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NEET 2026
Exam
NEET
Year
2026
Subject
Physics
Chapter
Chapter

NEET 2026 · Physics · Chapter

A neutron of mass m and a photon have the same de Broglie...

A neutron of mass mm and a photon have the same de Broglie wavelength λ\lambda. What is the ratio of the energy of the photon to the kinetic energy of the neutron? (Here cc is the speed of light and hh is Planck's constant)

Options

  1. Ah2mcλ\dfrac{h}{2mc\lambda}
  2. B2mcλh\dfrac{2mc\lambda}{h}
  3. Cmcλh\dfrac{mc\lambda}{h}
  4. Dhc2mλ\dfrac{hc}{2m\lambda}

Correct answer

B. 2mcλh\dfrac{2mc\lambda}{h}

Step-by-step solution

The energy of the photon is given by Ep=hcλE_p = \dfrac{hc}{\lambda}

The momentum of the neutron is p=hλp = \dfrac{h}{\lambda}

The kinetic energy of the neutron is En=p22m=h22mλ2E_n = \dfrac{p^2}{2m} = \dfrac{h^2}{2m\lambda^2}

The ratio of the energy of the photon to the kinetic energy of the neutron is:

EpEn=hcλh22mλ2=2mcλh\dfrac{E_p}{E_n} = \dfrac{\dfrac{hc}{\lambda}}{\dfrac{h^2}{2m\lambda^2}} = \dfrac{2mc\lambda}{h}

Answer: 2mcλh\dfrac{2mc\lambda}{h}
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