Question

A photon with a wavelength of 1.5 x 10^–8 m is emitted from an ultraviolet source into a vacuum.

(a) Calculate the energy of the photon.

(b) Calculate the de Broglie wavelength of an electron with kinetic energy equal to the energy of the photon.

(c) Describe an experiment that illustrates the wave properties of this electron.

Answer 1

(a) E = hc / λ … E = 1240 / 15 nm … E = 82.7 eV *1.6x10^–19J/eV = 1.33x10^–17 J

(b) K = ½ mv2 … 1.33x10^–17 = ½ (9.11x10^–31) v² … v = 5.4x10⁶ m/s

p = h / λ … mv = h / λ … (9.11x10^–31)(5.4x10⁶) = 6.63x10^–34 / λ … λ = 1.35x10^–10 m

(c) A beam of electrons shot through a double slit produces a double slit diffraction pattern with bands of maximums and minimums. This demonstrates interference which is a wave property. Davisson–Germer is also an experiment showing the wave nature of electrons.

Davisson–Germer experiment

(i)

(ii) Electrons were reflected from the crystal, with the angle of reflection equal to the angle of incidence. The fraction of electrons reflected was unusually large for certain values of θ. The same phenomenon has earlier been observed in connection with scattering of x–rays and explained as an interference effect.

(iii) It was concluded that electrons have wave properties, with their wavelength inversely proportional to their linear momentum, and that the mathematics of waves can be used to explain the behavior of what had been though to be “particles”.