Answers Clearly, from (a) and (b) above, thermal neutrons are a suitable probe for diffraction experiments; so a high energy neutron beam should be first thermalised before using it for diffraction. . # = . × – m # (yellow light) = .
× – m Resolving Power (RP) is inversely proportional to wavelength. Thus, RP of an electron microscope is about times that of an optical microscope. In practice, differences in other (geometrical) factors can change this comparison somewhat. .
– – . Js h p = = . × – kg m s – Use the relativistic formula for energy: E = c p + m c = × ( . ) × – + ( .
× . ) × – × ( . ) × – , the second term (rest mass energy) being negligible. Therefore, E = .
× – J = . BeV. Thus, electron energies from the accelerator must have been of the order of a few BeV. .
Use h m k T ; m He = kg This gives # = . × – m. Mean separation r = (V/N) / = (kT/p) / For T = K, p = . × Pa, r = .
× – m. We find r >> # . . Using the same formula as in Exercise .
, # = . × – m which is much greater than the given inter-electron separation. . (a) Quarks are thought to be confined within a proton or neutron by forces which grow stronger if 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 e V = ( / ) m v or e E = m a and e B v = m v /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 molecules 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 d d dE dp ( / ) = d dp p p is physically meaningful.