The half life of carbon-14 is 5700 years. A certain sample of wood has 20 grams of carbon -14 when it is alive. How many grams of carbon will it have after 5700 years.
A. 2 grams.
B. 5 grams.
C. 10 grams.
D. 40 grams.
The amount of carbon-14 in the wood will be halved every 5700 years.
After the first half-life, which is 5700 years, the wood will have 10 grams of carbon-14.
After the second half-life, which is another 5700 years, the wood will have 5 grams of carbon-14.
After the third half-life, which is another 5700 years, the wood will have 2.5 grams of carbon-14.
Since we're rounding to the nearest gram, after 5700 years, the wood will have 2 grams of carbon-14.
Therefore, the answer is A. 2 grams.
To determine how many grams of carbon-14 will remain after 5700 years, we need to use the concept of half-life. The half-life of carbon-14 is 5700 years, which means that after 5700 years, half of the original carbon-14 will have decayed.
So, after the first half-life of 5700 years, the amount of carbon-14 remaining will be 20 grams / 2 = 10 grams.
After the second half-life (another 5700 years), half of the remaining carbon-14 will decay again. Therefore, after 5700 years, the amount of carbon-14 remaining will be 10 grams / 2 = 5 grams.
Therefore, the correct answer is B. 5 grams.
To find out how many grams of carbon will remain after 5700 years, we need to use the half-life formula for exponential decay:
N(t) = N(0) * (1/2)^(t / half-life)
Where:
N(t) is the amount remaining after time t
N(0) is the initial amount
t is the time elapsed
half-life is the time it takes for the quantity to reduce by half
In this case:
N(t) is the unknown amount we need to find
N(0) is the initial amount, which is 20 grams
t is the time elapsed, which is 5700 years
half-life is 5700 years
Plugging in the values into the formula, we have:
N(t) = 20 * (1/2)^(5700 / 5700)
Simplifying:
N(t) = 20 * (1/2)^1
N(t) = 20 * 1/2
N(t) = 10 grams
Therefore, after 5700 years, the certain sample of wood will have 10 grams of carbon.
The correct answer is C. 10 grams.