = 100 x (0.5)10 = 0.098%


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