The Photoelectric Effect
If you shine a light of a high enough frequency onto the surface of a metal, it will emit electrons. For most metals, this frequency falls in the UV range.
- Free electrons on the surface of the metal absorb energy from the light, making them vibrate.
- If an electron abosrbs 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.
Three main conclusions:
- Conclusion One: For a given metal, no photoelectrons are emitted if the radiation has a frequency below a certain value - the threshold frequency.
- Conclusion Two: The photoelectrons are emitted with a variety of kinetic energies ranging from 0 to some maximum value. This value of maximum kinetic energy increasesb with the frequency of the radiationn, and is unaffected by the intensity of the radiation.
- Conclusion Three: The number of photoelectrons emitted per second is proportional to the intensity of the radiation.
The Photoelectric Effect and Wave Theory
According to wave theory:
- For a particular frequency of light, the energy carried is proportional to the intensity of the light.
- The energy carried by the light would be spread evenly over the wavefront.
- Each free electron on the surface of the metal would gail a bit of energy from each incoming wave.
- Gradually, each electron would gain enough energy to leave the metal.
- If the light had a lower frequency, it would take longer for the electrons to gain enough energy, but it would happen eventually. However, this doesn't happen - there's a threshold frequency. This cannot be explained by the wave theory of light.
- The higher the intenstiy of the wave, the more energy it should transfer to each electron (the kinetic energy of each electron should increase with intensity). However, the kinetic energy depends on the frequency, which also can't be explained by wave theory.
The Photon Model of Light
- E = hf = hc / λ [where h = Planck's Constant, c = speed of light in a vacuum]
- Einstein suggested that EM waves can only exist in discrete packets - photons.
- He saw these photons of light as having a one-on-one, particle-like interaction with an electron in a metal surface. It would transfer all its energy to that one specific electron.
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 the metal, it needs enough energy to break the bonds holding it there. This energy is called the work function energy (ϕ) and its value depends on the metal.
- If the energy gained from the photon is greater than the work function energy, the electron is emitted.
- If it isn't, the electron will release the energy as another photon. The metal will heat up, but no electrons will be emitted.
- Since, for electrons to be released, hf ≥ ϕ, the threshold frequency must be:
- f = ϕ / h
- The energy transferred to an electron is hf.
- The kinetic energy it wil be carrying when it leaves the metal is hf - any energy it's lost.
- The minimum amount of kinetic energy it can lose is the work function energy, so the maximum kinetic energy is given by:
- hf = ϕ + 1/2mv²
- The kinetic energy of the electrons is independent of the intensity, because they can only absorb one photon at a time.
- Electrons in an atom can only exist in certain well-defined energy levels. Each level is given a number, with n = 1 representing the ground state (lowest energy level).
- Electrons can move down a level by releasing energy in the form of photons.
- Since these transitions are between definite energy levels, the energy of each photon emitted can only take a certain allowed value.
- The energies involved are so tiny that it makes sense to use a more appropriate unit than the joule. The electronvolt (eV) is used instead.
- The electronvolt is defined as the kinetic energy carried by an electron after it has been accelerated through a potential difference of 1 volt.
- The energy carried by each photon is equal to the difference in energies between the two levels. ΔE = E2 - E1 = hf = hc / λ
- Fluorescent tubes contain mercury vapour, across which a high voltage is applied.
- When electrons in the mercury collide with fast-moving free electrons (accelerated by the high voltage), they're excited to a higher energy level.
- When these excited electrons return to their ground states, they emit photons in the UV range.
- A phosphorus coating on the inside of the tube absorbs these photons, exciting its electrons to much higher orbits. These elctrons then cascade down the energy levels, emitting many lower energy photons in the form of visible light.
- If you split the light from a fluorescent tube 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 corresponds to a particular wavelent of light emitted by the source.
- Since only certain photon energies are allowed, you only see the corresponding wavelengths.
- Each element has different energy levels, so the line spectrum can tell us what the element is.
- The spectrum of white light is continuous.
- If you split the light up with a prism, the colours all merge into each other - there are no gaps in the spectrum.
- Hot things emit a continuous spectrum in the visible and infrared.
- 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 of the electrons in the gas atoms 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 wavelength.
- If you compare the absorption and emission spectra of a particular gas, the black lines in the absorption spectrum line up to the bright lines in the emission spectrum.
As a wave:
- Light produces interference and diffraction patterns - alternating bands of dark and light.
- These can only be explained using waves interfering constructively or destructively.
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 stated that if 'wave-like' light showed particle properties (photons), 'particles' like electrons should be expected to show wave-like properties.
- The de Broglie equation relates a wave property (wavelength, λ) to a moving particle property (momentum, mv).
- λ = h / mv
- The de Broglie wave of a particle can be interpreted as a 'probability wave'. The probability of finding a particle at a point is directly proportional to the square of the amplitude of the wave at that point.
- Electron diffraction proved 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 wave theory, the spread of the lines in the diffraction patterns increases if the wavelength of the wave is greater. In electron diffraction experiments, 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 de Brogile equation above - if the velocity is higher, the wavelength is shorter and the spread of lines is smaller.
- In general, λ for electrons accelerated in a vacuum tube is about the same size as electromagnetic waves in the X-ray part of the spectrum.
Wave-Particle Duality (2)
Particles don't show wave-like properties all the time. You only get diffraction if a particle interacts with an object of about the same size as its de Brogile wavelength.
- A shorter wavelength gives less diffraction effects. This fact is used in the electron microscope.
- Diffraction effects blur detail on 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.