Thorium-234 has a half-life of 24 days. if you started with 100 gram sample of thorium-234, how much would remain after 48 days?
1 Answer
Explanation:
Think about what a nuclear half-life represents, i.e. the time needed for an initial sample of a radioactive substance to be halved.
In your case, you know that thorium-234 has a half-life of
This is of course equivalent to saying that every
So, if you start with
#A * 1/2 = A/2 -># after the passing of one half-life#A/2 * 1/2 = A/4 -># after the passing of two half-lives#A/4 * 1/2 = A/8 -># after the passing of three half-lives
#vdots#
and so on.
So, if you start with
#"100 g" * 1/2 = "50 g" -># after#24# days#"50 g" * 1/2 = "25 g" -># after#48# days
As you can see, you can calculate the amount of a sample that remains undecayed by using the equation
#color(blue)(A = A_0 * 1/2^n)" "# , where
In your case, you'd have
#n = (48 color(red)(cancel(color(black)("days"))))/(24color(red)(cancel(color(black)("days")))) = 2#
Therefore,
#A = "100 g" * 1/2^2 = "100 g" * 1/4 = color(green)("25 g")#