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Q.

The kinetic energy of a particle is equal to the energy of a photon. The particle moves at 5% of the speed of light. The ratio of the photon wavelength to the de Broglie wavelength of the particle is [No need to use relativistic formula for the particle.]

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a

40

b

4

c

2

d

80

answer is A.

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Detailed Solution

Let m be the mass of particle.mv22=hcλphoton , where symbols have their usual meanings. p22m=hcλphoton and p=hλparticle ⇒h22mλparticle 2=hcλphoton ⇒λphoton λparticle =2mch×λparticle =2mch×hmv =2c0.05c=40

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The kinetic energy of a particle is equal to the energy of a photon. The particle moves at 5% of the speed of light. The ratio of the photon wavelength to the de Broglie wavelength of the particle is [No need to use relativistic formula for the particle.]