De Broglie wavelength of an electron

Propagation_of_a_de_broglie_wave.svg

What is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 100 V?

Solution.

The electron accelerated through the potential difference gains kinetic energy.
Let’s write the equation of conservation of energy

eU = 0.5mv2 ,

where U – the potential difference, e – the charge of the electron 1.6*10-19 C, m – the mass of electron 9.11*10-31 kg.

Thus, the velocity will be

v = √(2eU/m) = √(2*1.6*10-19*100/9.11*10-31) ≈ 5.93*106 m/s.

De Broglie wavelength of an electron is given by the equation

λ = h/(mv) ,

where h is Planck’s constant 6.62*10-34 J*s.

Thus,

λ = 6.62*10-34 /(9.11*10-31*5.93*106) ≈ 1.2*10-10 m = 1.2 Å

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