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Inessa05 [86]
3 years ago
7

Carbon-14 is used to determine the time an organism was living. The amount of carbon-14 an organism has is constant with the atm

osphere, but when an organism dies the carbon-14 decays at a half-life of 5,730 years. If an archeologist measured the amount of carbon-14 in an organism and it was 25% of the total amount of atmospheric C-14, what is the age of the organism? 1432.5 years 5,730 years 11,460 years 17,190 years
Physics
2 answers:
lutik1710 [3]3 years ago
8 0

Answer:

The age of the organism is approximately 11460 years.

Explanation:

The amount of carbon-14 decays exponentially in time and is defined by the following equation:

\frac{n(t)}{n_{o}} = e^{-\frac{t}{\tau} } (1)

Where:

n_{o} - Initial amount of carbon-14.

n(t) - Current amount of carbon-14.

t - Time, measured in years.

\tau - Time constant, measured in years.

Then, we clear the time within the formula:

t = -\tau \cdot \ln \frac{n(t)}{n_{o}} (2)

In addition, time constant can be calculated by means of half-life of carbon-14 (t_{1/2}), measured in years:

\tau = \frac{t_{1/2}}{\ln 2}

If we know that \frac{n(t)}{n_{o}} = 0.25 and t_{1/2} = 5730\,yr, then the age of the organism is:

\tau = \frac{5730\,yr}{\ln 2}

\tau \approx 8266.643\,yr

t = -(8266.643\,yr)\cdot \ln 0.25

t \approx 11460.001\,yr

The age of the organism is approximately 11460 years.

N76 [4]3 years ago
4 0

Answer:

8

Explanation:

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