# Quantum Phenomena

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## Light - Wave or Particle

Light behaves like a wave... or a stream of particles. In the late 19th century scientists would show you that light is a wave. But the introduction of the photoelectric effect ruined everything - it stated that light acted as a particle called a photon. A photon is a quantum of EM radiation. When Max Planck was investigating black body radiation, he suggested that EM waves can only be released in discrete packets, called quanta. A single packet of EM radiation is called a quantum. The energy carried by one of these wave-packets had to be: E=hf or E=hc/wavelength, where h=Planck's constant = 6.63x10 to the power of -34 Js, f=frequency, and c=speed of light in a vacuum = 3x10 to the power of 8 metres per second. So the higher the frequency of the EM radiation, the more energy its wave-packets carry. Einstein went further and suggested that EM waves and the energy they carry can only exist in discrete packets, called photons. He believed that a photon acts as a particle, and will transfer either all or none of its energy when interacting with another particle, like an electron. Photon energies are usually given in electronvolts. The energies involved when talking about photons is so tiny you need another measurement. When you accelerate an electron between two electrodes, it transfers some electrical potential energy (eV) into kinetic energy. An electronvolt is defined as: The kinetic energy gained by an electron when it is accelerated through a potential difference of 1 volt. So 1 electronvolt = 1.6x10 to the power of -19 joules. Threshold voltage is used to find Planck's constant. You can find the value of Planck's constant by doing a simple experiment with light-emitting diodes. Current will only pass through an LED after a minimum voltage is placed across it - the threshold voltage. This is the voltage needed to give the electrons the same energy as a photon emitted by the LED. All of the electron's kinetic energy after it is accelerated over this potential difference is transferred into a photon. So by finding the threshold voltage for a particular wavelength LED, you can find Planck's constant. E=hc/wavelength=eV0. So h=(eV0)wavelength/c. You can use LED's to calculate Planck's constant. Connect a LED of known wavelength in an electrical circuit with a 6V battery, a voltmeter, a resistor and a current. Start off with no current, and then adjust the resistor until a current just flows through the circuit. Record the voltage across the LED, and the wavelength of light the LED emits. Repeat this with different wavelength LEDs. Plot a graph of threshold voltage against 1/wavelength, where wavelength is measured in meters. You should get a straight line graph with a gradient of hc/e - which you can use to find the value of h. hc/e = 1.24x10 to the power of -6, so h=gradient x e divided by c.

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## The Photoelectric Effect

Shining light on a metal can release electrons. If you shine light of a high enough frequency onto the surface of a metal it can emit electrons. For most metals this falls in the UV range. Free electrons on the surface of a metal absorb energy from the light, making them vibrate. If an electron absorbs enough energy, the bonds holding it to the metal break and the electron is released. This is called the photoelectric effect, and the electrons emitted are called photoelectrons. Conclusion 1 - For a given metal, no photoelectrons are emitted if the radiation is a frequency below a certain value known as the threshold frequency. Conclusion 2 - The photoelectrons are emitted with a variety of kinetic energies ranging from zero to some maximum value. This value of maximum kinetic energy increases with the frequency of the radiation, and is unaffected by the intensity. The number of photoelectrons emitted is proportional to the intensity of the radiation. The photoelectric effect couldn't be explained by wave theory. According to wave theory, for a particular frequency of light, the energy carried is proportional to intensity. The energy carried would spread evenly over the wavefront. Each free electron on the surface of the metal would gain a bit of energy from each incoming wave. Gradually each electron would gain enough energy to leave the metal. If the light had a low frequency the electrons would eventually gain enough energy - leaving no explanation for the threshold frequency. The kinetic energy should increase if there was more intensity, not just frequency. There is no explanation for kinetic energy only depending on frequency. The photon model explained the photoelectric effect nicely. According to the photon model, when light hits its surface, the metal is bombarded by photons. If one of these photons collides with a free electron, the electron will gain energy equal to hf. Before an electron can leave the surface of a metal, it needs enough energy to break the bonds holding it there. This energy is called the work function energy (symbol phi) and its value depends on the metal. It explains the threshold frequency. If the energy gained from the photon is greater than the work function energy, the electron can be emitted. If not, it will just shake about abit, then release the energy as another photon. The metal will heat up, but no electrons will be emitted. Since for electrons to be released hf> or equal to phi, the threshold frequency must be f=phi/h. (In theory, if a second photon hit the electron before it released the energy from the first, it could gain enough to leave the metal, but since electrons release excess energy after 0.00000001s, it isn't really going to happen. The photon model also explains the maximum kinetic energy. The energy transferred by an electron is hf. The kinetic energy it will be carrying when it leaves the metal will be hf - any energy it's lost on the way out. The minimum amount of energy it can lose is the work function energy, so the maximum kinetic energy is given by the equation hf=phi+0.5 x m x v squared. The kinetic energy of the electrons is independent of the intensity, because they can only absorb one photon at a time.

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## Energy Levels and Photon Emission

Electrons in atoms exist in discrete energy levels. Electrons can only exist in certain well-defined energy levels. Each level has a number, where n=1 is the ground state. Electrons can move down an energy level by emitting a photon. These transitions are between definite energy levels, so the energy of each photon can only have a certain allowed value. Energy levels labelled on a diagram can have energy units shown in joules, electronvolts or both. The energy carried by each photon is equal to the difference between the two levels on an energy level diagram. This equation shows this for between n=2 and n=1. Delta E=E2-E1=hf=hc/wavelength. Hot gases produce line emission spectra. If you heat a gas to a high enough temperature the electrons move to higher energy levels. As they fall back to the ground state these electrons emit energy as photons. If you split the light from a hot gas with a prism or diffraction grating you get a line spectrum. A line spectrum is seen as a series of bright lines against a black background. Each line on the spectrum corresponds to a particular wavelength of light emitted by the source. Since only certain photon energies are allowed, you only see the corresponding wavelengths. Shining white light through a cool gas gives an absorption spectrum. Continuous spectra contain all possible wavelengths. The spectrum of white light is continuous, and if you split the light up with a spectrum the colours merge into each other - there are no gaps in the spectrum. Hot things emit a continuous spectrum in the visible and infrared. Cool gases remove certain wavelengths from the continuous spectrum. You get a line absorption spectrum when light with a continuous spectrum of energy (white light) passes through a cool gas. At low temperatures, most electrons will be in their ground states. Photons of the correct wavelength are absorbed by the electrons to excite them to higher energy levels. These wavelengths are then missing from the continuous spectrum when it comes out the other side of the gas. You see a continuous spectrum with black lines in it corresponding to the absorbed wavelengths. If you compare the absorption and emission spectrum of a particular gas, the black lines in the absorption spectrum match up to the bright lines in the emission spectrum.

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## Wave-Particle Duality

Interference and diffraction show light as a wave. Light produces interferece and diffraction patterns. These can only be explained using waves interfering constructively or interfering destructively. The photoelectric effect shows light behaving as a particle. Einstein explained the results of photoelectricity experiments by thinking of the beam of light as a series of particle-like photons. If a photon of light is a discrete bundle of energy, then it can interact with an electron in a one-to-one way. All the energy in the photon is given to one electron. De Broglie came up with the wave-particle duality theory. Louis de Broglie suggested that if 'wave-like' light showed particle properties, 'particles' like electrons should be expected to show wave-like properties. The de Broglie equation links a wave property (wavelength) with a particle property (momentum, mv). h = Planck's constant = 6.63x10 to the power of -34 Js. Wavelength=h/mv. The de Broglie wave of a particle can be interpreted as a 'probability wave'. His ideas were just speculation, but later experiments confirmed the wave nature of electrons. Electron diffraction shows the wave nature of electrons. Diffraction patterns are observed when accelerated electrons in a vacuum tube interact with the spaces in a graphite crystal. This confirms that electrons show wave-like properties. According to the wave theory, the spread of the lines in the diffraction pattern increases if the wavelength is greater. In electron diffraction, a smaller accelerating voltage, i.e slower electrons, gives widely spaced rings. Increase the electron speed and the diffraction pattern circles squash together towards the middle. This fits in with the be Broglie equation - if the velocity is higher, the wavelength is shorter and the spread of lines is smaller. Particles don't show wave-like properties all the time. You only get diffraction if a particle interacts with an object about the same size as it's be Broglie wavelength. A tennis ball, for example. with mass 0.058kg and speed 100 metres per second has a be Broglie wavelength of 10 to the power of -34 m. That's smaller than the nucleus of an atom. There is nothing that small for it to interact with. A shorter wavelength gives less diffraction effects. This fact is used in the electron microscope. Diffraction effects blur detail in an image. If you want to resolve tiny detail in an image, you need a shorter wavelength. Light blurs out detail more than 'electron-waves' do, so an electron microscope can resolve finer detail than a light microscope. They can let you look at things as tiny as a single strand of DNA.

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