Question

An electron of mass m and a photon have same energy E. The ratio of de-Broglie wavelengths associated with them is ( c being velocity of light) ______.

Options

• `"c"(2"mE")^(1/2)`

• `1/"c"((2"m")/("E"))^(1/2)`

• `1/"c"(("E")/(2"m"))^(1/2)`

• `(("E")/(2"m"))^(1/2)`

Answer 1

An electron of mass m and a photon have same energy E. The ratio of de-Broglie wavelengths associated with them is ( c being velocity of light) `1/"c"(("E")/(2"m"))^(1/2)`.

Explanation:

For electron, `lambda_"e" = "h"/sqrt(2"ME")_"e"` and for photon,

`lambda_"p"="hc"/"E"_"P"`

∴ `lambda_"e"/lambda_"p" "h"/sqrt(2"ME")_"e" xx "E"_"p"/"hc"`

`lambda_"e"/lambda_"p" = 1/"c" ["E"/(2"m")]^(1/2)   ....( ∵ "E"_"p" = "E"_"e")`