The binding energy of the emitted electron is 5.48 x 10⁻²⁰ kJ/mol.
The given parameters;
- wavelength of the photon, λ = 0.954 nm = 0.954 x 10⁻⁹ m.
- kinetic energy of emitted photon, K.E = 959 eV
The binding energy of the electron is calculated as follows;
from Einstein's mass defect equation
[tex]\Delta E = \Delta mc^2\\\\[/tex]
Also, from Einstein's photo-electric equation;
E = φ + K.E
where;
φ is the binding energy of the electron on the metal surface
The energy of one mole of electron the emitted is calculated as;
[tex]E = hf = h\frac{c}{\lambda} \\\\E = \frac{(6.626 \times 10^{-34}) \times (3\times 10^8)}{0.954 \times 10^{-9}} \\\\E = 2.084 \times 10^{-16} \ J[/tex]
The kinetic energy of the emitted electron in Joules is calculated as;
K.E = 959 x 1.602 x 10⁻¹⁹ J
K.E = 1.536 x 10⁻¹⁶ J
The binding energy of the electron is calculated as;
φ = E - K.E
φ = 2.084 x 10⁻¹⁶ J - 1.536 x 10⁻¹⁶ J
φ = 5.48 x 10⁻¹⁷ J
φ = 5.48 x 10⁻²⁰ kJ/mol
Thus, the binding energy of the emitted electron is 5.48 x 10⁻²⁰ kJ/mol
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