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. 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 $ln\left|\frac{dN\left(t\right)}{dt}\right|$ 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. Nuclei of radioactive element A are produced at rate '$t^2$' at any time t. The element A has decay constant $\lambda$. Let N be the number of nuclei of element A at any time t. At time $t=t_0,\frac{dN}{dt}$ is minimum. N is :

Q. The rate at which a particular decay process occurs in a radioactive sample, is proportional to the number of radioactive nuclei present. If N is the number of radioactive nuclei present at some instant, the rate of change of N is $\frac{dN}{dt}=-\lambda N$.

The number of nuclei of B will first increase then after a maximum value, it will decreases, if