Question

Which of the following is not correct?

• A. $t_{1/2}=\frac{0.693}{k}$
• B. $N=N_0{e}^{-kt}$
• C. $\frac{1}{N}={\frac{1}{N}}_0=\ln k{t}_{1/2}$
• 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''
$\frac{-d{N}_t}{dt}=\lambda N$
where, $\lambda =$ radioactive constant
$N_t=N_0{e}^{-\lambda t}$
$\ln \frac{N}{N_0}=-kt$
$\ln \frac{N_0}{N}=kt$
$\therefore \frac{1}{N}-\frac{1}{N_0}=\ln k{t}_{1/2}$ 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.
$t_{1/2}=\frac{0.693}{\lambda }$