A radioactive substance decays to $\frac{1}{8}$th of its initial activity in 30 days. The half life of the radioactive substance expressed in days is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10
Formula for Radioactive decay -
$A=A_0\left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}$
where,
A, Remaining activity of substance
$A_0$, Initial activity
$t$, time elapsed = 30 days
$T_{1/2}$, half-life
$\frac{A}{A_0}=\frac{1}{8}$
$⇒\frac{1}{8}=\left(\frac{1}{2}\right)^{\frac{30}{T_{1/2}}}$
$⇒3ln2=\frac{30}{T_{1/2}}ln(2)$
$⇒T_{1/2}=10days$