On the basis of de Broglie hypothesis, obtain the relation for wavelength of an electron accelerated by a p.d of 'V' volt.
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L = h/mv
where L is wavelength
So,
mv = h/L
m^2 v^2 = h^2 / L^2
1/2 mv^2 = h^2 / 2mL^2
Here, kinetic energy is nothing but the work done by the electron to be accelerated in the electric field out of the potential.
So,
Work done = h^2/2mL^2
Voltage*Charge = h^2 / 2mL^2
V*e = h^2 / 2mL^2
L^2 = h^2 / 2meV
Thus, this is the final relationship.
Hence, we see
Wavelength is inversely proportional to √Voltage.
where L is wavelength
So,
mv = h/L
m^2 v^2 = h^2 / L^2
1/2 mv^2 = h^2 / 2mL^2
Here, kinetic energy is nothing but the work done by the electron to be accelerated in the electric field out of the potential.
So,
Work done = h^2/2mL^2
Voltage*Charge = h^2 / 2mL^2
V*e = h^2 / 2mL^2
L^2 = h^2 / 2meV
Thus, this is the final relationship.
Hence, we see
Wavelength is inversely proportional to √Voltage.
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