Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [a]}$$
In Figure 38.3, $I$ versus $\Delta V$;
The graph is mostly horizontal for $\Delta V\gt 0$ because all the current becomes independent of $\Delta V$ when $\Delta V\gt 0$. That's because the increase in voltage cannot change the number of electrons arriving per second and hence the current remains constant. Recalling that $I=\dfrac{dq}{dt}=\dfrac{Ne}{t}$ where $N$ is the nu,ber of electrons.
$$\color{blue}{\bf [b]}$$
It depends on the distance of the electron away from the surface of the metal plate. Some electrons are just on the surface and ejected at the minimum energy needed of $E_0$ while the deepest electrons need more than $E_0$ to escape from the plate. This means that there is a range of escape energies for the electrons which means the ejected electrons must have a range of kinetic energies.
$$\color{blue}{\bf [c]}$$
When an electron leaves the cathode with some energy $K$, and the anode has a potential $V$, the electron's energy changes as it moves toward the anode. If $V$ is positive, the electron gains energy, but if $V$ is negative, it loses energy.
The electron’s energy can’t go below zero, so if $V$ is very negative, it can push the electron back to the cathode before it even reaches the anode.
The emitted electrons have a maximum energy $K_{max}$. So when $eV=|K_{max}|$, then even the most energetic electrons (those with $K_{max}$) are stopped and turned back.
This point is called the stopping voltage where $V=V_{\rm stop}$, and it tells us the maximum energy of the electrons since it’s the point where even the fastest ones can't reach the anode.
In other words, when the stopping potential is applied, even the fastest (most energetic) electrons are just unable to reach the anode which means that all photoelectrons are stopped. Thus, the stopping potential is a direct measure of the maximum kinetic energy of the electrons, since the energy required to overcome the stopping potential exactly equals their kinetic energy.
