Relativistic corrections become necessary when the expression for the kinetic energy becomes comparable with mc², where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron?

Question

Philoid · Accepted Answer

We know the de Broglie wavelength is given by,

where h is the Planck’s constant, m is the mass and v is the velocity

(a) When, λ =10nm

(b) When, λ =10^–1nm

(c) When, λ =10^–4nm

(d) When, λ =10^–6nm

Hence, in cases (c) and (d) velocities are greater than the speed of light and hence relativistic corrections will become important for an electron.

Relativistic corrections become necessary when the expression for the kinetic energy becomes comparable with mc2, where m is the mass of the particle. At what de Broglie wavelength will relativistic corrections become important for an electron?