Question

A radioactive substance has a half life of four months, Three fourth of the substance will decay in

• A. three months
• B. four months
• C. eight months
• D. twelve months

Answer 1

Answer: (C)

eight months

Substance left undecayed, $N_0-\frac{3}{4}{N}_0=\frac{1}{4}{N}_0$
$\frac{N}{N_0}=\frac{1}{4}={\left(\frac{1}{2}\right)}^n$

$\therefore$ Number of atoms left undecided, $n=2$ i.e, in two half lives
$\therefore$ $t=nT=$$2\times 4=8$ months