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

The mammoth bone is 22726 years old.

Step-by-step 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 = (ln(2))/(t_(1/2)) = (ln(2))/(5700 y) = 1.22 \cdot 10^(-4) y`

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

`t = (ln((N(t))/(N_(0))))/(-\lambda) = (ln(0.0625))/(-1.22 \cdot 10^(-4)) = 22726 y`

Therefore, the mammoth bone is 22726 years old.

I hope it helps you!