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QUANTUM PHYSICS

 

The Photo-Electric Effect

 

photons

observations

wave theory

Einstein

Millikan

 

 

 

History

 

Hertz discovered the photo-electric effect in 1887.

 

His experiment concerned two parallel metal electrodes, with a p.d. across them. He observed that when ulta-violet light was shone on the electrodes an electric spark jumped between them.

 

Many of the properties of the effect were established by Hallwachs and Lenard in the years leading up to Einstein's theory in 1905.

 

 

The Photon Model

 

Max Planck(1901) first proposed the idea that light was emitted as discrete packets of energy called quanta. He also showed that each packet (quantum) had energy given by the equation:

 

Planck equation for quantum energy

 

where,

 

E = energy (J)
h = Planck's constant, 6.626 x 10-34 Js
ν(nu) = frequency of light radiation (Hz, s-1)

 

However, Einstein, as part of his photo-electric effect theory, described these quanta as streams of particles, which he termed photons.

 

 

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Observations

 

1. Emission of photo-electrons only occurs if the frequency of incident radiation exceeds a minimum value called the 'threshold frequency'.

 

2. The emission of photo-electrons starts immediately the surface becomes irradiated(provided the frequency of the radiation is above the thresh-hold frequency).

 

3. If the incident radiation has a frequency above the thresh-hold frequency:

 

( no. electrons emitted/sec. ) proportional sign ( radiation intensity )

 

4. Increasing the frequency of the incident radiation has the effect of increasing the kinetic energy of all emitted electrons. Hence the maximum kinetic energy an electron may have is increased by increasing frequency.

 

5. Radiation intensity is independent of electron kinetic energy. The kinetic energy of electrons is soley controlled by the radiation frequency.

 

 

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Wave Theory Predictions

 

Classical wave theory predicts that energy is carried in the wave-front.

 

Electrons absorb the energy from the wave until the level exceeds the work function*.

 

Electrons are then released from the surface of the metal.


*W (or Phi Φ) work function - minimum energy to remove an electron

 

 

Three main predictions come from this classical explanation:

 

1. Radiation intensity is proportional to the resulting maximum electron kinetic energy.

 

(radiation intensity) proportional sign (maximum electron kinetic energy)

 

2. The effect should occur for any frequency of light.

 

3. There is a delay between the radiation contact with the surface and the first release of electrons.

 

 

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Einstein's Photo-Electric Effect Theory

 

 

the photo-electric effect

 

 

The theory is based on a beam of light being considered as a stream of photons, each with energy hν.

 

Before explaining the theory in more detail, it is important to appreciate what is meant by 'the intensity of light'.

 

Consider photons emitted from a point source.

 

The sphere around the point, where the photons arrive, enlarges with distance from the point.

 

So at large distances the photons are spread out over a large area.


Note there is no diminuition of photon energy, whatever the distance travelled.

 

Intensity (I) beam of light proportional sign (no.photons/m2/sec.)

 

Einsein's big idea: In essence, this was that when a photon collides with an electron, there are two possible outcomes:

 

1. The photon reflects from the electron with no energy transfer.

 

2. The photon is absorbed by the electron and gives up ALL its energy to it.

 

Photons are paired with electrons. So there is no question of one photon sharing energy with more than one electron.

 

intensity of light proportional sign ( no. electrons emitted by a surface)

 

or more accurately,

(no.photons/m2/sec.) proportional sign( no. electrons/m2/sec.)

 

So when a photon arrives at the surface, an electron is emitted. This explains the instantaneous nature of the phenomenon.

 

The photon energy received is used to overcome the forces holding the electron within the surface and to give it kinetic energy to escape.

 

Einstein's photo-electric effect equation describes this process in more detail:

 

Einstein's photo-electric effect equation

 

Note this involves the maximum electron kinetic energy. Many electrons emerge from the surface with less than the maximum energy. This is a result of energy lost in collisions before they are free.

 

W is called the 'work function' of the surface.

It is a measure of the energy that binds each electron into the surface. The constant is different for different materials.

 

That there must be a minimum frequency for electron emission is implicit.


If,

equation for less energetic photons

 

there is not enough energy available to release an electron.

 

However, that particular frequency for an electron to be released is given by:

 

threshold frequency equation

 

where νo is the threshold frequency.

 

Using c = νoλo and substituting for νo = c/λo , the threshold wavelength λo is given by:

 

maximum photo-electric effect wavelength

 

 

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Millikan's Apparatus - stopping potential

 

 

photo-electric effect apparatus

 

 

In 1916 Millikan devised a series of experiments that completely vindicated Einstein's theory.

 

Using monochromatic light, the apparatus tested three surfaces in turn (lithium, sodium and potassium).

 

He found that altering the potential between the surface and the electron collector electrode, altered the 'electron current'.


When a small positive potential was applied to the metal, only electrons with enough KE escaped to impact on the collector electrode.

 

The remainder were pulled back to the surface. So only a small electric current was detected at the electrode.


With increased positive potential, the electron current was reduced.


Eventually there came a point when the current reduced to zero. This corresponded to electrons with the maximum KE being stopped from reaching the collector.

 

This p.d. between both electrodes is called the stopping potential V .

 

We can now integrate 'stopping potential' into the photo-electric effect equation.

 

The work done by an electron in moving against the 'stopping potential'(ie against the 'electric field' ) is equal to the maximum KE of the electron.

 

stopping potential and KE

 

from Einstein's photo-electric effect equation:

 

Einstein's photo-electric effect equation

 

substuting for KE,

 

stopping potential and photo-electric effect equation

 

rearranging into the form for a straight line ' y = mx + c '

 

stopping potential graph equation

 

For different materials, a plot of V against frequency ν(nu) is a straight line, with intercepts on the V-axis and the ν-axis.

 

 

photo-electric effect graph

 

 

intercept on V-axis ( ν = 0 ) is:      graph intercept on V-axis

 

intercept on the ν-axis (V = 0 ) is: graph v- intercept

 

where νo is the threshold frequency

 

 

The gradient is given by :                     gradient of photo-electric effect graph

 

notes

 

1. For different materials the graph has the same gradient, but different intercepts.

 

2. From the graph, measurements of W (the work function) and h (Planck's constant) can be made.

 

 

 

 

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