Two very small slits are positioned a distance of 1.50 nm from each other. A beam of electrons passes through both slits and create an interference pattern on a screen that is positioned 10 cm away from the slits. (a) What energy in electron-Volts (eV)s must each electron have in order for the location between the m = 1 maximum and m = 2 maximum of the electron diffraction pattern to be 0.50 mm? Ignore relativity. (b) What energy in eV must each electron have if you do not ignore relativity? Note: it is the momentum that determines the de Broglie wavelength and thus you need to relate this momentum to the relativistic kinetic energy of the electron using E? = (mc²)² + (pc)? and E = K + mc². (c) Continuing with the relativistic correction, by what factor will a photon's energy be greater than the energy of an electron that creates this same diffraction pattern? (d) Continuing with the relativistic correction, what is the Lorentz factor of each neutron in a beam of neutrons that creates the same diffraction pattern as the
Two very small slits are positioned a distance of 1.50 nm from each other. A beam of electrons passes through both slits and create an interference pattern on a screen that is positioned 10 cm away from the slits. (a) What energy in electron-Volts (eV)s must each electron have in order for the location between the m = 1 maximum and m = 2 maximum of the electron diffraction pattern to be 0.50 mm? Ignore relativity. (b) What energy in eV must each electron have if you do not ignore relativity? Note: it is the momentum that determines the de Broglie wavelength and thus you need to relate this momentum to the relativistic kinetic energy of the electron using E? = (mc²)² + (pc)? and E = K + mc². (c) Continuing with the relativistic correction, by what factor will a photon's energy be greater than the energy of an electron that creates this same diffraction pattern? (d) Continuing with the relativistic correction, what is the Lorentz factor of each neutron in a beam of neutrons that creates the same diffraction pattern as the
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Transcribed Image Text:Two very small slits are positioned a distance of 1.50 nm from each other. A beam of
electrons passes through both slits and create an interference pattern on a screen that
is positioned 10 cm away from the slits.
(a) What energy in electron-Volts (eV)s must each electron have in order for the
location between the m = 1 maximum and m = 2 maximum of the electron
diffraction pattern to be 0.50 mm? Ignore relativity.
(b) What energy in eV must each electron have if you do not ignore relativity? Note: it is
the momentum that determines the de Broglie wavelength and thus you need to relate
this momentum to the relativistic kinetic energy of the electron using E? = (mc²)² +
(pc)? and E = K + mc².
(c) Continuing with the relativistic correction, by what factor will a photon's energy be
greater than the energy of an electron that creates this same diffraction pattern?
(d) Continuing with the relativistic correction, what is the Lorentz factor of each
neutron in a beam of neutrons that creates the same diffraction pattern as the
electrons?
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