Q24.44 P A fabric remnant from a burial s... [FREE SOLUTION]

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_{$^{14} C$}

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

Now we can calculate how old the fabric is

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

Hence, the fabric is old $2546.6$ years

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Organic Chemistry

Nuclear Chemistry

Chemical Reactions

The Earths Atmosphere

Inorganic Chemistry

Study anywhere. Anytime. Across all devices.

91影视

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

Chemical Analysis

Organic Chemistry

Nuclear Chemistry

Chemical Reactions

The Earths Atmosphere

Inorganic Chemistry

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?