Question

A mammoth skeleton has a carbon-14 decay rate of 0.49 disintegrations per minute per gram of carbon (0.49 dis/min⋅gC ). You may want to reference (Pages 950 - 955) section 20.6 while completing this problem. Part A When did the mammoth live? (Assume that living organisms have a carbon-14 decay rate of 15.3 dis/min⋅gC and that carbon-14 has a half-life of 5715 yr.)

Answer 1

Answer:

t = 28379.5 years

Explanation:

To find when did the mammoth live, we need to use the exponential decay equation:          

$\frac{N_{t}}{N_{0}}= \frac{1}{2}^ \frac{t}{t_{1/2}}$  

where, N(t)/N(0): ratio decay rate, t: time to find, t(1/2): half-life

   

$\frac{0.49}{15.3} = \frac{1}{2}^ \frac{t}{5715}$  

$Log(0.032) = \frac{t}{5715} \cdot Log(0.5)$

$t= \frac {5715 \cdot Log(0.032)}{Log(0.5)}$  

$t= 28379.5 years$

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