The energy of a photon is equal to the K.E. of a proton. The energy of a photon is E. If `lamda_(1)` and `lamda_(2)` are the de broglie wavelengths of proton and photon, then `(lamda_(1))/(lamda_(2))` is proportional to :

Options

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

Answer

B

Explanation

For photon `E_(ph)=(hc)/(lambda_(2)), lambda_(2)=(hc)/(E_(ph))`
For photon `E_(p)=1//2 mv^(2)=((mv)^(2))/(2m)=(p^(2))/(2m)`
`rArr p= sqrt(2mE_(p))`
`:.` for proton
`lambda_(1)=(h)/(p)=(h)/(sqrt(2mE_(p)))`
But `E_(ph)=E_(p)=E`
`:. (lambda_(1))/(lambda_(2))-(h)/(sqrt(2mE))xx(E)/(hc)= (sqrt(E))/(sqrt(2)C)`
`:. (lambda_(1))/(lambda_(2)) prop sqrt(3)`