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zepelin [54]
2 years ago
8

(Radiocarbon dating) Carbon extracted from an ancient skull contained only one-sixth as much 14C as carbon extracted from presen

t-day bone. How old is the skull?
Mathematics
1 answer:
muminat2 years ago
8 0

Answer:

14734 years

Step-by-step explanation

We know the decay rate with time is given by;

\frac{dN}{dt}=-kN

Where K = 0.0001216 (radioactive decay constant)

Also we know the number of atoms remaining to decay in proportion to original number of atoms is given by;

Nt=N_{0} e^{-kt}

Where,

N_{0} = N(0)

Here we will find  t_{0}  such that  N(t_{0} )=\frac{1}{6}N_{0}

So we can say;

N(t_{0} )=\frac{1}{6}N_{0} ⇔  N_{0}e^{-kt_{0} }  =\frac{1}{6} N_{0}

⇒ e^{-kt_{0} } =\frac{1}{6}

Taking natural log  on both sides. we get

ln(e^{-kt_{0} }) = ln (\frac{1}{6} )

⇒ -kt_{0}  = ln(1)-ln(6)

-kt_{0} =-1.79175946923

t_{0}  = \frac{1.79175946923}{0.0001216}  = 14734 (approx)

So, the skull is approximately 14734 years old

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