The half-life of a certain radioactive element is about
1500 years. After
2800 years, what percentage P of a sample of this element remains?
you have to multiply by 1/2 every 1500 years. So, the fraction remaining after t years is
(1/2)^(t/1500)
So, after 2800 years, the fraction remaining is
(1/2)^(2800/1500) = 2^-1.8667 = 0.2742 = 27.42%
Note that 2800 is almost 3000, or two half-lives. At t=3000, 1/2^2 = 1/4 = 0.25 will be left. So, we haven't quite reached that level yet.
what is 100*e^(-.692*2800/1500) ?
Put this in your google search window:
100*e^(-.692*28/15)=
To find the percentage of a sample of an element that remains after a certain amount of time, we can use the formula:
P = (1/2)^(t/h) * 100%
Where:
P is the percentage of the sample that remains
t is the amount of time that has passed
h is the half-life of the element
In this case, the half-life is 1500 years and the time that has passed is 2800 years. So, we can substitute these values into the formula:
P = (1/2)^(2800/1500) * 100%
To simplify the expression, divide 2800 by 1500:
P = (1/2)^(1.8667) * 100%
Using a calculator:
P ≈ 30.46%
Therefore, after 2800 years, approximately 30.46% of the sample of the radioactive element remains.
To find the percentage of a radioactive element that remains after a certain amount of time, we need to use the concept of half-life.
The half-life of a radioactive element is the amount of time it takes for half of the material to decay or disintegrate.
In this case, we are given that the half-life of the radioactive element is 1500 years. This means that after every 1500 years, the amount of the element remaining will be halved.
To determine the percentage of the sample that remains after 2800 years, we can:
1. Calculate the number of half-lives that have occurred by dividing the number of years (2800) by the half-life (1500):
Number of half-lives = 2800 years / 1500 years per half-life = 1.87 half-lives
2. Now, we need to calculate how much of the sample is remaining after 1.87 half-lives. To do this, we use the formula:
Remaining percentage = (1/2)^(number of half-lives) * 100
Plugging in the value of 1.87 for the number of half-lives:
Remaining percentage = (1/2)^(1.87) * 100
3. Using a calculator, we find that (1/2)^1.87 ≈ 0.4009.
Multiplying this value by 100, we get:
Remaining percentage ≈ 0.4009 * 100 ≈ 40.09%
Therefore, after 2800 years, approximately 40.09% of the original sample of the radioactive element remains.