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The decay rate of at the time of Harappa civilization was 15 decays per gram of carbon sample. If a sample from the site today shows a decay rate of 9 decays per gram, the age of the Harappa civilization can be said to be ______ × 103 yr. [C14 Half-life of yrs.] [answer upto one decimal place]
Correct answer is between '4.0,4.4'. Can you explain this answer?
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To determine the age of the Harappa civilization, we can use the concept of half-life. The half-life of carbon-14 is approximately 5730 years.
If the decay rate of the carbon sample from the site today is 9 decays per gram, and the decay rate at the time of the Harappa civilization was 15 decays per gram, we can calculate the number of half-lives that have passed.
9 decays per gram is 60% (9/15) of the decay rate at the time of the Harappa civilization. This means that the sample has gone through approximately 60% of its half-life.
Using the formula for calculating half-lives:
(1/2)^n = 0.6
Where n is the number of half-lives that have passed.
Solving for n:
n = log base (1/2) of 0.6
Using a calculator, we find that n is approximately 0.736
Since each half-life of carbon-14 is approximately 5730 years, we can multiply this by the number of half-lives to get the age of the Harappa civilization.
Age = 0.736 * 5730 years
Age ≈ 4217.28 years
Therefore, the age of the Harappa civilization can be said to be approximately 4217.28 years.
If the decay rate of the carbon sample from the site today is 9 decays per gram, and the decay rate at the time of the Harappa civilization was 15 decays per gram, we can calculate the number of half-lives that have passed.
9 decays per gram is 60% (9/15) of the decay rate at the time of the Harappa civilization. This means that the sample has gone through approximately 60% of its half-life.
Using the formula for calculating half-lives:
(1/2)^n = 0.6
Where n is the number of half-lives that have passed.
Solving for n:
n = log base (1/2) of 0.6
Using a calculator, we find that n is approximately 0.736
Since each half-life of carbon-14 is approximately 5730 years, we can multiply this by the number of half-lives to get the age of the Harappa civilization.
Age = 0.736 * 5730 years
Age ≈ 4217.28 years
Therefore, the age of the Harappa civilization can be said to be approximately 4217.28 years.
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The decay rate of at the time of Harappa civilization was 15 decays per gram of carbon sample. If a sample from the site today shows a decay rate of 9 decays per gram, the age of the Harappa civilization can be said to be ______ × 103yr. [C14Half-life of yrs.] [answer upto one decimal place]Correct answer is between '4.0,4.4'. Can you explain this answer?
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