The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25% of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:
Options

Question

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25% of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:

G1 Physics · Accepted Answer

For photon, λₚ = hc/Eₚ For electron, λₑ = h/(mₑvₑ) Also, Kₑ = ½mₑvₑ² So, mₑvₑ = 2Kₑ/vₑ Therefore, λₑ = hvₑ/(2Kₑ) Given, vₑ = 0.25c Hence, λₑ = h(0.25c)/(2Kₑ) = hc/(8Kₑ) Since λₚ = λₑ, hc/Eₚ = hc/(8Kₑ) Therefore, Kₑ/Eₚ = 1/8