An ancient skull has a carbon-14 content of 1.563% of that

Problem 81P Chapter 17

Introductory Chemistry | 5th Edition

Introductory Chemistry | 5th Edition

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Problem 81P

An ancient skull has a carbon-14 content of 1.563% of that found in living organisms. How old is the skull?

Step-by-Step Solution:

Step 1 of 2

Solution 81P:

Here, we are going to calculate the old of the skull.

Step1:

Half life period of the carbon-14 is 5730 years

We know,

t1/2 = $\frac{0.693}{K}$

k = $\frac{0.693}{t1/2}$

= $\frac{0.693}{5730\ yr}$

= 1.209x 10-4 yr-1

Step 2:

We know,

-kt = ln $\frac{rate\ 1}{rate\ 0}$ = ln $\frac{1.563}{100}$ = -4.15856

$\Rightarrow{}t=\$ $\frac{0.693}{k}$ = $\frac{4.15856}{1.209x10-4/yr}$ = 3.43967 x 104 yr

= 34396.7 yr

Thus, the skull is 34396.7 years old.

Note, if we take, -4.159 instead of -4.15856

Step 2 of 2

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