study guides for every class

that actually explain what's on your next test

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.

congrats on reading the definition of decay equation. now let's actually learn it.

ok, let's learn stuff

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$^{-1}$).

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.

"Decay equation" also found in:

© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.