the half-life of carbon-11 is 20 minutes. How long will it btake for 600g of carbon-11 to decay to 30g?
To 1/20?
1/20=e^(-.692t/thalf)
ln .05=-.692t/20min
I get about 87 min. gross check. That is about 4 half lives, or (1/2)^4= 1/16 about .05, check.
The half-life of carbon-14 is 5730 years. If a sample contains 15 milligrams of
carbon-14, about how much carbon-14 was in the sample 15,000 years ago?
To determine the time it takes for 600g of carbon-11 to decay to 30g, we can use the concept of half-life. The half-life of carbon-11 is given as 20 minutes.
Here's the step-by-step explanation of how to calculate the time:
1. Calculate the number of half-lives:
Since the half-life is 20 minutes, divide the total time elapsed by the half-life to find out the number of half-lives that have passed. Let's denote this as "n".
n = (total time elapsed) / (half-life)
2. Calculate the remaining mass after each half-life:
The remaining mass after each half-life is given by:
remaining mass = initial mass / (2^n)
Here, the initial mass is 600g and n is the number of half-lives calculated in step 1.
3. Solve for "n" when the remaining mass is 30g:
Set the remaining mass to 30g and solve for "n" in the equation from step 2:
30 = 600 / (2^n)
Rearrange the equation to solve for "n":
2^n = 600 / 30
2^n = 20
4. Calculate the time it takes to reach the remaining mass of 30g:
Multiply the number of half-lives "n" by the half-life (20 minutes) to get the total time elapsed.
total time elapsed = n * (half-life)
Substituting the value of "n" obtained in step 3 into the equation will give us the result.
By following these steps, you should be able to determine the time it takes for 600g of carbon-11 to decay to 30g.