Carbon-14 has a half-life of 5730 years. How much of a 144 g sample of carbon-14 will remain after 100,000 years?

0.001 g

Explanation:

From the question given above, the following data were obtained:

Half-life (t½) = 5730 years

Original amount (N₀) = 144 g

Time (t) = 100,000 years

Amount remaining (N) =?

Next, we shall determine the number of half-lives that has elapsed. This can be obtained as follow:

Half-life (t½) = 5730 years

Time (t) = 100,000 years

Number of half-lives (n) =?

n = t / t½

n = 100,000 / 5730

n ≈ 17

Finally, we shall determine the amount remaining. This can be obtained as follow:

Original amount (N₀) = 144 g

Number of half-lives (n) = 17

Amount remaining (N) =?

N = 1/2ⁿ × N₀

N = 1/2¹⁷ × 144

N = 1/131072 × 144

N = 0.000007 × 144

N ≈ 0.001 g

Thus, the amount remaining after 100000 years is 0.001 g