Answer the following questions:
$(a)$ Quarks inside protons and neutrons are thought to carry fractional charges $[(+2/3)e, (-1/3)e]$. Why do they not show up in Millikan's oil-drop experiment?
$(b)$ What is so special about the combination $e/m$? Why do we not simply talk of $e$ and $m$ separately?
$(c)$ Why should gases be insulators at ordinary pressures and start conducting at very low pressures?
$(d)$ 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?
$(e)$ The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:
$E = h\nu, p = \frac{h}{\lambda}$
But while the value of $\lambda$ is physically significant,the value of $\nu$ (and therefore,the value of the phase speed $\nu\lambda$) has no physical significance. Why?

(N/A) Quarks carry fractional charges,but they are confined within protons and neutrons by strong nuclear forces. They cannot be isolated,so Millikan's experiment,which measures the charge of free particles,only detects integral multiples of $e$.
$(b)$ In electromagnetic fields,the motion of an electron is governed by equations involving $e$ and $m$ only as the ratio $e/m$ (specific charge). For example,$v = \sqrt{2V(e/m)}$ and $v = Br(e/m)$. Thus,the dynamics are determined by this ratio.
$(c)$ At ordinary pressures,gas molecules are dense,leading to frequent collisions and recombination of ions,preventing them from reaching electrodes. At low pressures,the mean free path increases,allowing ions to reach electrodes and conduct electricity.
$(d)$ The work function is the minimum energy to remove an electron from the surface. Electrons inside the metal occupy different energy levels. When a photon hits,an electron may lose energy through collisions before escaping,resulting in a distribution of kinetic energies.
$(e)$ The absolute energy of a particle is arbitrary up to an additive constant,making the frequency $\nu$ (linked to absolute energy) physically non-unique. However,the wavelength $\lambda$ is related to momentum,which is measurable. Consequently,the phase speed $\nu\lambda$ is not physically significant,whereas the group speed $v_g = d\nu/d(1/\lambda) = p/m$ represents the particle's velocity.