Question

An electron and a proton have the same de-broglie wavelength. Prove that the energy of electron is greater.

Answer 1

According to De-Broglie, the wavelength of the particle in terms of kinetic energy is,



Here,  is wavelength, h is Planck’s constant, m is mass of the particle and KE is the kinetic energy of the particle.

From the above formula, De-Broglie wavelength is inversely proportional to the square root of mass of the particle and kinetic energy of the particle.

The mass of the electron is small compared to the mass of the proton. Basing on the mass, the De-Broglie wavelength of the electron is large compared to proton.