Question

If the kinetic energy of a free electron double, its de-Broglie wavelength changes by the factor ______.

Options

• 1/2

• `1//sqrt2`

• `sqrt2`

• 2

Answer 1

If the kinetic energy of a free electron doubles, its de-Broglie wavelength changes by the factor `underline(1//sqrt2)`.

Explanation:

Let λ be de-Broglie wavelength of electron, when its kinetic energy is E. Then,

`lambda = "h"/sqrt(2"mE")`

Let λ′ be de-Broglie wavelength of electron, when its kinetic energy is doubled. Then,

`lambda' = "h"/sqrt("2m" xx "2E")`

`= 1/sqrt2 xx "h"/sqrt"2mE" = 1/sqrt2 lambda`