# Wave-particle duality

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• Created by: Monikak
• Created on: 11-01-16 11:57

## Newton's corpuscles vs Huygens' waves

Newton's theory: light is a stream of small particles - 'corpuscles'. Explains reflection and refractions:

1.Reflection: no loss of speed. Component of velocity perp to mirror reverses direction, while component parallel to mirror remains unchanged. Since magnitute of both components remains the same, angle of incidence=angle of relflection.

2.Refraction: light is attracted to the surface of the substance hence travels quicker (Huygens said it travels slower) in the substance. Component of velocity perpendicular to sufrace is increased, component parallel stays the same.

Wave theory rejected because:

-impossible to measure speed of light in air vs substance

-Newton had a stronger scientific rep than Huygens

-wave theory considered light to be longitudinal wave hence couldn't explain polarisation

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## Singificance of Young's double slit experiment

Young showed that light produces an intereference when passed through two slits. Interference is a wave property!

-waves spread out at the double slits --> undergo diffraction

-double slits act as coherent sources of waves

-parallel equally spaced bright and dark fringes are produced on screen

-bright fringe-light waves arrive in phase-constructive interference-waves reinforce

-dark fringe-light waves arrive 180deg out of phase-destructive interference-waves cancel

Number of fringes depends on fringe width and distance apart.

Newton's theory predicted just two fringes.

Youngs wave theory was not accepted until it was experimentally proven that light travels slower in water than air. With this scientists realised than light is a transverse waveform which explained polarisation also.

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## Maxwell's discovery of EM waves

J.C.Maxwell showed mathematically that alternating current in a wire produces an alternating magnetic field which generates an alternating electric field and so on. EM waves are transverse and made up of magnetic and electric waves which are in phase and perpendicular to each other.

ε0 Relates to electric field strength due to a charged object in free space

μRelates to the magnetic flux density due to a current-carrying wire in free space

If asked to describe EM wave:

• draw diagram
• electric and magnetic waves are in phase
• perepndicular to each other and the direction in which the wave is travelling
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## Hertz's discovery of radio waves

Hertz discovered that radio waves are produced when high voltage sparks jump across an air gap.

- radio waves produced by a spark-gap transmitter spread out from spark gap and pass through detector loop

- waves passing through a detector loop cause a voltage to be induced in detector loop due to changing magentic field flux, which makes more sparks jump across the detector gap

Hertz discovered that radio waves are reflected from metal surfaces, pass straight through insulators, and are polarised.

Measured wavelength of radio waves by creating a stationary wave - flat metal sheet used to reflect waves back towards the transmitter. Detector moved along the line, distance between nodes(points where sparks were not produced) x 2 = wavelength.

Demonstrated radio waves are polarised by rotating a dipole detector until the signal was 0, after a 90deg rotation - at 90, no magnetic flux passes through the loop

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## Implications of photoelectricity

Electrons are emitted from a metal when light above a certain frequency is shone on the surface.

- threshold frequency: minimum frequency of incident light on a certain metal at which photoelectrons are emitted from its surface

-photoelectric emission occurs at the same instant the light is incident on the surface

-photoelectrons have a range of kinetic energies which depend on type of metal and frequency

-no of photoelectrons emitted per second is proportional to intensity of light

Wave theory failed to explain this because according to it light of any frequency should cause emission. Also it predicted that the lower the frequency of light, the longer it should take for the electrons to gain sufficient kinetic energy to leave the surface.

Basically wave theory couldn't account for thershold frequency, instantenous emission of photoelectrons and their maximum kinetic energy SO classical wave theory was rejected in favour of the photon theory.

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## Einstein's explanation of photoelectricity

Einstein's photon theory (1905) explained photoelectricity.

He borrowed the basic idea from Plack who reasoned that energy of a vibrating atom can only be in multiples of a basic amount or 'quantum' of energy.

Einstein said that EM radiation is made up of wave packets of electromagnetic energy - photons. Each carrying energy E=hf. The photon is the least quantity of EM radiation and is considered massless.

In order for a photoelectron to escape the surface of the metal it needs to:

• absorb a single photon and therefore gain energy = hf
• use energy equal to the work function ϕ of the metal to escape

Therefore to explain why the photoelectrons have a max kinetic energy: EKmax = hf − ϕ

The photon has dual wave-particle nature, and its particle properties are observed in the photoelectric effect, while wave properties in diffraction and interference experiments such as Young's double slit experiment.

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## Stopping potential and its measurement

Einstein realised that each electrons absorbs the energy of just one photon (=hf) and uses some of it to overcome the work function of the metal. The remainder is its maximum kinetic energy.

EKmax = hf − ϕ

In practice this can be measured by making the metal plate (from which photoelectrons are emitted) or 'cathode' increasingly positive so that the electrons have to do work to get to the anode.

Then the max kinetic energy is reduced by eV where V is the pd of the cathode relative to the anode. When the max KE is reduced to 0, then hf − ϕ = eV, and V is the stopping potential at which photoelectric emission is stopped.

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## Wave-particle duality

De Broglie hypothesised that not only light, but all matter has a dual wave-particle nature.

He put poward the equation: mv (particle momentum) x λ = h

This was only a hypothesis until couple of years later when an experiment showed that a beam of electrons was diffracted when passed through a thin metal foil. X-ray diffraction was already investigated and a similar result showed that electrons were also diffracted and therefore showed wave-like nature.

Angles of diffraction

• increased when the speed of the electrons was decreased (because λ increased) vice versa

For different electron speeds, the angle of diffraction was measured and used to work out the de Broglie wavelength of the electron.

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## Electron Microscopes (T.E.M.)

To form an image of an atom, the electrons need to have a de Broglie wavelength of about 0.1nm - this is an 'order of magnitude' value, which gives an anode potential of about 150V.

Transmission electron microscope

1. Electron gun produces electrons through thermionic emission by heating the metal filament. The electrons are passed through a small hole in the annode which is at constant pd relative to the filament.The electrons emerge from the hole all at the same speed which depends on the pd of the annode.

2. Magnetic condenser lens produces a magnetic field which forces the electrons into a parallel beam, directed at the very thin sample.

3. Objective lens deflects the scattered electrons so that they form an enlarged inverted first image.

4. Magnifier lens focuses the electrons from the central area of the first image to form a magnified final image on the screen.

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## T.E.M. cont.

Amount of detail depends on resolving power of the microscope, this is the smallest separation between two objects so that they can still be seen apart.

Resolving power depends on the amount of diffraction that occurs when the electrons scattered by the sample pass through the objective lens. The smaller the wavelength, the less diffraction, the higher the resolving power.

Limitations on the amount of detail seen in a T.E.M image:

• Sample thickness: speed of electrons passing through a material reduces, de Broglie wavelength increases, more diffraction => resolving power decreases
• Lens abberations: electrons scattered from a given point on the sample may have different speeds due to thermionic emission and also due to passing through different thicknesses of the sample so they could be focused differently on the screen
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## S.T.M.

Scanning Tunneling misroscope

Fine-tipped metal probe scans the surface of the material under investigation at a height of about 1nm.

Probe is at a constant negative potential relative to the surface (-1V) so that the electrons only travel in one direction.

The gap between the surface at the tip is so small that there's a small but finite probability that electrons will 'tunnel' across it.

Piezoelectric transducers control the movement of the microscope.

Tunneling current increases if the gap is made smaller and decreases if the gap is made bigger - in constant height mode the current is recorded and used to map the height of the surface on a computer. In constant current mode, the current is kept constant by feeding back changes in tunneling current to the transducers which adjust the height. The signal to the transducer is recorded and used to map the height of the surface on a computer screen.

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