Question

The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 73% of

in the carbon-14 expected in living matter, when did the tree die?
The tree died about ] years ago.
Do not round until the final answer. Then round to the nearest whole number.)

Answer 1

Time 2 540 years

Explanation:

T = 5 600 yares - Half-life

73% - Carbon content

N = 0.73·N₀

Decay constant:

λ = ln 2 / T = 0.693 / 5600 ≈ 0.000124 (years)⁻¹

Law of radioactive decay:

N = N₀·e^(-λ·t)

0.73·N₀ = N₀·e^(-λ·t)

0.73 = e^(-λ·t)

ln (0.73) = -λ·t

t = ln (0.73) / (-λ) = ln (0.73) / (- 0.000124) ≈ 2 540 years