Question

The half life period of a first order radioactive decay of an element is $5$ days. The time (in days) taken for $8g$ of this element to decay to $1g$ is:

• A. $15$
• B. $25$
• C. $40$
• D. $10$

Answer 1

The correct option is A $15$

The formula for the rate constant for the first order reaction is as follows:

$k=\frac{0.693}{t_{\left(1/2\right)}}$

$k=\frac{0.693}{5}=0.1386da{y}^{-1}$

Now, the formula for the time ;

$t=\frac{2.303}{k}\times log\frac{8}{1}$

$t=15days$