Type the correct answer in the box. express your answer to three significant figures.

the half-life of carbon-14 is 5,730 years. dating organic material by looking for c-14 can’t be accurately done after 50,000 years.

suppose a fossilized tree branch originally contained 4.30 grams of c-14. how much c-14 would be left after 50,000 years?

use the formula n = n0 .

a tree branch that originally had 4.3 grams of carbon-14 will have
grams after 50,000 years.

A tree branch that originally had 4.3 grams of carbon-14 will have  9.4586 x 10⁻³ grams after 50,000 years.

Explanation:

The integral rate law of a first order reaction:

kt = ln ([A₀]/[A]),

where, k is the rate constant of the reaction,

t is the time of the reaction (t = 50,000 years),

[A₀] is the initial concentration of carbon-14 ([A₀] = 4.30 g).

[A] is the remaining concentration of carbon-14.

k = ln 2/(t1/2) = 0.693 / (5,730 years) = 1.21 x 10⁻⁴ years⁻¹.

∵ kt = ln ([A₀]/[A]).

(1.21 x 10⁻⁴ years⁻¹)(50,000 years) = ln ((4.30 g)/[A]).

6.047 = ln ((4.30 g)/[A]).

Taking the exponential of both sides:

422.893 = ((4.30 g)/[A])

∴ [A] = (4.30 g)/(422.893) = 9.4586 x 10⁻³ g.

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