and Matter (b) Obtain the de Broglie wavelength associated with thermal neutrons at room temperature ( ºC). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments. . An electron microscope uses electrons accelerated by a voltage of kV.
Determine the de Broglie wavelength associated with the electrons. If other factors (such as numerical aperture, etc.) are taken to be roughly the same, how does the resolving power of an electron microscope compare with that of an optical microscope which uses yellow light? . The wavelength of a probe is roughly a measure of the size of a structure that it can probe in some detail.
The quark structure of protons and neutrons appears at the minute length-scale of – m or less. This structure was first probed in early ’s using high energy electron beams produced by a linear accelerator at Stanford, USA. Guess what might have been the order of energy of these electron beams. (Rest mass energy of electron = .
MeV.) . Find the typical de Broglie wavelength associated with a He atom in helium gas at room temperature ( ºC) and atm pressure; and compare it with the mean separation between two atoms under these conditions. . Compute the typical de Broglie wavelength of an electron in a metal at ºC and compare it with the mean separation between two electrons in a metal which is given to be about × – m.
[ Note: Exercises . and . reveal that while the wave-packets associated with gaseous molecules under ordinary conditions are non-overlapping, the electron wave-packets in a metal strongly overlap with one another. This suggests that whereas molecules in an ordinary gas can be distinguished apart, electrons in a metal cannot be distintguished apart from one another.
This indistinguishibility has many fundamental implications which you will explore in more advanced Physics courses.] . Answer the following questions: (a) Quarks inside protons and neutrons are thought to carry fractional charges [(+ / ) e ; (– / ) 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 + , p = h But while the value of # is physically significant, the value of + (and therefore, the value of the phase speed +# ) has no physical significance. Why?