Question

A formally living, organic sample has been excavated from an archeological dig. It is known that this sample is supposed to contain 3.2 micrograms of Carbon-14. Tests show it currently has 2.1 micrograms of Carbon-14.

Using the fact that Carbon-14 has a half-life of approximately 5730 years, how long ago did this specimen die?

(Round your answer to the nearest whole number year.)

Answer 1

• This specimen died 3482 years ago

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Let the number of passed years be x.

Use the equation for half-life:

• 
  `N(t) = N_0 * (1/2)^(x/th)`, where N(t) - remaining quantity, N₀ - initial quantity, x - time passed, th - half-life period

Substitute given values and solve for x:

• 
  `2.1 = 3.2*(1/2)^(x/5730)`
• 
  `(1/2)^(x/5730) = 2.1/ 3.2`
• 
  `x/5730=log\ (2.1/3.2) /\ log\ (1/2)`
• 
  `x = 5730*log\ (2.1/3.2) /\ log\ (1/2)`
• 
  `x=3482`