A proton has kinetic energy E = 100 ke V which is equal to that of a photon. The wavelength of photon is `lambda_(2)` and that of proton is `lambda_(1)`. The ratio `lambda_(2)//lambda_(1)` is proportional to

Options

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

Answer

B

Explanation

For photon: `E=hv`
or `E=(hv)/(lamda)`
`implieslamda_2=(hc)/(E)`
For proton: `E=(1)/(2)m_pv_p^2`
`E=(1)/(2)(m_p^2v_p^2)/(m)impliesP=sqrt(2mE)`
`P=(h)/(lamda_1)`
`implieslamda_1=(h)/(p)=(h)/(sqrt(2mE))`
`(h_2)/(lamda_1)=(hc)/(Exx(h)/(sqrt(2mE)))propE^((-1)/(2))`