A 5 g sample of a radioactive element takes 102 days to reduce into 3 g. Calculate the half-life and identify the element.

• Radioactive decay takes place when an unstable nucleus becomes stable. The instability arises due to a mismatch between the number of neutrons and protons. Only a few configurations of neutrons and protons are stable.

• This decay will be exponential in nature and is given by,

$\boxed{\mathbf{N}\mathbf{=}{\mathbf{N}}_{\mathbf{0}}{\mathbf{e}}^{\mathbf{-}\mathbf{0}\mathbf{.693}\left(\frac{t}{t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\right)}}$

Here N₀ is the original number of radioactive nuclei present, t is the time, and t_1/2 is the half-life of the radioactive sample. This is known as the exponential law of radioactive decay.