Question

If $20$gm of radioactive substance due to radioactive decay reduces to $10$gm in $4$ minutes then in what time $80$gm of then what time $80$gm of the same substance will reduce to $10$ gm?

• A. $1.8$min
• B. $12$min
• C. $16$min
• D. $20$min

Answer 1

The correct option is B $12$min

$20gm$ substance reduces to $10gm$ ( became half in $4$ min so, $T_{1/2}=4min$ Again,

$\Rightarrow m=m_0{\left(\frac{1}{2}\right)}^{t/T_{1/2}}$

$10=80{\left(\frac{1}{2}\right)}^{t/4}$

$\frac{1}{8}={\left(\frac{1}{2}\right)}^{t/4}$

$\frac{1}{8}={\left(\frac{1}{2}\right)}^3={\left(\frac{1}{2}\right)}^t/4$

$\therefore t=12min$

Hence, the answer is $12min.$