Physics » Radioactivity and Nuclear Physics » Half-Life and Activity

# Summarizing Half-Life and Activity

## Half-Life and Activity Summary

• Half-life $${t}_{1/2}$$ is the time in which there is a 50% chance that a nucleus will decay. The number of nuclei $$N$$ as a function of time is

$$N={N}_{0}{e}^{-\mathrm{\lambda t}},$$

where $${N}_{0}$$ is the number present at $$t=0$$, and $$\lambda$$ is the decay constant, related to the half-life by

$$\lambda =\cfrac{0\text{.}\text{693}}{{t}_{1/2}}.$$

• One of the applications of radioactive decay is radioactive dating, in which the age of a material is determined by the amount of radioactive decay that occurs. The rate of decay is called the activity $$R$$:

$$R=\cfrac{\text{Δ}N}{\text{Δ}t}.$$

• The SI unit for $$R$$ is the becquerel (Bq), defined by

$$\text{1 Bq}=\text{1 decay/s.}$$

• $$R$$ is also expressed in terms of curies (Ci), where

$$1\phantom{\rule{0.25em}{0ex}}\text{Ci}=3\text{.}\text{70}×{\text{10}}^{\text{10}}\phantom{\rule{0.25em}{0ex}}\text{Bq.}$$

• The activity $$R$$ of a source is related to $$N$$ and $${t}_{1/2}$$ by

$$R=\cfrac{0\text{.}\text{693}N}{{t}_{1/2}}.$$

• Since $$N$$ has an exponential behavior as in the equation $$N={N}_{0}{e}^{-\mathrm{\lambda t}}$$, the activity also has an exponential behavior, given by

$$R={R}_{0}{e}^{-\mathrm{\lambda t}},$$

where $${R}_{0}$$ is the activity at $$t=0$$.

## Glossary

### becquerel

SI unit for rate of decay of a radioactive material

### half-life

the time in which there is a 50% chance that a nucleus will decay

an application of radioactive decay in which the age of a material is determined by the amount of radioactivity of a particular type that occurs

### decay constant

quantity that is inversely proportional to the half-life and that is used in equation for number of nuclei as a function of time

### activity

the rate of decay for radioactive nuclides

### rate of decay

the number of radioactive events per unit time

### curie

the activity of 1g of $${}^{\text{226}}\text{Ra}$$, equal to $$\text{3.70}×{\text{10}}^{\text{10}}\phantom{\rule{0.25em}{0ex}}\text{Bq}$$