The maximum kinetic energy is 0.91 eV
What is Work Function of a Metal ?
A Work Function of a Metal is the minimum energy required to liberate an electron from a metal surface. From the formula;
hF = hf + E
- hF = energy for liberation or illumination
- hf = work function = 2.8 eV
Given that a Barium has a work function of 2.48eV. What is the maximum kinetic energy ?
Convert eV to Joule by multiplying by 1.6 x [tex]10^{-19}[/tex]
hf = 2.48 x 1.6 x [tex]10^{-19}[/tex]
hf = 3.968 x [tex]10^{-19}[/tex] J
If the metal is illuminated by UV light of wavelength 365nm,
E = hF = hc/λ
Where
- C = speed of light = 3 x [tex]10^{8}[/tex] m/s
- h = Planck constant = 6.6 x [tex]10^{-34}[/tex] Js
- λ = wavelength = 365 x [tex]10^{-9}[/tex] m
Substitute all the parameters
hF = (6.6 x [tex]10^{-34}[/tex] x 3 x [tex]10^{8}[/tex]) / 365 x [tex]10^{-9}[/tex]
hF = 1.98 x [tex]10^{-25}[/tex] / 365 x [tex]10^{-9}[/tex]
hF = 5.42 x [tex]10^{-19}[/tex] Joule
The maximum kinetic energy will be
hF = hf + E
Make E the subject of formula
E = hF - hf
E = 5.42 x [tex]10^{-19}[/tex] - 3.968 x [tex]10^{-19}[/tex]
E = 1.452 x [tex]10^{-19}[/tex] J
Convert Joule back to eV by dividing by 1.6 x [tex]10^{-19}[/tex]
E = 1.452 x [tex]10^{-19}[/tex] / 1.6 x [tex]10^{-19}[/tex]
E = 0.9075 eV
Therefore, the maximum kinetic energy is 0.91 eV approximately
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