Question

What is half-life?

Answer 1

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 × `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 × `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 = (10.0" g")/2^4 = (10.0" g")/16` = 0.625 g