<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 $t_{1/2} \ = \ \frac{t \ ln(2)}{ln(\frac{N_0}{N})} \tag{3}$ --- Return [[Home|Home]] | [[Nuclear Physics]] | [[The Nucleus]] | [[Shell Model of the Nucleus]] | [[Modes of Decay]] | [[Half-Life]] | [[Fission]] | [[Fusion]]