Nuclear Radiation: Exponential Law of Decay

Nuclear Radiation: Exponential Law of Decay

Exponential Law of Decay: Overview

  • The Exponential Law of Decay is a fundamental concept in understanding nuclear radiation.
  • It explains how the number of unstable nuclei in a sample decreases over time.
  • Radioactive decay is a random process but averages out to an observable pattern over time.

Meaning of Radioactive Decay

  • Radioactive decay refers to the process whereby an unstable nucleus loses energy by emitting radiation.
  • Most common types of radiation are alpha, beta and gamma radiation.
  • Each type of nucleus in a radioactive sample has a particular probability per unit time of decaying, regardless of how long it has already existed. This is referred to as the decay constant (λ).

Formula for Exponential Decay

  • The equation for radioactive decay is given as N = N₀e^-λt, where:
    • N represents the number of radioactive nuclei that haven’t decayed after time t.
    • N₀ is the original number of radioactive nuclei.
    • t is the elapsed time.
    • λ is the decay constant.

Half-Life

  • The half-life is another important concept related to exponential decay.
  • It is the time taken for half the nuclei in a radioactive material to decay.
  • The half-life can be calculated using the decay constant with the formula tₕₐₗf = 0.693 / λ.

Characteristics of Exponential Decay

  • The graph of number of undecayed nuclei against time is a decreasing exponential curve, since the rate of decay decreases as the number of remaining nuclei decreases.
  • The time taken for the remaining undecayed nuclei to halve is always the same, regardless of the initial amount.

Applicability of Exponential Decay

  • It’s essential to understand the exponential decay law’s applicability in nuclear medicine, carbon dating, predicting the behaviour of nuclear waste and in power industry.

Key Constants & Values

  • The decay constant, λ, varies for each radioactive isotope. It is a measure of how fast a substance undergoes radioactive decay.
  • The larger the decay constant, the more quickly the substance in question will decay.
  • The time, t, measures how long the decay process has been occurring.