Question

The activity of a radioactive substance falls to $87.5$% of the initial value of $5$ years. What is the half-life of the element? Calculate the time in which the activity will fall by $87.5$%.

Answer 1

Case-I $Ao=100$

$A=87.5$

$t=5$ year

$5=\frac{2.303\times t1/2}{0.693}\times log\left(\frac{100}{87.5}\right)$

$t1/2=25.9$

$=26$ years

Case II $Ao=100$

$A=100-87.5=12.5$

$t=\frac{2.303\times 26}{0.693}\times log\left(\frac{100}{12.5}\right)$

$t=78.0$ years