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!