<p align="right">Last Update: <font color="#4f81bd">July, 29, 2024</font></p>
## BIG IDEAS
- Half-life represents the time it takes for half of a given sample of a radioactive substance to decay.
- Follows an exponential decay model.
- A critical tool in fields like archaeology (carbon dating), medicine (radiopharmaceuticals), and nuclear physics.
### Formula
$t_{1/2} \ = \ \frac{ln(2)}{\lambda} \tag{1}$
where $\lambda$ is the decay constant.
### Decay Law
$N(t) \ = \ N_0 (\frac{1}{2}) ^{\frac{t}{t_{1/2}}} \tag{2}$
where $N_0$ is the initial quantity, $N$ is the remaining quantity, and $t$ is the time elapsed.
Rearrange this equation to isolate the $t_{1/2}$, half-life
$t_{1/2} \ = \ \frac{t \ ln(2)}{ln(\frac{N_0}{N})} \tag{3}$
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