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 $t$. Where, $\frac{dN\left(t\right)}{dt}$ 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 $4.16 \mathrm{yr}$, the value of $p$ is

Assertion $\left(\mathrm{A}\right)$- When ultraviolet light is incident on a photocell, its stopping potential is $V_0$ and the maximum kinetic energy of the photoelectrons is $K_{\max }$. When the ultraviolet light is replaced by $X$-rays, both $V_0$ and $K_{\max }$ increase.

Reason $\left(\mathrm{R}\right)$- Photoelectrons are emitted with speeds ranging from zero to a maximum value, because of the range of frequencies present in the incident light.

The above is a plot of binding energy per nucleon $E_{\mathrm{b}}$ against the nuclear mass $M$. $A$, $B$, $C$, $D$, $E$, and $F$ corresponds to different nuclei. Consider four reactions

$\left(\mathrm{I}\right) A+B\to C+\epsilon$
$\left(\mathrm{II}\right) C\to A+B+\epsilon$
$\left(\mathrm{III}\right) D+E\to F+\epsilon$
$\left(\mathrm{IV}\right) F\to D+E+\epsilon$

,where $\epsilon$ is the energy released. In which reaction is $\epsilon$ positive?