Radioactive Decay

Radioactive decay is a spontaneous process in which unstable nuclei lose energy by emitting radiation. This process follows an exponential decay law.

The Decay Law

The number of undecayed nuclei at time \( t \) is given by:

\[ N(t) = N_0 e^{-\lambda t} \]

• \( N_0 \): initial number of nuclei
• \( N(t) \): number of nuclei remaining after time \( t \)
• \( \lambda \): decay constant (probability of decay per unit time)

Half-life (\( t_{1/2} \))

The half-life is the time required for half the radioactive nuclei to decay. It is related to the decay constant by:

\[ t_{1/2} = \frac{\ln 2}{\lambda} \]

Key Characteristics

• Radioactive decay is random and spontaneous
• It does not depend on external factors like temperature or pressure
• The decay curve is exponential — never reaches zero

Application Tips

• Use \( N = N_0 \cdot \left( \frac{1}{2} \right)^{t/t_{1/2}} \) for problems involving discrete half-lives
• If asked for mass or activity instead of number of atoms, the same formula applies

Example 1:Half-life Calculation Example 2: Using the Decay Formula

Written by Thenura Dilruk