How many atoms will remain after 3 half-lives?

Question

Beginning with n atoms of an unstable nuclide, how many atoms will remain after 3 half-lives? After 5 half-lives?

Answer 1

atoms = 0.5^x

x=#of half lives

so # atoms = 0.5^3=0.125  or 1/8 after 3 or 1/2*1/2*1/2=1/8

so # atoms = 0.5^5=0.01325 or 1/32 after 5 or 1/2*1/2*1/2*1/2*1/2=1/32

Answer 2

1 / 2 = 1/2

1/2 / 2 = 1/4

1/4 / 2 = 1/8th of original atoms after 3 half lives.

1/8 / 2 = 1/16th

1/16th / 2 = 1/32nd of original atoms after 5 half lives.

Answer 3

After each half-life, the number of atoms is reduced to 1/2 of the number before the half-life. Hence, after 3 half-lifes, the number of atoms remaining is (1/2)*(1/2)*(1/2)*n = n/8. Similarly, after 5 half-lifes, the number of atoms remaining is n/(2^5) = n/32.