A radioactive sample initially contains N- atoms. After three half lives the number of atoms that

disintegrated is ?

(1/2)^3 = 1/8

so, 7/8 have disintegrated.

To determine the number of atoms that have disintegrated after three half-lives, we can use the formula:

Nf = Ni / (2^n)

Where:
- Nf is the final number of atoms remaining
- Ni is the initial number of atoms
- n is the number of half-lives

In this case, the number of half-lives is three (n=3), and the initial number of atoms is N.

So, after three half-lives, the number of atoms that have disintegrated is:

Nf = N / (2^3)
Nf = N / 8

Therefore, the number of atoms that have disintegrated after three half-lives is N/8.

To find the number of atoms that disintegrated after three half-lives, we need to first understand what a half-life is.

The half-life of a radioactive substance is the amount of time it takes for half of the atoms in a sample to undergo radioactive decay. During radioactive decay, the atoms of the substance break down and transform into different elements, releasing radiation in the process.

After one half-life, half of the original sample will have decayed, leaving N/2 atoms. After the second half-life, half of the remaining N/2 atoms will decay, leaving (N/2)/2 = N/4 atoms. After the third half-life, half of the remaining N/4 atoms will decay, leaving (N/4)/2 = N/8 atoms.

So, after three half-lives, the number of atoms that disintegrated is N - N/8 = 7N/8 atoms.