30.16 A 12.0-g sample of carbon from living matter decays at the rate of 186.5 d

Question

30.16 A 12.0-g sample of carbon from living matter decays at the rate of 186.5 decays/minute due to the radioactive C14 in it. a. What will be the decay rate of this sample in 1000 years? b. What will be the decay rate of this sample in 50000 years? (in decays/minute) 30.16 A 12.0-g sample of carbon from living matter decays at the rate of 186.5 decays/minute due to the radioactive C14 in it. a. What will be the decay rate of this sample in 1000 years? b. What will be the decay rate of this sample in 50000 years? (in decays/minute)

Explanation / Answer

Half life (T) of C-14 is 5730 years. Sometimes it is also taken to be 5700.

- dN/dt = (dN/dt)₀ ∙ (1/2)^(t/τ)

a. 186.5 (1/2)^(1000/5730) = 165.25decays/min

b. 186.5 (1/2)^(50000/5730) = .44 decays/min

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