Question

The half life of a radioactive substance is $T _{0}$. At $t=0$, the number of active nuclei are $N_{0}$. Select the correct alternative.

• A. The number of nuclci decayed in time internal $0-t$ is $N_{0} e^{-\lambda t}$
• B. The number of nuclei decayed in time interval $0-t$ is $N_{0}\left(1-e^{-\lambda t}\right)$
• C. The probability that a radioactive nuclei does not decay in interval $0-t$ is $e^{-\lambda t}$
• D. The probability that a radioactive nuclei does not decay in interval $1-e^{-\lambda t}$

Answer 1

Answer: (B), (C)

Using radioactive decay equation $N=N_{0} e^{-\lambda t}$ we have
At $t=0$ number of nuclei are $N_{1}=N_{0}$ and at time $t$ number of nuclei left are $N_{2}=N_{0} e^{-\lambda t}$
Thus number of nuclei decayed in time $t$ are $\left(N_{1}-N_{2}\right)=$ $N_{0}\left(1-e^{-\lambda t}\right)$
Probability that a radioactive nuclei does not decay in $t=0$ to
$t: \frac{N}{N_{0}}=\frac{N_{0} e^{-\lambda t}}{N_{0}}=e^{-\lambda t}$