A manuscript is alleged to be 1000 years old. If it currently has 98% of its original carbon-14 (carbon-14 has a half-life of 5750 years), how old is the manuscript? Is it a forgery?

171 years old; a forgery

1068 years old; a forgery

168 years old; a forgery

1000 years old; not a forgery

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• Amy
Lv 7
4 months ago

A manuscript might be written on paper, other plant material, or animal skin. Living things absorb carbon from the environment by photosynthesis, eating, etc. The original proportion that is the isotope carbon-14 stays fairly constant, so we know the original amount that was in a sample. After the plant or animal dies, the carbon-14 decays into nitrogen.

The decrease of carbon-14 is exponential. The "half-life" is the amount of time it takes for half of the carbon-14 to be destroyed.

Thus, the amount remaining obeys the equation:

Amount of C14 = Original amount * (1/2)^N

where N is the number of half-lives since the source died.

Of course after N=1 half-lives, the amount of C14 is 1/2 of the original. After N=2 half-lives, the amount of C14 is 1/4 of the original (half of what was left at N=1). After N=3 half-lives, the amount of C14 is 1/8 of the original. And so on.

Your sample has 98% remaining, so we solve for N:

98% * original amount = original amount * (1/2)^N

N = 0.029

and then multiply by the length of a carbon-14 half-life.

If a manuscript alleged to be 1000 years old is written on paper less than 200 years old, then obviously it's a forgery.