The activity of a sample of radioactive material is measured,and found to be 880 Bq. After 160 minutes the activity has fallen to 55 Bq. What is the half-life of Bq?
1 Answer
Explanation:
Before doing anything else, make sure that you understand what's going on here.
You're dealing with a sample of radioactive material that has an activity equal to
A becquerel,
#color(blue)("1 becquerel" = "1 decay"/"1 s")#
This means that you have
#"1 Bq" = "1 s"^(-1)#
So, an activity of
Now, after
As you know, nuclear half-life is simply the time needed for a sample of radioactive material to decay to half of its initial size.
The equation that establishes a relationship between the amount left undecayed,
#color(blue)(A = A_0 * 1/2^n)" "# , where
Plug in your values to get
#55 color(red)(cancel(color(black)("Bq"))) = 880 color(red)(cancel(color(black)("Bq"))) * 1/2^n#
This is equivalent to
#55/880 = 1/2^n#
#1/16 = 1/2^n implies 2^n = 16#
You will thus have
#2^n = 16 implies n = 4#
Therefore, four half-lives must pass in order for the activity of the sample to go from
Since the number of half-lives can be thought of as
#color(blue)(n = "given period of time"/"half-life" = t/t_"1/2")#
you can say that
#t_"1/2" = t/n#
This will get you
#t_"1/2" = "160 minutes"/4 = color(green)("40. minutes")#