Explanation:
The half-life [tex]h[/tex] of a radioactive isotope refers to its decay period, which is the average lifetime of an atom before it disintegrates.
In this case, we are given the half life of two elements:
beryllium-13: [tex]h_{B-13}=5(10)^{-10}s=0.0000000005s[/tex]
beryllium-15: [tex]h_{B-15}=2(10)^{-7}s=0.0000002s[/tex]
As we can see, the half-life of beryllium-15 is greater than the half-life of beryllium-13, but how great?
We can find it out by the following expression:
[tex]h_{B-15}=X.h_{B-13}[/tex]
Where [tex]X[/tex] is the amount we want to find:
[tex]X=\frac{h_{B-15}}{h_{B-13}}[/tex]
[tex]X=\frac{2(10)^{-7}s}{5(10)^{-10}s}[/tex]
Finally:
[tex]X=400[/tex]
Therefore:
The half-life of beryllium-15 is 400 times greater than the half-life of beryllium-13.
