To determine the half life of a radioactive element a student plots a graph of $ln\left|\frac{dN\left(t\right)}{dt}\right|$ versus $t$. Here $\frac{dN\left(t\right)}{dt}$ is the rate of radio active decay at time $t$. If the number of radio active nuclei of this element decreases by a factor of $p$ after $4.16years$, the value $p$ is:

Q. To determine the half life of a radioactive element, student plots a graph of $ln|dN\left(t\right)/dt|$ versus $t$. Here $dN\left(t\right)/dt$ is the rate of radioactive decay at time $t.$ If the number of radioactive nuclei of this element decreases by a factor of $p$ after $4.16$ years, the value of $p$ is ......

Q. To determine the half life of a radioactive element, student plots a graph of $\ln \left|\frac{dN\left(t\right)}{dt}\right|$ versus $t$. Here $dN\left(t\right)/dt$ is the rate of radioactive decay at time $t$. If the number of radioactive nuclei of this element decreases by a factor of $p$ after $4.16\text{years}$, the value of $p$ is ____. (Round off the nearest integer) $(e^{4.16}=64.07)$

Q. To determine the half life of a radioactive element, a student plots a graph of \(\ln \left | \dfrac{dN(t)}{dt} \right |~\text {versus t. Here}\dfrac {dN(t)}{dt}\) is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by
a factor of p after 4.16 years, the value of p is

Q. Nuclei of a radio-active element $A$ are being product at a constant rate $\alpha$. The element has a decay constant $\lambda$. At time $t=0$ there are $N_0$ nuclei of the element present.
(a) Calculate the number of nuclei $A$ as a function of time $t$.
(b) If $\alpha =2N_0\lambda$, calculate the number of nuclei of $A$ after one half-life of $A$, and also the limiting value of $N$ as $t\to \infty$.

Q. Nuclei of a radioactive element is produced at constant rate $\alpha$ and they decay with decay constant $\lambda$. At $t=0$, the number of nuclei is 0. The number of active nuclei at time $t$ is