Decay equation

Definition

The decay equation models the decrease in the quantity of a radioactive substance over time. It typically takes the form $N(t) = N_0 e^{-\lambda t}$, where $N(t)$ is the quantity at time $t$, $N_0$ is the initial quantity, and $\lambda$ is the decay constant.

5 Must Know Facts For Your Next Test

1. The decay constant ($\lambda$) represents the probability of decay per unit time.
2. Half-life ($t_{1/2}$) is related to the decay constant by the formula $t_{1/2} = \frac{\ln(2)}{\lambda}$.
3. The decay equation follows an exponential law, meaning that as time increases, the quantity of the substance decreases exponentially.
4. In nuclear physics, this equation helps in predicting how long it will take for a given amount of a radioactive isotope to decay to a certain level.
5. The units for the decay constant ($\lambda$) are inverse time (e.g., s$^{-1}$ or year$^{-1}$).

Related terms

Half-life:

The time required for half of a sample of a radioactive substance to disintegrate.

Decay Constant:

A parameter representing the probability per unit time that a given nucleus will decay.

Radioactive Isotope: An isotope whose nucleus undergoes spontaneous disintegration, emitting radiation.