Scientists at Oak Ridge National Laboratory confirmed the existence of element 104 by creating 3000 atoms of it. If radioactive decay caused the number of atoms to drop by half within 4.0 s, how many atoms were left after 12 s?
Show work please!
Thank you!
To determine the number of atoms left after 12 seconds, we need to calculate the number of half-lives within that time frame.
First, let's find the number of half-lives in 12 seconds. We know that the half-life of the element is 4 seconds, so we can divide the total time (12 s) by the half-life (4 s):
Number of half-lives = Total time / Half-life
Number of half-lives = 12 s / 4 s
Number of half-lives = 3
This means that in 12 seconds, there would have been 3 half-lives.
Next, we need to calculate the remaining amount of atoms after each half-life.
For each half-life, the number of atoms is halved. So after the first half-life, there would be 3000 atoms / 2 = 1500 atoms.
After the second half-life, there would be 1500 atoms / 2 = 750 atoms.
And after the third half-life, there would be 750 atoms / 2 = 375 atoms.
Therefore, after 12 seconds, there would be 375 atoms of element 104 left.