Modes of Radioactive Decay

Radioactive Decay

• The intensity of radiation produced by a substance is directly proportional to the rate of decay and the amount of the substance.
• Radioactive decay follows first-order kinetics.
• There are three principal modes of decay: alpha, beta, and gamma decays.

Characteristics of Radioactive Decay

• The probability of decay is a constant, characteristic of all radioactive decay.
• The rate of decay is constant in time and proportional to the number of nuclei.

Decay Constant and Equation

• The decay constant (λ) is the constant of proportionality.
• The differential equation that describes the situation is: 𝑑𝑁(𝑡) = -𝜆𝑁(𝑡)
• The equation for the number of nuclei at time t is: 𝑁(𝑡) = 𝑁(0)𝑒 −𝜆𝑡

Half-Life

• An isotope's half-life allows us to determine how long a sample of a useful isotope will be available, and how long a sample of an undesirable or dangerous isotope must be stored before it decays to a low-enough radiation level.
• The half-life is a measure of the time it takes for the material to decay to half of its initial amount.

Example Calculations

• At t=0, 𝑁(0) = 𝑁(0) = 10
• At t=1, 𝑁(1) = 8 = 10 ∗ 𝑒 −𝜆∗1
• The decay constant (λ) can be calculated from the equation: 𝑙𝑛 (0.8) = −𝜆