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

The absolute value of energy E (but not momentum p) of any particle is arbitrary to within an additive constant. Hence, while `lambda` is physically significant, absolute value of ν of a matter wave of an electron has no direct physical meaning. The phase speed `vlambda` is likewise not physically significant. The group speed given by
`(dv)/(d(1//lambda))=(dE)/(dp)=(d)/(dp)((p^(2))/(2m))=(p)/(m)`
is physically meaningful.