Q.Half life 67Ga is 78 h. How long will it take to decay 12% of sample of Ga?
(Ans. 14.44)

The half-life, $t_{1/2}$, of a radioelement is the time needed for a given number of its nuclei to decay to exactly half their initial value. Substituting $N = N_0/2$ at $t=t_{1/2}$ into the decay-constant expression gives the simple, reciprocal relationship $t_{1/2} = \frac{0.693}{\lambda}$ (equivalently $\lambda = \frac{0.693}{t_{1/2}}$), where 0.693 is $\ln 2$. A short half-life means a large decay constant (fast decay); a long half-life means a small decay constant (slow decay). Every radioisotope has its own fixed, characteristic half-life, and together with the exponential decay law this relationship is the standard tool for solving decay problems: finding an unknown half-life from an observed fraction of sample remaining after a known time, finding a decay constant from a known half-life, or finding how long it takes for a given fraction of a sample to decay.