An electron with speed $v$ and a photon with speed c have the same de-Broglie wavelength. If the kinetic…

An electron with speed $v$ and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are Ee and Pe and that of photon are Eph and Pph respectively. Which of the following is correct?
  1. EeEph=2cv
  2. EeEph=v2c
  3. pepph=2cv
  4. pepph=v2c

Solution

We have, λp=hpp and λe=hpe

Given here, λe=λp, then pp=pe

Ratio of their energy is EphEe=hcλPpe22m=2mcpe=2mcmv=2cv

Asked in: JEE Main 2022 (26 Jun Shift 1)

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