Q.Answer the following questions:

Each part probes a different foundational idea in this chapter and the physics that surrounds it — quark confinement, why e/m (not e or m alone) governs charged-particle dynamics, gas discharge physics, the electron-energy distribution behind the photoelectric effect, and why only the de Broglie wavelength (not frequency) of a matter wave is physically meaningful. …

1. Why don't fractional quark charges show up in Millikan's experiment? Quarks are never found as free, isolated particles — a fundamental property of the strong nuclear force called quark confinement means quarks always exist bound together inside composite particles (like protons and neutrons), and no experiment has ever isolated a single free quark. Millikan's oil-drop experiment measures the charge sitting on a free, isolated oil droplet, which can only ever pick up whole, isolated charges (electrons or ions) — never an isolated fractional quark charge, since none exists in a free state to be picked up. Hence oil drops always show charge in integer multiples of $e$, never fractions of it.
2. Why is e/m special, rather than e and m separately? The quantity e/m (specific charge) is what directly determines how a charged particle moves in electric and magnetic fields — for example, in the equation of motion $m\vec{a} = q(\vec{E}+\vec{v}\times\vec{B})$, dividing through by $m$ shows the particle's acceleration depends only on the ratio $q/m$, not on $q$ and $m$ individually. Experiments that observe a charged particle's deflection or circular path in known fields (like J.J. Thomson's original cathode-ray experiment) can therefore measure e/m directly from the observed trajectory, without needing to know $e$ or $m$ separately. Determining $e$ and $m$ individually requires a further, independent experiment (such as Millikan's oil-drop experiment, which measures $e$ alone) — e/m is simply the combination that appears naturally in, and is measurable from, the dynamics.
3. Why are gases insulators at ordinary pressure but conduct at low pressure? At ordinary (high) pressure, gas molecules are packed closely together, so the mean free path (average distance a charged particle can travel between collisions) is very short. Any free ion or electron produced by a stray ionising event loses its energy in frequent collisions before it can gain enough energy to ionise another molecule, and recombines quickly — so no sustained current flows, and the gas behaves as an insulator. At very low pressure, molecules are spaced far apart, so the mean free path is much longer; a charged particle accelerated by an applied field can now travel far enough between collisions to build up enough kinetic energy to ionise the next molecule it hits, releasing more free electrons which repeat the process — this cascading "avalanche" of ionisation allows a sustained current to flow, so the low-pressure gas conducts (the operating principle of a gas discharge tube).
4. Why is there an energy distribution among photoelectrons, not one fixed energy? …