The energy of the incoming photon, Eotal, is conserved in photoelectron spectroscopy. Therefore, the energy of the incoming photon is equal to the , plus the , so The energy of the incoming photon can also be expressed as , and the kinetic energy of the outgoing electron can be expressed as . The energy required to eject the electron corresponds to the . Substituting these expressions into the original expression for Ewtal produces the desired relationship between the speed of the ejected electron and the frequency of the incoming radiation,

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Chapter6: The Periodic Table And Atomic Structure
Section: Chapter Questions
Problem 6.103PAE: 6.103 Atomic absorption spectroscopy is based on the atomic spectra of the elements being studied....
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In photoelectron spectroscopy (PES), ultraviolet radiation is directed at an atom or a molecule. Electrons are ejected from the
valence shell and their kinetic energies are measured. Because the energy of the incoming ultraviolet photon is known and the
kinetic energy of the outgoing electron is measured, the ionization energy, I, can be deduced from the fact that the total energy
is conserved.
The speed of the ejected electron, v, and the frequency of the incoming radiation, v, are related by the equation
hv = I + m,u?
where h is Planck's constant and m, is the mass of an electron. Show that this relationship is true by completing the statement.
The energy of the incoming photon, Eotal, is conserved in photoelectron spectroscopy. Therefore, the energy
of the
incoming photon is equal to the
plus the
, so
The energy of the incoming photon can also be expressed as
and the kinetic energy of the
outgoing electron can be expressed as
. The energy required to eject the electron corresponds
to the
. Substituting these expressions into the original expression for E1otal produces the
desired relationship between the speed of the ejected electron and the frequency of the incoming radiation,
Answer Bank
Egjecticn = mu?
energy to eject the electron, Eejection
Eotal = hv
Exinetic =I
Exinetic = m,u?
E1otal
kinetic energy of the outgoing electron, Exinetic
Eotal = Eejection + Exinetic
hv = I+ +m,u²
jonization energy, I
Transcribed Image Text:In photoelectron spectroscopy (PES), ultraviolet radiation is directed at an atom or a molecule. Electrons are ejected from the valence shell and their kinetic energies are measured. Because the energy of the incoming ultraviolet photon is known and the kinetic energy of the outgoing electron is measured, the ionization energy, I, can be deduced from the fact that the total energy is conserved. The speed of the ejected electron, v, and the frequency of the incoming radiation, v, are related by the equation hv = I + m,u? where h is Planck's constant and m, is the mass of an electron. Show that this relationship is true by completing the statement. The energy of the incoming photon, Eotal, is conserved in photoelectron spectroscopy. Therefore, the energy of the incoming photon is equal to the plus the , so The energy of the incoming photon can also be expressed as and the kinetic energy of the outgoing electron can be expressed as . The energy required to eject the electron corresponds to the . Substituting these expressions into the original expression for E1otal produces the desired relationship between the speed of the ejected electron and the frequency of the incoming radiation, Answer Bank Egjecticn = mu? energy to eject the electron, Eejection Eotal = hv Exinetic =I Exinetic = m,u? E1otal kinetic energy of the outgoing electron, Exinetic Eotal = Eejection + Exinetic hv = I+ +m,u² jonization energy, I
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