Chemistry - Chemical Kinetics Question with Solution | TestHub

The radioactive decay follows first-order kinetics.

The decay constant $\lambda$ is given by:

$\lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{10}=0.0693{\text{ min}}^{-1}$

The time required for the substance to reduce to $20\%$ is calculated using the first-order rate equation:

$t=\frac{2.303}{\lambda }\log \left(\frac{N_0}{N_t}\right)$

Substituting $N_0=100$ and $N_t=20$:

$t=\frac{2.303}{0.0693}\log \left(\frac{100}{20}\right)$

$t=\frac{2.303}{0.0693}\log 5$

Using $\log 5=0.699$:

$t=\frac{2.303\times 0.699}{0.0693}=23.23\text{ min}$

Answer: $23.23$ minute