An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is :

Solution

Physics sir · 4 steps

Same wavelength means same momentum, so write both energies in terms of p and divide.

1. Equal momentum. The de Broglie relation λ = h/p holds for both particles. Equal wavelengths therefore give equal momenta, and we call the common value p.
2. Electron energy. For the electron, p = mv, so Kₑ = 1/2mv² = 1/2(mv)v = pv/2.
3. Photon energy. A photon has no rest mass, and its energy and momentum are linked by E = pc. All of this energy is kinetic.

   Kₑ/Eₚₕₒₜₒₙ = (pv/2)/pc = v/2c

4. So. The ratio of the electron's kinetic energy to the photon's energy is v/2c, which is option (c).

The idea to keep. Equal de Broglie wavelengths always mean equal momenta. Then use K = pv/2 for a material particle and E = pc for a photon.

Answer from the NTA final answer key. Solution by PrepWiser.