Question

Which of the following is not correct?

• A. $ t_{1/2}=\frac{0.693}{k} $
• B. $ N=N_{0}e^{-kt} $
• C. $ \frac{1}{N}=\frac{1}{N}_{0}=\ln \,kt_{1/2} $
• D. None of the above

Answer 1

Answer: (C)

According to the law of radioactive decay ''The quantity of a radioactive element which disappears in unit time (rate of disintegration) is directly proportional to the amount present''
$\frac{-d N_{t}}{d t}=\lambda N$
where, $\lambda=$ radioactive constant
$N_{t}=N_{0} e^{-\lambda t}$
$\ln \frac{N}{N_{0}}=-k t$
$\ln \frac{N_{0}}{N}=k t$
$\therefore \frac{1}{N}-\frac{1}{N_{0}}=\ln k \,t_{1 / 2}$ is not correct.
Half-life period is defined as the time required by a given amount of the element to decay to onehalf of its initial value.
$t_{1 / 2}=\frac{0.693}{\lambda}$