Decay equation
from class:
College Physics I – Introduction
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.
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5 Must Know Facts For Your Next Test
- The decay constant ($\lambda$) represents the probability of decay per unit time.
- Half-life ($t_{1/2}$) is related to the decay constant by the formula $t_{1/2} = \frac{\ln(2)}{\lambda}$.
- The decay equation follows an exponential law, meaning that as time increases, the quantity of the substance decreases exponentially.
- 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.
- The units for the decay constant ($\lambda$) are inverse time (e.g., s$^{-1}$ or year$^{-1}$).
Review Questions
- What does the decay constant ($\lambda$) represent in the context of nuclear decay?
- How is half-life ($t_{1/2}$) related to the decay constant?
- Explain why radioactive substances follow an exponential decay pattern.
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