Question

The radioactive element americium-241 has a half-life of 432 years. Suppose we start with a 40-g mass of americium-241.
How much will be left after 353 years? Compute the answer to three significant digits.

Answer 1

A half life of 432 years means that the mass of A-241 is\[m=m(0)2^{-t/432}\]

Answer 2

Look at how, when t=432, then it becomes 2^-1, or half, of m(0). That is the definition of a half-life!

Answer 3

Do you understand that far?

Answer 4

yes sort of, im trying to figure it out now ha

Answer 5

Fair enough. And when t=2*432, then it is 2^-2, which is half of a half (i.e. 1/4), and in another 432 it will be 1/8 (half of a half of a half of the original mass).

Answer 6

When I say it is 2^-2, or course I mean
m=m(o)*2^-2