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A proton has kinetic energy E = 100 keV...

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

A

`E^2`

B

`E^((-1)/(2))`

C

`E^-1`

D

`E^((1)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
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))`
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