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The half-life of Carbon-14 is 5730 years. Suppose a fossil is found with 50% of Carbon-14 as compared to a living sample. How old is the fossil?

User Kimkevin
by
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2 Answers

4 votes

Answer: 5730 years

Step-by-step explanation:

Because it takes 5730 years for half of a sample of carbon-14 atoms to decay. It says that 50% of the carbon atoms have decayed so that means that 5730 years have elapsed for that fossil.

User Zsolt
by
9.4k points
3 votes

Answer:

5732 years

Step-by-step explanation:

Radioactive decay can be determined by using the equation:


N_t = N_0e^(- \lambda t)

where;


N_t = number of decayed atoms at time (t)


N_0 = initial number of decayed atoms


\lambda = decay constant

So, if we equate the natural log of the above; we have:


In(N_t) = In(N_0)-\lambda t


\frac{In(N_t)} { In(N_0)}} = -\lambda t

where;


\lambda =
(0.693)/(t_(1/2))


\lambda =
(0.693)/(5730)


\lambda =
1.209*10^{-4


In((50)/(100)) =-(1.209 *10^(-4))*t


-0.693 = -(1.209*10^(-4))*t


t= (0.693)/(1.209*10^(-4))

t = 5732.01 years

t = 5732 years.

Hence, the fossil is 5732 years old.

User Rafia
by
8.4k points
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