Question

A non-relativistic electron with mass m accelerates through a potential difference V that is in volts.

a. What is the relationship between the kinetic energy and the momentum of the electron? (Hint: Use your classical mechanics knowledge)

b. Use the above relation and the conservation of energy to derive the de Broglie wavelength ? = √ ℎ2 2??? .

c. Use the above expression to find the de Broglie wavelength of a proton that has been accelerated from rest through a potential 50.0 V.

Answer 1

a)

When the electron is accelerated through a potential difference of , electron gains kinetic energy

Kinetic energy of electron is

Momentum of electron

b)

Debroglie wavelength of electron is

c)

For proton, mass , charge , Potential applied

Debroglie wavelength of proton is