Question

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

Answer 1

Correct Answer - B
`K_("particle") = (1)/(2) mv^(2)` also `lambda = (h)/(mv)`
`rArr K_(particle) = (1)/(2) ((h)/(lambda v)).v^(2) = (vh)/(2 lambda)` ….(i)
`K_("photon") = (hc)/(lambda)` ….(ii)
`:. (K_("particle"))/(K_("photon")) = (v)/( 2c) = ( 2.25 xx 10^(8))/( 2 xx 3 xx 10^(8)) = (3)/(8)`