# Quantum phenomena

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## The photoelectric effect

• When radiation of a high enough frequency is shone onto the surface of a metal, it will instantly emit electrons. The frequency is normally in the UV range.
• The free electrons on or near the surface of a metal absorb energy from the radiation and start vibrating.
• If it absorbs enough energy, the bonds holding it to the metal break and it is released. The electron emitted is called a photoelectron.

The photoelectric effect shows:

• Threshold frequency - for a given metal, no photoelectrons are emitted if the radiation has a frequency below a certain value.
•  Maximum kinetic energy - The photoelectrons are emitted with a variety of different Eks ranging from 0 to a max. value. This value increases with the frequency of the radiation.
• The intensity of the radiation - the amount of energy per second hitting an area of the metal. The max. Ek of the photoelectrons is unaffected by varying the intensity.
• The number of photoelectrons emitted per second is proportional to the intensity of the radiation.
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## The photoelectric effect and wave theory

wave theory incorrectly predicted that:

• emission should take place with waves of any frequency.
• Emission would take longer using low intensity waves than high intensity but would still occur.

E (energy of a photon) = hf = hc/wavelength (for EM waves)

• when EM radiation hits a metal, the surface is bombarded by photons. If one of these collides with an electron, the electron will gain energy equal to hf.
• Work function - the min. energy needed by an electron to leave the metals surface. It's value depends on the metal.
• If the energy gained from the photon is GREATER than the work function, the electron is emitted. If it is LESS THAN the work function, the electron will shake and release the energy as another photon and the metal will simply heat up. Therefore,

Threshold frequency, fo = Work function / planks constant, h

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## Maximum kinetic energy

• The energy transferred from EM radiation to an electron is the energy it absorbs from 1 photon
• The KE it will be carrying when it leaves the metal is hf - any other energy losses, which are the reason the emitted electrons have a range of kinetic energies.

Ek = hf - % (work function)                                  Ek = 1/2mv^2

therefore 1/2mv^2 = hf - %

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## Energy levels in atoms

The electron volt:

• electron volt (eV) - the unit of energy equal to the work donewhen an electron is moved trhough a pd of 1 volt.
• 1 eV = 1.6 x 10^-19 J

Discrete energy levels in atoms:

• Electrons can only exist in certain well-defined energy level shells. Each level has a number wiht n=1 representing the lowest level (ground state).
• excited atom - when one or more of its electrons is in an energy level higher than the n=1.
• electrons can move down a level by emitting a photon.
• the energy of the photon is equal to the energy lost by the electron and therefore, the atom.

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## Electron transitions

• The energy of the photon emitted after a transition = the difference between the 2 levels of the transition.
• Electrons can also move up energy levels if they absorb a photon with the exact energy difference between the two levels. If the photon's energy is smaller or larger than the difference, it will not be absorbed by the electron.
• excitation - the movement of an electron to a higher energy level
• the energy of the emitted photon, hf = E1 - E2

ionisation:

• ionisation - process of creating ions.
• ionisation energy - the amount of energy needed to remove an electron from its ground state.
• ground state - the lowest energy state of an atom
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## Photon emission - fluorescent tubes

• contain mercury vapour, across which a high voltage is applied.
• when the fast-moving electrons (emitted by electrodes and accelerated by the voltage) collide with the electrons in the mercury atoms , the mercury electrons are excited to a higher energy level.
• When these return to their ground states, they lose energy by emitting high energy photons in the UV range.
• a phosphorus coating on the inside of the tube absorbs these photons, exciting its electrons to much higher shells. These electrons then cascade down the levels and lose energy by emitting many lower energy photons of visible light.
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## Line emission spectra and light absorption spectra

Line emission spectra:

• if you split the light from a fluorescent tub with a prism or diffraction grating, you get a line spectrum
• A line spectrum is a series of bright lines against a black background. Each line corresponds to a particular wavelength of light emitted by the source.
• line spectra provide evidence for descrete energy levels.

Line absorption spectra:

• white light has a continuous spectra - there are NO GAPS in the spectrum.
• you get a line absorption spectrum when light with a continuous spectrum passes through a cool gas.
• At low temp. most of the electrons will be in their ground states.
• Photons of the correct wavelength are absorbed by the electrons to excite them to a higher energy level.
• These wavelengths are then missing from the continuous spectrum that appears.
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## wave-particle duality

• diffraction - when a beam of light passes through a narrow gap, it spreads out. Diffraction can only be explained using waves. If the light acted like particles, the particles in the beam would either not get through (if too big) or just pass through and not change the beam size.
• photoelectric effect - this can only be explained using particle-like photons. If a photon of light is a discrete packet of energy, then it can interact with an electron in a one-to-one way. All the energy of the photon is given to the electron.
• De Broglie - this equation relates a wave property (wavelength) to a moving particle property (momentum, mv)

(/\ de broglie wavelength in m)     /\ = h/mv (m in kg)   (v in ms^-1)

• The de Broglie wave of a particle can be interpreted as a 'probability wave'.
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