Consider the de Broglie wavelength of an electron and a proton. Which wavelength is smaller if the two particles have (a) the same speed (b) the same momentum (c) the same energy?

De Broglie wavelength is given by

Where =Planck’s constant; =mass of the particle; =momentum and =velocity of the particle

Mass of electron kg; mass of proton kg

(a) Electron and Proton both have same speed

The wavelength of proton is smaller than that of electron.

(b) Electron and Proton both have same momentum

The wavelength of proton is equal to that of electron.

(c) Electron and Proton have same energy

De Broglie Wavelength is also given by

Where =Energy of the particle

The wavelength of proton is smaller than that of electron.