# How does radioactive decay relate to half-life?

Feb 10, 2014

The half-life of a radioactive nucleus is the time required for one-half of the material to decay into a more stable substance.

For example, Sr-90 has a half-life of about 25 years. It will have an intensity of 100% when new. After one half-life (25 years), its intensity will be cut to 50% of the original. After two half-lives
(50 years), it will have an intensity of 25% of the original. After ten half-lives (250 years), less than one-thousandth of the original activity will remain.

The equation for the graph is

N_t = N_0e^(-λt)

where

${N}_{0}$ is the initial quantity of the radioactive nuclei
${N}_{t}$ is the quantity that still remains after a time t,
t_½ is the half-life of the decaying nucleus,
λ is the decay constant for the nucleus and is calculated by the formula

λ = ln2/t_½

If the half-life is 25 years, the decay constant is

λ = ln2/t_½ = 0.693/(25 yr) = =0.028 yr⁻¹.

That is, 2.8 % of the material decays every year.