Answer the following questions:
(a) Quarks inside protons and neutrons are thought to carryfractional 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 ν, p = `lambda/h`
But while the value of `lambda` is physically significant, the value of ν (and therefore, the value of the phase speed ν `lambda`) has no physical significance. Why?

Explanation

(a) The quarks having fractional charges are thought to be confined within a proton and a neutron. These quarks are bounded by forces. These forces become stronger when the quarks are tried to be pulled apart That is why, the quarks always remain together. It is due to this reason that through fractional charges does exist in nature but the observable charges are always intergral multiple of charges of electron.
(b) The motion of electron in the electric and magnetic field is related with the basic equations
`eV=1/2mv^(2) and Bev=(mv^(2))/r`
All these equation involve e and m together, i.e., there is no equation in which e or m occuring alone. As a result of it, we study `e//m` of electron and do not talk of e and m separately far an electron.
(c) At ordinary pressures a few positive ions and electrons produced by the ionisatation of the gas molecules by energetic rays (like X-rays, `gamma`-ray, cosmic rays etc. coming from outer space and entering the earth's atmosphere) are not able to reach their respectively electrods, even at high voltages, due to their frequent collisions with gas molecules and recombinations. That is why the gasses at ordinary pressures are insulators. At low pressures, the density of the gas decreases, the mean free path of the gas molecules becomes larages. Now under the effect of external high voltage, the ions aquire sufficient energy before they collide with molecules causing further ionisation. Due to it, the number of ions in the gas increases and it becomes a conductor.
(d) By work function of a metal , we mean the minimum energy required for the electron in the highest level of conduction band to get out of the metal. Since all the electrons in the metal do not belong to that level but they occupy a continous band of levels, therefore, for the given incident radiation, electrons knocked off from different levels come out with different energies.
(e) De-Broglie wavelength associated with the moving particle is `lambda=h/p or p=h/lambda`
Energy of the wave E is `E=hv=(hc)/lambda` , Energy of moving particle `=1/2 (p^(2))/m = 1/2 ((h//lambda)^(2))/m= 1/2 (h^(2))/(lambda^(2)m)`
For the relations of E and p, we note that ` lambda` is physically sufficient but v has no direct physical significance.