The energy of a photon is equal to the kinetic energy of a
proton. The energy of the photon is E. Let `lambda_1`be the de-Broglie wavelength of the
proton and `lambda_2` be the wavelength of the photon. The ratio `(lambda_1)/(lambda_2)` is proportional to
(a)`E^0` (b) `E^(1//2)` (c ) `E^(-1)` (d)`E^(-2)`

Options

A. `E^(0)`
B. `E^(1//2)`
C. `E^(-1)`
D. `E^(-2)`

Answer

b

Explanation

For photon, `E=1/2mv^(2)=1/2mv^(2)=1/2 (m^(2)v^(2))/m`
or `mv=sqrt(2mE)`
`lambda_(1)=h/(hv)=h/(sqrt(2mE))`
For photon, `E=hv_(2)=(hc)/(lambda_(2))` or `lambda_(2)=(hc)/E`
`:. (lambda_(1))/(lambda_(2))=(h//sqrt(2mE))/(hc//E)=1/csqrt(E/(2m)) prop E^(1//2)`