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MCAT Physics Question — Half Life

If the half-life of carbon-14 is 5700 years, and some plant remains from an archeological dig site have 1/8 the carbon-14 found in the atmosphere, what is the approximate age of the remains in the dig site in years?


  1. 700
  2. 5700
  3. 17000
  4. 45000
Click for Explanation

The half-life is the time it takes for 1/2 of a radioactive substance to decay. For example, 20 units of a substance with a half-life of 5 years will have 10 units remaining after 5 years. In this example, carbon-14 has undergone 3 half-lives: 1 → ½; ½ → ¼; ¼ → 1/8.

3 x 5700 years = 17100 years.

  1. 700, incorrect, This answer results from multiplying the amount of sample by the half life, 5700/8.
  2. 5700, incorrect, This is the half-life, not the amount of time elapsed during three half-lives.
  3. 17000, correct.
  4. 45000, incorrect, This answer results from multiplying the half-life by the remaining fraction: 5700 x 8.

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