Question

The half-life of a radioactive material is $24.1$ days, How long will a sample take to decay $90\%$ of it?
$(lo{g}_{e}2=0.6931)$

Answer 1

Suppose Initial amount is $N_0$ then final amount $N$ will be $\frac{100-90}{100}{N}_0=N_0/10$

Now using following relation with given data in eqaution-1 , $N=N_0{e}^{-\lambda t}$

we get $e^{\lambda t}=10$ so $\lambda t=lo{g}_{e}10=2.3$

So time , $t=2.3/\lambda =\frac{2.3}{0.6931/t_{1/2}}=3.318\times 24.1=79.96days$ nearly $80days$