A radioactive isotope has a half life of 8.1 days. If the sample starts with 25 grams, how much will there be after 90 days?

90 days is 90/8.1 = 11.111 half-lives, so there would be

25*(1/2)^11.111 left

THANK YOU!!

To calculate the amount of a radioactive isotope remaining after a certain time, we can use the formula:

N(t) = N(0) * (1/2)^(t/h)

Where:
N(t) is the amount remaining after time t,
N(0) is the initial amount,
t is the elapsed time, and
h is the half-life of the isotope.

In this case, the initial amount (N(0)) is 25 grams, the elapsed time (t) is 90 days, and the half-life (h) is 8.1 days.

Plugging these values into the formula, we get:

N(90) = 25 * (1/2)^(90/8.1)

Now, let's calculate this value using a calculator or a spreadsheet.

N(90) = 25 * (0.5)^(11.11)

N(90) = 25 * 0.1111

N(90) ā‰ˆ 2.78 grams

After 90 days, there will be approximately 2.78 grams of the radioactive isotope remaining.