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Chapter 4: Q17E (page 134)
Determine the Compton wavelength of the electron, defined to be the wavelength it would have if its momentum were.
Compton Wavelength of the electron
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An electron in an atom can "jump down" from a higher energy level to a lower one, then to a lower one still. The energy the atom thus loses at each jump goes to a photon. Typically, an electron might occupy a level for a nanosecond. What uncertainty in the electron's energy does this imply?
Verify the claim made in a section 4.4 that if all results of a repeated experiment are equal, the standard deviation, equation (4.13) Will be0.
A free particle is represented by the plane wave functionwhere SIunits are understood. What are the particle鈥檚 momentum, Kinetic energy, and mass? (Note: In nonrelativistic quantum mechanics, we ignore mass/internal energy, so the frequency is related to kinetic energy alone.)
Aman walks at, known to within an uncertainty (unrealistically small) of.
(a) Compare the minimum uncertainty in his position to his actual physical dimension in his direction of motion ,from front to back.
(b) Is it sensible to apply the uncertainty principle to the man?
A brag diffraction experiment is conducted using a beam of electrons accelerated through apotential difference. (a) If the spacing between atomic planes in the crystal is, at what angles with respect to the planes will diffraction maximum be observed? (b) If a beam of-rays products diffraction maxima at the same angles as the electron beam, what is the-ray photon energy?
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