Question

Consider a neutral metal with a work function of 2.0 eV ( 1 eV = 1.602 10^-19 J). The metal absorbs a

photon of wavelength 200 nm.

a) Could an electron be ejected? If so, what would the speed of the electron be?

b) What is the speed of an electron with a wavelength of 10 nm?

c)If we measure the momentum of the electron from part b) to within 1% uncertainty ( p=p = 1% ), what is the minimum uncertainty in the position of the electron

Answer 1

a)      Work function of metal, W = 2.0 eV

Wavelength of photon, ? = 200 nm.

The energy of radiation must be equal to or greater than the work function of metal to show photoelectric effect (to eject the electron).

We need to convert wavelength of radiation into energy expressed in eV units.

E_radiation = hc/? = 6.626 x 10^-34 J s x 3.0 x 10⁸ m s^-1/200 x 10^-9 m = 9.939 x 10^-19 J

Now convert this value into eV.

We know that:

1 J = 6.24 × 10¹⁸ eV

Therefore:

9.939 x 10^-19 J = 9.939 x 10^-19 x 6.24 × 10¹⁸ eV = 6.2 eV

Therefore the electron will eject from the metal.