Finish up the photoelectric effect We recall that: When an electron moves through a potential difference of 1V, then 1eV of energy is transferred. This is the same as the work done on the electron. When the electron is accelerated through this potential difference its kinetic energy increases (equating work done to change in energy). We can write: 𝑒𝑉= 1 2 𝑚 𝑣 2

Finish up the photoelectric effect This equation applies to any type of charged particle We can rearrange this to find the speed of the electron: 𝑣= 2𝑒𝑉 𝑚

Stopping potential The stopping potential (V0) is the potential difference which gives rise to the maximum kinetic energy of the electrons 𝑒 𝑉 0 = 𝐾𝐸 𝑚𝑎𝑥 = 1 2 𝑚 𝑣 2 So, if the stopping potential is found to be 1.83V, the maximum kinetic energy of the photoelectrons must be 1.83eV or 1.83 x 1.6 x 10-19 = 2.93 x 10-19J

To understand wave-particle duality

Introduction Interference and diffraction effects, such as the Young’s slit experiment, can only be explained by the wave model of light However the photoelectric effect led Einstein to propose that light can behave as a stream of particles called photons This led other scientist to start thinking about, if waves can behave like particles, - can particles of matter behave as waves?

Louis de Broglie In 1924 the French physicist Louis de Broglie proposed that all matter, regardless of its mass, can have wave and particle properties. This is known as wave-particle duality. He was awarded the Nobel prize in physics in 1929 for this insight.

How can we demonstrate wave particle duality? To prove that particles can also act as waves, you have to show the particles exhibiting a wave like characteristic or property, such as diffraction or interference. We would normally describe electrons as particles, as they have a mass and a charge. They can be accelerated and deflected by electric and magnetic fields. This behaviour is associated with particles

Apparatus used to show electron diffraction A narrow beam of electrons (from an electron gun) is accelerated in a vacuum tube and directed at a thin layer of polycrystalline graphite. This has carbon atoms arranged in many different layers.

Electron diffraction Electrons are diffracted in certain directions only as they emerge from the gaps between the atomic layers. The gap between the carbon atoms is so small that it is similar to the wavelength of the electrons and so the electrons diffract. Because the carbon atoms are not lined up in the same direction as in a diffraction grating, this gives a pattern of rings (rather than the parallel lines seen when light diffracts.

The wavelength of electrons In developing wave particle duality, de Broglie realised that the wavelength, λ, of a particle is inversely proportional to its momentum, 𝑝. λ∝ 1 𝑝

The de Broglie Equation This led to the de Broglie equation λ= ℎ 𝑝 or λ= ℎ 𝑚𝑣 λ is the wavelength of a particle (m), h is the planck constant, p is the momentum of the particle in kgms-1( since p=mv) The wavelength of a particle can be altered by changing the speed of the particle.

Example Calculate the wavelength of an electron moving at 3 x 107 ms-1. (mass of an electron is 9x10-31kg) ℎ 𝑚𝑣 = 6.626× 10 −34 9× 10 −31 ×3 × 10 7 =2.46 × 10 −11 𝑚

Davisson and Germer In 1927 two American physicists called Davisson and Germer confirmed de Broglie’s equation by accelerating electrons of charge e through a potential difference of V they observed a pattern of electron diffraction from which they could calculate the electron’s wavelength

Davisson and Germer Equate the work done to accelerate the electrons with the kinetic energy transferred to the electrons eV = 1 2 𝑚 𝑣 2 and rearrange 2𝑒𝑉 𝑚 = 𝑣 2 , so 𝑣= 2𝑒𝑉 𝑚 Substitute into the de Broglie equation λ= ℎ 𝑚𝑣 ⇒ λ= ℎ 2𝑚𝑉𝑒 Two american physicists confirmed de Broglie’s equation by observing the behaviour of electronsthat had been defracted from the surface of a nickel crystal.

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