The de - Broglie wavelength of a particle moving with a velocity `2.25 xx 10^(8) m//s` is equal to the wavelength of photon. The ratio of kinetic energy of the particle to the energy of the photon is (velocity of light is `3 xx 10^(8) m//s`

Options

A. `1//8`
B. `3//8`
C. `5//8`
D. `7//8`

Answer

b

Explanation

Let `m_(1)`=mass of particle and `m_(2)` =equivalent mass of photon moving with velocity of light `c=3xx10^(8)ms^(-1)` having the same de-broglie wavelength as that of particle. Then
`m_(1)v=m_(2)c` or `(m_(1))/(m_(2))=c/v=(3xx10^(8))/(2.25xx10^(8))=3/2.25`
`(E_(1))/(E_(2))=(1/2 m_(1)v^(2))/(m_(2)c^(2))=1/2xx((m_(1))/(m_(2)))xx(v/c)^(2)`
`=1/2xx2/2.25xx(2.25/3)^(2)=3/8`