Chapter 24: Q24.44 P (page 1104)

A fabric remnant from a burial site has a $^{14} {C/}^{12} C$ ratio of $0.735$ of the original value. How old is the fabric?

Short Answer

Expert verified

The fabric is $2546.6$ years old

Step by step solution

Carbon dating

All the living organism contains $^{14} C$ . As the organism dies its amount decreases slowly. Using $^{14} C$ half-life the age of the organism can be determined.

Calculation

_{$^{14} {C/}^{12} {C=0.735(whichmeansthatN}_{t} {/N}_{0} =0.735)$}

- The half-life of_{$^{14} {Cist}_{1/2} =5730yr$}.

First, let us calculate the decay constant of_{$^{14} C$}

_{$\begin{matrix} k= \frac{ln(2)}{t_{1/2}} \\ = \frac{0.693}{5730yr} \\ {=1.209×10}^{-4} {yr}^{-1} \end{matrix}$}

Now we can calculate how old the fabric is

_{$\begin{matrix} ln (\frac{N_{t}}{N_{0}}) =-kt \\ t= \frac{-ln (\frac{N_{1}}{N_{0}})}{k} \\ = \frac{-ln(0.735)}{{1.209×10}^{-4} {yr}^{-1}} \\ =2546.6yr \end{matrix}$}

Hence, the fabric is old $2546.6$ years

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A fabric remnant from a burial site has a $^{14} {C/}^{12} C$ ratio of $0.735$ of the original value. How old is the fabric?

Short Answer

Step by step solution

Carbon dating

Calculation

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A fabric remnant from a burial site has a14C/12C ratio of 0.735of the original value. How old is the fabric?

Short Answer

Step by step solution

Carbon dating

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Chemistry Branches

Physical Chemistry

Chemical Analysis

Nuclear Chemistry

Inorganic Chemistry

Kinetics

Study anywhere. Anytime. Across all devices.

A fabric remnant from a burial site has a $^{14} {C/}^{12} C$ ratio of $0.735$ of the original value. How old is the fabric?