Question

Answer the following questions:

(a) Quarks inside protons and neutrons are thought to carry fractional charges $\left[\right(+2/3)e;(1/3\left)e\right]$. 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 n $\lambda )$ has no physical significance. Why?

Answer 1

(a) Quarks are considered to be confined within a proton or neutron by forces that grow stronger as one tries to pull them apart. It, therefore, seems that though fractional charges may exist in nature, observable charges are still integral multiples of e.

(b) Both the basic relations, $eV=\left(1/2\right)m{v}^2$ or $eE=ma$ and $eBv=m{v}^2/r$, for electric and magnetic fields, respectively, show that the dynamics of electrons is determined not by e, and m separately but by the combination e/m .

(c) At low pressures, ions have a chance to reach their respective electrodes and constitute a current. At ordinary pressures, ions have no chance to do so because of collisions with gas molecule and recombination.

(d) Work function merely indicates the minimum energy required for the electron in the highest level of the conduction band to get out of the metal. Not all electrons in the metal belong to this level. They occupy a continuous band of levels. Consequently, for the same incident radiation, electrons knocked off from different levels come out with different energies.

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