If m is the mass of an electron and c is the speed of light, the ratio of the wavelength of a photon of energy E to that of the electron of the same energy is

Options

A. `c sqrt((2m)/(E))`
B. `sqrt((2m)/(E))`
C. `sqrt((2m)/(c E))`
D. `sqrt((m)/(E))`

Answer

A

Explanation

Energy `, E = (h c)/(lambda_(p))`
or `lambda_(p) = (hc)/(E)`
and `Delta_(e) = (h)/(p)= (h)/(sqrt(2mE))`
`therefore (lambda_(p))/(lambda_(e)) = ((hc)/(E))/((h)/(sqrt(2mE)))`
or `(lambda_(p))/(lambda_(e)) = (csqrt(2mE))/(E) = csqrt((2m)/(E))`