Question

A photon and an electron (mass m) have the same energy E. The ratio `(λ_"photon"//λ_"electron")` of their de Broglie wavelengths is ______. (c is the speed of light)

Options

• `sqrt(E/(2m))`

• `csqrt(2mE)`

• `csqrt((2m)/E)`

• `1/c sqrt(E/(2m))`

Answer 1

A photon and an electron (mass m) have the same energy E. The ratio `(λ_"photon"//λ_"electron")` of their de Broglie wavelengths is `bbunderline(csqrt((2m)/E))`.

Explanation:

For photon 

E = `(hc)/(λ_(ph))`

`λ_(ph) = (hc)/E`  ...(i)

For electron

`λ_e = h/sqrt(2mE)`   ...(ii)

Solving the equation. (i) and (ii)

`λ_(ph)/λ_e = ((hc)/E)/(h/sqrt(2mE))`

= `(hc)/E xx sqrt(2mE)/h`

= `csqrt(2mE)/E`

= `csqrt((2m)/E)`