How long will it take 200 mg of carbon-14 to decay to the point where only 75 mg remain if the half-life is 5770 years?
See your post above.
2 half years
To determine how long it will take for 200 mg of carbon-14 to decay to 75 mg, we need to understand the concept of half-life.
The half-life of a substance is the time it takes for half of the initial quantity to decay. In this case, the half-life of carbon-14 is given as 5770 years.
To find the time it takes for 200 mg to decay to 75 mg, we can approach it in the following steps:
1. Determine how many half-lives are required for the initial quantity (200 mg) to decay to the final quantity (75 mg).
- Since each half-life reduces the amount by half, we can calculate the number of half-lives needed by dividing the initial quantity by the final quantity: 200 mg / 75 mg ≈ 2.67
2. Calculate the time it takes for the given number of half-lives.
- Multiply the number of half-lives (2.67) by the half-life period (5770 years) to obtain the time it takes for the decay: 2.67 * 5770 years ≈ 15,395.9 years
Therefore, it will take approximately 15,395.9 years for 200 mg of carbon-14 to decay to the point where only 75 mg remain, given the half-life of 5770 years.