A tree sample was uprooted and buried 60,000 years ago during part of the Wiscon

Question

A tree sample was uprooted and buried 60,000 years ago during part of the Wisconsin glaciation. The carbon-14 was not replenished after the tree stopped growing. The half-life of carbon-14 is T=5700 years.

Part A

How many years after it was buried was the radioactive carbon-14 (14C) in the root reduced by a factor of 1/2? Express your answer using two significant figures.

Part B

How many years after it was buried was the radioactive carbon-14 (14C) in the root reduced by a factor of 1/8? Express your answer using two significant figures.

Part C

How many years after it was buried was the radioactive carbon-14 (14C) in the root reduced by a factor of 1/16? Express your answer using two significant figures.

Part D

What fraction remained after 60,000 years? Express your answer using two significant figures.

Explanation / Answer

given,

half life of the carbon-14 = 5700 years

so root will be reduced to factor of 1/2 in one half life that is 5700 years

root will be reduced to factor of 1/8 in three half life (as 1/2 in first half life, 1/2 in second half life, 1/2 in third half life so (1/2 * 1/2 * 1/2 = 1/8)

so three half life = 3 * 5700

three half life = 17100 years

the root reduced by a factor of 1/8 in 17100 years

similarily

the root reduced by a factor of 1/16 in 5700 * 4 years

the root reduced by a factor of 1/16 in 22800 years

fraction remained after 60000 years = 1/2^(60000 / 5700)

fraction remained after 60000 years = 0.00067805231

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