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xxTIMURxx [149]
3 years ago
14

The carbon−14 decay rate of a sample obtained from a young tree is 0.266 disintegration per second per gram of the sample. Anoth

er wood sample prepared from an object recovered at an archaeological excavation gives a decay rate of 0.178 disintegration per second per gram of the sample. What is the age of the object? (The half-life of carbon−14 is 5715 years.) × 10 years Enter your answer in scientific notation.
Chemistry
1 answer:
Novosadov [1.4K]3 years ago
5 0

Answer:

  • <u><em>3.30 × 10³ years</em></u>

Explanation:

1) <u>Carbon-14 disintegration rate of a young (alive) tree</u>: 0.266 per second per gram.

2)<u> Carbon-14 disintegration rate of a wood sample prepeared from an object recovered at an archaelogical excavation (dead matter):</u> 0.178 per second per gram.

3) <u>Ratio of decay</u>: A/A₀ = 0.178 / 0.266 = 0.669

4) <u>Half-life equation</u>: A/A₀ = (1/2)ⁿ, where n is the number of half-lives since the object died.

5) <u>Substitute and solve for n</u>:

  • 0.669 = (1/2)ⁿ

nlog(1/2)=log(0.669)\\ \\n=\frac{log(0.669)}{log(1/2)}\\ \\n=0.578

That means that 0.578 half-life has elapsed since the wood with which the object was created was dead matter.

6) <u>Convert number of half-lives to years</u>:

  • 0.578 half-life × 5715 years/half-life = 3,303 years = 3.30 × 10³ years.
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