2,500 atoms
Given:
A radioactive sample contains 10,000 atoms.
Question:
After two half-lives, how many atoms—of any type—remain in the sample?
The Process:
In the calculations of half-lives, the expressions are the following:
[tex]\boxed{ \ N = \frac{N_o}{2^n} \ }[/tex]
where [tex]\boxed{ \ n = \frac{t}{t_{1/2}} \ }[/tex] are used. In these expressions;
In our case above, there is no need for half-life. The number of half-lives will be counted immediately.
There are two ways to solve this problem.
First Way
We had two half-lives, therefore n = 2.
[tex]\boxed{ \ N = \frac{10,000}{2^2} \ }[/tex]
[tex]\boxed{ \ N = \frac{10,000}{4} \ }[/tex]
Thus, there are 2,500 atoms remain in the sample.
Second Way
[tex] \ \ \ \ \ \ \ \ \ \ \downarrow \ \ \ \ \ \ \ \ [/tex]
[tex] \ \ \ \ \ \ \ \ \ \ \downarrow \ \ \ \ \ \ \ \ [/tex]
- - - - - - - - - -
Notes:
The half-life of radioactive decay is the time required for half of the initial amount of the substance to disintegrate. The shorter the half-life of radioactive decay, the higher the rate of radioactive decay and the more radioactivity. The half-life is the characteristic property of each element.
