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.