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) Quarks, having fractional charges, I thought to be confined within a proton or neutron. They are bound together by strong force and these forces will grow stronger if one tries to pull them apart. Therefore, it seems that thought fractional charges may exist in nature, observable are still integer multiples `(pm"ne")` of charges on an electron ( e)
(b) Both the basic relations , (i) motion of charge in an electric field given by
`eV=1/2mv^2" or "eE = ma ` and
(ii) motion of charge in magnetic field given by
`eBv=(mv^2)/r`
show that dynamics of electrons is determined not by e and m separately but the combination e/m.
(c) At low pressure condition , the ions have change to reach their respective electrodes and constitution electric current. As a result , the number of ions available in the gas increases and it becomes conducting . At ordinary pressure , molecules of gas suffer collisions with each other. Ions and electrodes formed are not able to reach the respective electrodes because of collisions with gas molecules and recombination . So , the gasses are insulators at ordinary pressure.
(d) Work function of a metal is the minimum energy required for the electron in the highest level of the conduction band to escape the metal .However ,all the electrons in the metal do not belong to this level . They occupy a continuous band of levels. Therefore , for the same incident radiation , electrons emitted from different levels come out with different energies.
(e) The absolute energy E ( but not momentum P) of any practical is arbitrary within the additive constant . Therefore wavelength ..is physically significant, but the absolute value of frequency (v) of a matter wave of an electron has no direct physical meaning. Therefore , the product of ( phase speed) is not physically significant.