archeologists continue to debate the arrival of the first humans in the western hemisphere. radiocarbon dating of charcoal from a cave in chile was used to establish the earliest date of human habitation in south america as 8700 years ago. this procedure involves comparing the 14c present in a sample of charcoal to the 14c present in a living tree of the same age. 1st attempt see hint what fraction of the 14c initially present remained in the charcoal after 8700 years? the half-life of 14c is 5730 years. (write the answer as a number with a decimal.)

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AnnuG AnnuG · Answer 1 · 2022-12-21T08:55:07+01:00

7/20 is the fraction of the 14c carbon was initially present and remained in the charcoal after 8700 years

Carbon is a chemical element with the symbol C and atomic number 6.

It is non-metallic and tetravalent – its atom makes four electrons available to form covalent chemical bonds.

k = ln 2) / half life

k = ln 2 / 5730 years

k = 1.21 x 10⁻⁴ (1/years)

ln [A]ₙ / [A]₀ = -kt

[A]ₙ = Amount of concentration at time t (here t = 8700 years)

[A]₀ = Amount of concentration of carbon present initially

( [A]ₙ / [A]₀ ) = X

ln X = - 1.21 x 10⁻⁴ (1/years) * 8700

ln X = -1.05

On taking natural log both side

X = 0.35

( [A]ₙ / [A]₀ ) = 0.35

i.e.

( [A]ₙ / [A]₀ ) = 7/20

7:20 is the fraction of the 14c when initially present to the remained in the charcoal after 8700 year.

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