Wave Particle Duality Advanced Higher Mechanics Topic 9 By the Fantastic Four Introduction Wave-Particle duality shows: – Light can act like a wave and like a particle. – Other particles can act as waves Main experiment for showing light as particles is the photoelectric effect. The Photoelectric Effect Cathode and anode in a vacuum. Quartz window to illuminate the cathode using an ultraviolet light. Sensitive ammeter shows photocurrent Potentiometer provides stopping potential to reduce photocurrent to zero. The Photoelectric Effect cont… Energy of photoelectrons depends on the frequency of the light. Below the threshold frequency, no electrons are emitted Hence, light cannot be considered as waves in this case but as a stream of particles, called photons (1905 Einstein’s quantum theory of light) Energy E of a photon: E = hf Where f = frequency of beam of light h = Planck’s constant (6.6310^34 Js) This can also be written as E = hc (v=f ) The Photoelectric Effect cont… When a photon is absorbed by the cathode, its energy is used in exciting an electron. Photoelectron is emitted when the energy is sufficient for an electron to escape from an atom Conservation of energy relationship for the photoelectric effect: hf = hf + ½ mv² hf is the energy of incident photon hf is the work function (min. energy required to produce photoelectron) ½ mv² is the kinetic energy of photoelectron Compton Scattering E=hf Compton Scattering Conservation of linear momentum Wave-Particle Duality of particles We know light can behave as particles. The equation = h/ρ links a property of waves (wavelength) with a property of particles (momentum). In 1924, Louis de Broglie suggested particles have a wavelength. Using the above equation, we can work out the ‘de Broglie’ wavelength of particles. In most cases, this wavelength is VERY small. Example Find the de broglie wavelength of an electron travelling at 4 x 105 ms-1. – The momentum of the electron is ρe = meve = 9.11 x 10-31 x 4 x 105 = 3.64 x 10-25 kgms-1 – The de Broglie wavelength is therefore: e = h / ρe = 6.63 x 10-34 = 1.82 x 10-9 m 3.64 x 10-25 – If the velocity is above about 0.1c, then relativistic calculations are needed to be done. This is not needed for this course. People like Jannik can also use this to work out the wavelength of a bowel of Shreddies. Wave Properties Two properties of waves are: – Interference • If you hit a ball in snooker, the balls don’t combine to make one big ball, nor do they disappear altogether. – Diffraction • If a train travels through a tunnel, it does not spread out when it leaves the tunnel, it continues along the track. – We have seen these effects before. Electron Diffraction An object like a train has a wavelength many times smaller than the width of the tunnel. However, as shown before, electrons have a very small wavelength. This wavelength is about the same size as the spacing between atoms on a crystalline solid. Therefore, an electron can diffract when passing through a crystal. Diffraction Pattern Here is a typical pattern from an electron diffracting through a crystalline solid. The different diffraction amounts is due to the atomic spacing in the solid and the wavelength of the incident beam. Electron Microscope What you NEED to know. The equations, E = hf and ρ = h/λ How to use the above equations. Describe and explain the photoelectric effect. Describe and explain electron diffraction. Know that a de Broglie wavelength of a particle is extremely small, other than on an atomic or sub-atomic level.