Radioactive Decay and Half-life

When a substance decays, the mass of the initial isotope decreases exponentially as it is replaced by the new element. At any one instant, the mass M of isotope left is given by

M = M₀e^-λt

where λ is a constant and M₀ is the initial mass.This means that the mass drops by a constant factor in equal intervals of time.

The half-life of a radioactive isotope t_½ is the time taken for the mass of the isotope to decrease by half the initial mass.