Question

A fossil mammoth bone was found to contain 6.25% carbon-14 percent isotope and 93.75% nitrogen-14 daughter isotope. If the half-life of carbon-14 is 5700 years old, how old is the mammoth bone?

Answer 1

Answer:

The mammoth bone is 22726 years old.

Explanation:

We can find how hold is the mammoth bone using the decay equation:

$N(t) = N_{0}*e^{-\lambda t}$   (1)

Where:

N(t): is the quantity at time t = 6.25%N₀

N₀: is the initial quantity

λ: is the decay constant

First, we need to find λ:

$\lambda = \frac{ln(2)}{t_{1/2}} = \frac{ln(2)}{5700 y} = 1.22 \cdot 10^{-4} y$

Now, by solving equation (1) for t we have:

$t = \frac{ln(\frac{N(t)}{N_{0}})}{-\lambda} = \frac{ln(0.0625)}{-1.22 \cdot 10^{-4}} = 22726 y$      

Therefore, the mammoth bone is 22726 years old.

I hope it helps you!