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Juli2301 [7.4K]
3 years ago
11

A seashell has only 3.1% of its c-14 left. The half life of c-14 is 5740 years. How old is the seashell

Chemistry
1 answer:
Slav-nsk [51]3 years ago
6 0

The seashell is <u>28747.96 years old.</u>

<u />

Why?

If we need to calculate how old is something, we can use the equation for radioactive decay rate. It's possible using the C-14 half-life (5740 years) as reference. Remember, C-14 is used because all the living things take up the element from the atmosphere, when an organism dies, the amount of carbon starts to decay (very slowly).

Decay rate half life:

N_{t}=N_{o}*e^{-l*t}

Where,

N_o} is the initial number of atoms (undecayed)

N_{t} is the the number of atoms at time (undecayed)

l is the decay rate

Now, isolating the decay rate of the formula, we have:

{N_{t}=N_{o}*e^{-l*t}\\\\ln(\frac{N_{t}}{N_{o}})=-l*t\\

Also, we can get the value of the decay rate (half life), using the following formula:

l=\frac{0.693}{5740}=1.207x10^{-4}

Then, using the given information, we have:

ln(\frac{3.1}{100})=-1.207x10^{-4}*t

-3.47=-1.207x10^{-4}*t

-3.47=-1.207x10^{-4}*t\\\\t=\frac{-3.47}{1.207x10^{-4}}=28748.96years

Hence, the seashell is 28748.96 years old.

Have a nice day!

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