How to find binding energy of an electron?
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The incoming photon will transmit its energy to the electron.
If this energy is high enough to overcome the binding energy of the electron, the electron will be emitted from the surface with a kinetic energy KE.
Now, the difference between the energy of the incoming photon and the kinetic energy of the emitted electron will be equal to the binding energy.
Ebinding=Ephoton−KE
The energy of the photon is directly proportional to its frequency, ν
E=h⋅ν
Frequency is inversely proportional to wavelength, λ. This means that you can write
ν⋅λ=c
and therefore
E=h⋅cλ , where
h - Planck's constant, equal to 6.626⋅10−34J s
c - the speed of light in a vacuum, usually given as 3⋅108m s−1
Use this equation to find the energy of the incoming photon - do not forget to convert the wavelength from nanometers to meters!
E=6.626⋅10−34Js⋅3⋅108ms−10.990⋅10−9m
E=2.01⋅10−16J
Next, focus on converting the kinetic energy of the electron from electron-volts to joules
953eV⋅1.602⋅10−19J1eV=1.53⋅10−16J
This means that the binding energy for one electron will be
Ebinding=2.01⋅10−16J−1.53⋅10−16J
Ebinding=4.80⋅10−17J
To get the binding energy for one mole of electrons, use the Avogadro's number, which tells you that one mole contains exactly 6.022⋅1023"things" in it.
In this case, one mole of electrons will contain 6.022⋅1023 electrons.
4.80⋅10−17Je−⋅Avogadro's number6.022⋅1023e−1 mole e−=2.89⋅107J mol−1
Finally, convert this from joules per mole to kilojoules per mole
2.89⋅107Jmol⋅1 kJ103J=2.89⋅104kJ mol−1
If this energy is high enough to overcome the binding energy of the electron, the electron will be emitted from the surface with a kinetic energy KE.
Now, the difference between the energy of the incoming photon and the kinetic energy of the emitted electron will be equal to the binding energy.
Ebinding=Ephoton−KE
The energy of the photon is directly proportional to its frequency, ν
E=h⋅ν
Frequency is inversely proportional to wavelength, λ. This means that you can write
ν⋅λ=c
and therefore
E=h⋅cλ , where
h - Planck's constant, equal to 6.626⋅10−34J s
c - the speed of light in a vacuum, usually given as 3⋅108m s−1
Use this equation to find the energy of the incoming photon - do not forget to convert the wavelength from nanometers to meters!
E=6.626⋅10−34Js⋅3⋅108ms−10.990⋅10−9m
E=2.01⋅10−16J
Next, focus on converting the kinetic energy of the electron from electron-volts to joules
953eV⋅1.602⋅10−19J1eV=1.53⋅10−16J
This means that the binding energy for one electron will be
Ebinding=2.01⋅10−16J−1.53⋅10−16J
Ebinding=4.80⋅10−17J
To get the binding energy for one mole of electrons, use the Avogadro's number, which tells you that one mole contains exactly 6.022⋅1023"things" in it.
In this case, one mole of electrons will contain 6.022⋅1023 electrons.
4.80⋅10−17Je−⋅Avogadro's number6.022⋅1023e−1 mole e−=2.89⋅107J mol−1
Finally, convert this from joules per mole to kilojoules per mole
2.89⋅107Jmol⋅1 kJ103J=2.89⋅104kJ mol−1
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The energy of the photon is
E_photon = h∙c / λ
= h∙c / λ
= 4.1357×10-15eVs ∙ 3.0×10+8m/s / 0.947×10-9m.
= 1310eV
The binding energy of a single electron equals the difference of the photon energy and the energy of the emitted electron
E_bind = E_photon - E_kin
= 1310eV - 985eV
= 325eV
= 5.207×10-17J
So thew binding energy of mole of electron is
E_bind = 5.207×10-17J ∙ 6.022×10-17mol⁻¹
= 31357J/mol
= 31.357kJ/mol
E_photon = h∙c / λ
= h∙c / λ
= 4.1357×10-15eVs ∙ 3.0×10+8m/s / 0.947×10-9m.
= 1310eV
The binding energy of a single electron equals the difference of the photon energy and the energy of the emitted electron
E_bind = E_photon - E_kin
= 1310eV - 985eV
= 325eV
= 5.207×10-17J
So thew binding energy of mole of electron is
E_bind = 5.207×10-17J ∙ 6.022×10-17mol⁻¹
= 31357J/mol
= 31.357kJ/mol
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