Question

Half life of ${}^{24}Na$ is $14.8$ hours. In what period of time will a sample of this element lose $90$% of its activity?

Answer 1

$t1/2=14.8$hr

$A_0=100$ (initial amount)

$A=10$ (left over amount)

$t=?$

$t1/2=\frac{0.693}{K}$ (for first order)

$K=0.0468{hr}^{-1}$

$t=\frac{2.303}{K}log\frac{Ao}{A}$

$t=\frac{2.303}{0.0468}\times log\left(\frac{100}{10}\right)$

$t=49.90$ hr