# What is half-life?

May 18, 2014

Half-life (t_½) is the time required for a quantity to fall to half its value.

In nuclear chemistry, the half-life is the time needed for half of the radioactive atoms to decay.

For example, carbon-14 has a half-life of 5730 yr.

If we start with 10.0 g of carbon-14, the amount remaining after 5730 yr (1 half-life) will be 10.0 g × ½ = 5.00 g.

After 2 half-lives, the amount remaining will have decreased to 2.50 g.

10.0 g × ½ × ½ = 10.0 g × $\frac{1}{2} ^ 2$ = 2.50 g

After 3 half-lives, the amount remaining will have decreased to 1.25 g.

10.0 g × ½ × ½ × ½ = 10.0 g × $\frac{1}{2} ^ 3$ = 1.25 g

After 4 half-lives, the amount remaining will have decreased to 0.625 g.

The general formula to calculate the amount remaining after a given number $n$ of half-lives is

N = N_0 × 1/2^n = N_0/2^n

Thus, after four half-lives, the formula gives

$N = {N}_{0} / {2}^{n} = \frac{10.0 \text{ g")/2^4 = (10.0" g}}{16}$ = 0.625 g