A half-life is the time needed for a amount of radioactive material to fall to half the amount as measured in the beginning of the time period. It describes the property of radioactive decay or the quantity which exists after exponential decay.
The half-life describes the quantity which has undergone exponential decay. The opposite to half-life is doubling time. The exponential decay half-life process can be described by three equations as seen below:
N(t)= N_0 (〖1/2)〗^(t⁄t_(1⁄2) ) (1)
N(t)= N_0 e^((-t)⁄τ) (2)
N(t)= N_0 e^(-λt) (3)
N0 is the initial quantity of the substance that will decay
N(t) is the quantity that still remains after time t
T1/2 is the half-life of the decaying quantity
Τ is the mean lifetime of the decaying quantity
Λ is the decay constant of the decaying quantity.
For processes with two or more exponential-decay processes simultaneously the equation is as followed
1/T_(1⁄2) = 1/t_1 + 1/t_2 +⋯