A single electron ion M(2-1)+ with atomic number Z<84 emits a photon during an unknown electronic transition from some initial state n; to some final state nf. The photon then strikes an osmium surface, which has a work function = 5.93 eV and causes an electron to be emitted. Many such photons create a beam of electrons (all with the same kinetic energy) that is directed at a single crystal nickel sample at normal incidence. The electrons are scattered from the crystal and it is observed that they do so with only two (2) non-zero diffraction angles (i.e., 2 different values of 0). From the DeBroglie-Bragg relation it is determined that the diffraction corresponds to a lattice spacing of a = 352.4 pm.

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a = lattice spacing
(a) What is the largest possible angular momentum of the electron when it is at its
after the electronic transition? (Hint: first use the Bragg diffraction condition to get the range of
wavelengths of the emitted electrons. Then use the DeBroglie relationship to find the range of
the electron kinetic energies. Finally, apply this information to Bohr model to find the constraint
on (inequality containing) Z, n; and ni.)
hal state nf
(b) What is the greatest possible energy of the electron when it is at its final state nț after the
electronic transition?
Transcribed Image Text:D A G F E В E В a = lattice spacing (a) What is the largest possible angular momentum of the electron when it is at its after the electronic transition? (Hint: first use the Bragg diffraction condition to get the range of wavelengths of the emitted electrons. Then use the DeBroglie relationship to find the range of the electron kinetic energies. Finally, apply this information to Bohr model to find the constraint on (inequality containing) Z, n; and ni.) hal state nf (b) What is the greatest possible energy of the electron when it is at its final state nț after the electronic transition?
A single electron ion MZ-1)+ with atomic number Z<84 emits a photon during an unknown
electronic transition from some initial state n; to some final state nf. The photon then strikes an
osmium surface, which has a work function O = 5.93 eV and causes an electron to be emitted.
Many such photons create a beam of electrons (all with the same kinetic energy) that is directed
at a single crystal nickel sample at normal incidence. The electrons are scattered from the
crystal and it is observed that they do so with only two (2) non-zero diffraction angles (i.e., 2
different values of 0). From the DeBroglie-Bragg relation it is determined that the diffraction
corresponds to a lattice spacing of a = 352.4 pm.
Transcribed Image Text:A single electron ion MZ-1)+ with atomic number Z<84 emits a photon during an unknown electronic transition from some initial state n; to some final state nf. The photon then strikes an osmium surface, which has a work function O = 5.93 eV and causes an electron to be emitted. Many such photons create a beam of electrons (all with the same kinetic energy) that is directed at a single crystal nickel sample at normal incidence. The electrons are scattered from the crystal and it is observed that they do so with only two (2) non-zero diffraction angles (i.e., 2 different values of 0). From the DeBroglie-Bragg relation it is determined that the diffraction corresponds to a lattice spacing of a = 352.4 pm.
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