Editing Specific activity (section)

===Relationship between ''λ'' and T<sub>1/2</sub>===

Radioactivity is expressed as the decay rate of a particular radionuclide with decay constant ''λ'' and the number of atoms ''N'':

: <math>-\frac{dN}{dt} = \lambda N.</math>

The integral solution is described by [[exponential decay]]:

: <math>N = N_0 e^{-\lambda t},</math>

where ''N''<sub>0</sub> is the initial quantity of atoms at time ''t'' = 0.

[[Half-life]] '''T<sub>1/2</sub>''' is defined as the length of time for half of a given quantity of radioactive atoms to undergo radioactive decay:

: <math>\frac{N_0}{2} = N_0 e^{-\lambda T_{1/2}}.</math>

Taking the natural logarithm of both sides, the half-life is given by

: <math>T_{1/2} = \frac{\ln 2}{\lambda}.</math>

Conversely, the decay constant ''λ'' can be derived from the half-life ''T''<sub>1/2</sub> as

: <math>\lambda = \frac{\ln 2}{T_{1/2}}.</math>