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

Options

A. 40
B. 4
C. 2
D. 80

Answer

A

Explanation

Let m be the mass of particle.
`(mv^2)/(2)=(hc)/(lamda_("photon"))`, where symbols have their usual meanings.
`(p^2)/(2m)=(hc)/(lamda_("photon"))`
and `p=(h)/(lamda_("photon")implies(h^2)/(2mlamda_("particle")^2)=(hc)/(lamda_("photon"))`
`implies(lamda_("photon"))/(lamda_("particle"))=(2mc)/(h)xxlamda_("particl"e)=(2mc)/(h)xx(h)/(mv)`
`=(2c)/(0.05c)=40`