Calculate the de-Broglie wavelength of an electron acelerated from rest through a potential difference of 100 V?

Louis de Broglie’s famous equation states that Wave Nature (Wavelength), and Particle Nature, (Momentum), are linked by the following equation.

Wavelength = Planck’s Constant/Momentum

However, Momentum and Kinetic Energy could be linked to:

Momentum = sqrt2 x Mass 2 x Kinetic Energy [As K.E. = 0.5mv2, Momentum = mv]

However, let us suppose that the entire Kinetic Energy of the particle is used to overcome the Potential Different. In this case,

K.E = Energy needed by an electron to cross given potential difference

= Charge of Electronx Potential Difference

= 1.6×10(-19) Cx100 V

= 1.6×10(-17) J

Additionally, an electron’s mass is 9.1×10(-31)kg).

Required momentum = sqrt(2) x 9.1×10(-31)) x 1.6×10(-171)) kg m.s(-1)

= 5.39×10(-24)kg m s(1)

This is how you can plug this value of momentum into de Broglie’s equation.

Wavelength = Planck’s Constant/Momentum

= 6.626×10(-34)/ 5.39×10(-24) m

= 1.2293 x 10.(-10)

1.2293 A

We hope it helps!

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