# The Binding Energy of Electrons?

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An X-ray photon of wavelength 0.954 nm strikes a surface. The emitted electron has a kinetic energy of 935 eV.

What is the binding energy of the electron in kJ/mol?

[KE =1/2 mv^2; 1 electron volt (eV) = 1.602 x 10^- 19 J]

• The Binding Energy of Electrons? -

Energy of photon:
E = hc/λ
h = Planck’s constant = 6.626•10⁻³⁴ J•s = 4.14•10⁻¹⁵ eV•s
c = speed of light = 3•10⁸ m/s
λ = wavelength = 0.954 nm = 0.954•10⁻⁹m

E = 4.14•10⁻¹⁵•3•10⁸ / 0.954•10⁻⁹ =
=1302 eV

Binding energy is the difference between the energy of the photon and the kinetic energy of the electron:
E(b)= E(ph) – E(e) = 1302 - 935 = 367 eV
1 eV = 1.6•10⁻¹⁹J
367 eV = 5.87•10⁻¹⁷ J
The answer above is per electron, so for a mole of electrons, you multiply by Avogadro's number, 6.022•10²³ moles⁻¹.
5.87•10⁻¹⁷•6.022•10²³=3.536•10⁷J/mol=3.536•10⁴ kJ/mol

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