Question

How much energy is imparted to an electron so that its de-Broglie wavelength reduces from 10^-10 m to 0.5 × 10^-10 m? (E =energy of electron)

Options

• 4E

• 2E

• E

• 3E

Answer 1

3E

Explanation:

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

`lambda_1/lambda_2 = sqrt("E"_2/"E"_1) => (1 xx 10^-9)/(0.5 xx 10^-9) = sqrt("E"_2/"E"_1)`

`therefore 2 = sqrt("E"_2/"E"_1)`

`therefore "E"_2/"E"_1 = 4`

`therefore "E"_2 = 4"E"_1`