1.

A photon and a proton have the same de-Broglie wavelength lamda. Prove that the energy of the photon is (2mlamdac//h) times the kinetic energy of the proton.

Answer»

Solution :We KNOW that, energy ofa photon of WAVELENGTH `lamda," "E_("photon")=hv=(hc)/(lamda)`. . (i)
and KINETIC energy of a proton is `K_("proton")=(1)/(2)mv^(2)`
If de-Broglie wavelength of proton be `lamda`, then
`lamda=(h)/(mv) or v=(h)/(mlamda)`
`therefore K_("proton")=(1)/(2)m((h)/(mlamda))^(2)=(h^(2))/(2mlamda^(2))` . . (ii)
Dividing (i) by (ii), we have
`(E_("photon"))/(K_("proton"))=(hc//lamda)/(h^(2)//2mlamda^(2))=(hc)/(lamda)XX(2mlamda^(2))/(h^(2))=(2mlamdac)/(h)`
or `E_("photon")=(2mlamdac)/(h)*K_("proton")`.


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