The de Broglie wavelength of an electron is the same as that 50 keV X-ray photon. The ratio of the energy of the photon to the kinetic energy of the electron is (the energy equivalent of electron mass is 0.5 MeV)

Options

A. `1 : 50`
B. `1 : 20`
C. `20 : 1`
D. `50 :1`

Answer

C

Explanation

Energy of photon,
`E = (hc)/(lamda) = 50 xx 10^(3) eV`
Kinetic energy of electron,
`K = (1)/(2) mv^(2) = (h^(2))/(2mlamda^(2)) [ :' v = (h)/(m lamda)]`
`:. (E)/(K) = (hc)/(lamda) xx (2m lamda^(2))/(h^(2)) = (2m.c^(2))/((hc)/(lamda)) = (2 xx 0.5 xx 10^(6))/(50 xx 10^(3)) = (20)/(1)`
i.e., `E : K = 20 : 1`