Question

The half life of carbon-14 is 5730 years. How old is a bone if it presently contains 0.3125 g of carbon-14, but it was estimated to have originally contained 80 g of carbon-14?

Answer 1

The age of the bone is 45840 years.

We'll begin by calculating the number of half-lives that has elapsed.

Amount remaining (N) = 0.3125 g

Initial amount (N₀) = 80 g

Number of half-lives (n) =?

N × 2ⁿ = N₀

0.3125 × 2ⁿ = 80

Divide both side by 0.3125

2ⁿ = 80 / 0.3125

2ⁿ = 256

2ⁿ = 2⁸

n = 8

Thus, 8 half-lives has elapsed

Finally, we shall determine the age of the bone.

Half-life (t½) = 5730 years

Number of half-lives (n) = 8

Time (t) =?

t = n × t½

t = 8 × 5730

t = 45840 years

Therefore, the age of the bone is 45840 years.

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