A) Answer the following question: Quarks inside protons and neutrons are thought to carry fractional charges $[(+\frac{2}{3})e;(-\frac{1}{3})e]$.Why do they not show up in Millikan’s oil-drop experiment?

B) Answer the following question: What is so special about the combination $\frac{e}{m}$? Why do we not simply talk of 𝑒 and 𝑚 separately?

C) Answer the following question: Why should gases be insulators at ordinary pressures and start conducting at very low pressures?

D) Answer the following question: Every metal has a definite work function. Why do all photoelectrons not come out with the same energy if incident radiation is monochromatic? Why is there an energy distribution of photoelectrons?

E) Answer the following question: The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:
$E=hv),(p=\frac{h}{\lambda })$
But while the value of $\lambda$ is physically significant, the value of v (and therefore, the value of the phase speed $v\lambda )$ has no physical significance. Why?

A) Quarks inside protons and neutrons carry fractional charges. This is because nuclear force increases extremely if they are pulled apart. Therefore, fractional charges may exist in nature; observable charges are still the integral multiple of an electrical charge.

B) As we know that the relations for electric field and magnetic field are
$eV=\left(\frac{1}{2}\right)m{v}^2$
$v=\sqrt{2V\frac{e}{m}}$
And $eBv=\frac{m{v}^2}{r}$
$v=Br\frac{e}{m}$

These relations include 𝑒 (electric charge), 𝑣 (velocity), m (mass), V (potential), r (radius), and B (magnetic field).
We see that the dynamics of an electron is determined not by e and m separately, but by the ratio $\frac{e}{m}$.

C) At atmospheric pressure, the ions of gases have no chance of reaching the electrodes because of collision and recombination with other gas molecules. Hence, gases are insulators at atmospheric pressure.
At low pressures, ions have a chance of reaching their respective electrodes and constitute a current. Hence, they conduct electricity at these pressures.

D) Work function merely indicates the minimum energy required for the electron in the highest level of the conduction band to get out of the metal. Not all electrons in the metal belong to this level. They occupy a continuous band of levels. Consequently, for the same incident radiation, electrons knocked off from different levels come out with different energies.

E) The absolute value of energy of a particle is arbitrary within the additive constant. However, the momentum of an electron is physically significant.
Since frequency (v) associated with the electron is related to the energy $(E=hv)$, the frequency also does not have a physical significance. The wavelength is associated with momentum $(p=\frac{h}{\lambda })$, it has direct physical significance.
Therefore, the product $v\lambda$ (phase speed) also does not have physical significance but group speed $=\frac{dE}{dp}=\frac{p}{m}$ has significance physically.