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Sagot :
Potential difference required in an electron microscope to give an electron wavelength of 4. 5 nm will be 0.063 V.
The difference in potential between two points that represents the work involved or the energy released in the transfer of a unit quantity of electricity from one point to the other is called potential difference.
The wavelength of an electron is calculated for a given energy (accelerating voltage) by using the de Broglie relation between the momentum p and the wavelength λ of an electron
lambda = 4.5 nm = 4.5 * [tex]10^{-9}[/tex] m
h = [tex]6.626 * 10^{-34}[/tex] J s
e = 1.6 * [tex]10^{-19}[/tex] C
m = 9.1 * [tex]10^{-31}[/tex] kg
Energy = eV
lambda = h / [tex]\sqrt{2mE}[/tex] = h / [tex]\sqrt{2m(eV)}[/tex]
[tex](lambda)^{2}[/tex] = [tex]h^{2}[/tex] / (2m (eV))
V = [tex]h^{2}[/tex] / (2 m e [tex](lambda)^{2}[/tex] )
V = [tex](6.626 * 10^{-34} )^{2}[/tex] / 2 * 9.1 * [tex]10^{-31}[/tex] * 1.6 * [tex]10^{-19}[/tex] * [tex](4.9 * 10^{-9}) ^{2}[/tex]
V = 0.063 V
To learn more about wavelength of an electron here
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