Question

According to de-Broglie hypothesis, the ratio of wavelength of an electron and that of photon having same energy 'E' is (m = mass of electron, c = velocity of light) ____________.

Options

• `"c" xx sqrt((2"m")/"E")`

• `1/"c" xx sqrt((2"m")/"E")`

• `1/"c" xx sqrt("E"/(2"m"))`

• `"c" xx sqrt(("E")/(2"m"))`

Answer 1

According to de-Broglie hypothesis, the ratio of wavelength of an electron and that of photon having same energy 'E' is `"c" xx sqrt((2"m")/"E")`.

Explanation:

`"E" = "hc"/lambda     lambda_"p" = "hc"/"E"`

Wavelength of electron

`lambda_"e" = "h"/"mv" = "h"/"p"`

`1/2 "mv"^2 = "E"`

`therefore "p"^2/(2"m") = "E"`

`lambda_"e" = "h"/sqrt(2"mE")`

`therefore lambda_"p"/lambda_"e" "hc"/"E" xx sqrt(2"mE")/"h"`

` = "c" sqrt((2"m")/"E")`