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JIPMER 2017
Exam
JIPMER
Year
2017
Subject
Physics
Chapter
Dual Nature of Matter

JIPMER 2017 · Physics · Dual Nature of Matter

The wavelength λ of a photon and the de-Broglie wavelength of an...

The wavelength λ\lambda of a photon and the de-Broglie wavelength of an electron have the same value. Find the ratio of energy of photon to the kinetic energy of electron in terms of mass mm, speed of light cc and planck constant.

Options

  1. Aλmch\frac{\lambda m c}{h}
  2. Bhmcλ\frac{h m c}{\lambda}
  3. C2hmcλ\frac{2 h m c}{\lambda}
  4. D2λmch\frac{2 \lambda m c}{h}

Correct answer

D. 2λmch\frac{2 \lambda m c}{h}

Step-by-step solution

The de-Broglie wavelength h=hmv⇒v=hmλ...(i)h=\frac{h}{m v} \Rightarrow v=\frac{h}{m \lambda}...(i) Ep=hcλE_p=\frac{h c}{\lambda} (since λ\lambda is same )...(ii))...(ii) Kinetic energy of photon =EpEe=hc/λ121mu2=2hcλmv2=\frac{E_p}{E_e}=\frac{h c / \lambda}{\frac{1}{2} 1 m u^2}=\frac{2 h c}{\lambda m v^2} Substituting value of vv from Eq. (i), we get EpEe=2hcλm(hmλ)2=2λmch\frac{E_p}{E_e}=\frac{2 h c}{\lambda_m\left(\frac{h}{m \lambda}\right)^2}=\frac{2 \lambda m c}{h}
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