An element whose half-life is 3 years has N atoms. How many atoms would have decayed after 9 years

Answer Details

If an element has a half-life of 3 years, it means that after 3 years, half of the atoms in a sample of that element will have decayed. After another 3 years (a total of 6 years), half of the remaining atoms will have decayed. After another 3 years (a total of 9 years), half of the remaining atoms will have decayed again.
So, after 9 years, the number of atoms remaining would be 1/2 x 1/2 x 1/2 times the original number of atoms, or (1/2)^3 times N.
Simplifying this expression, we get (1/8) times N. Therefore, the number of atoms that would have decayed after 9 years would be the original number of atoms minus (1/8) times the original number of atoms, or 7/8 times N.
So, the answer is 7 N atoms8.