Use this paragraph: The half-life of carbon-14 is 5,700 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 5,700 years?
(1 point)
Responses
5 grams
5 grams
2 grams
2 grams
40 grams
40 grams
10 grams
10 grams
To find out how many grams of carbon-14 the wood sample will have after 5,700 years, we can use the concept of half-life. The half-life of carbon-14 is 5,700 years, which means that after this time period, half of the carbon-14 in the sample will have decayed.
Since the wood sample initially has 20 grams of carbon-14 when it is alive, after 5,700 years, half of it will have decayed. So, we can calculate the remaining amount using the equation:
Final amount = Initial amount * (1/2)^(Number of half-lives)
In this case, the number of half-lives is 1 because we are considering the decay after 5,700 years.
Plugging in the values, we get:
Final amount = 20 grams * (1/2)^(1)
Final amount = 20 grams * 1/2
Final amount = 10 grams
Therefore, after 5,700 years, the wood sample will have 10 grams of carbon-14 remaining.
So, the correct answer is:
10 grams
To determine how many grams of carbon will be left after 5,700 years, we need to understand the concept of half-life. The half-life of carbon-14 is the amount of time it takes for half of the radioactive material to decay. In this case, it takes 5,700 years for half of the carbon-14 in the sample to decay.
Since the initial sample had 20 grams of carbon-14, after 5,700 years, half of it will have decayed, leaving us with 10 grams.
Therefore, the correct answer is 10 grams.