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Einstein’s Theory of Relativity was a totally out-of-the-world idea! However, Einstein did not win a Nobel Prize for that. He won a Nobel Prize based on his paper on The Photoelectric Effect.
Most of what we learnt until now – Newtonian mechanics, thermodynamics, electromagnetism – are all considered classical physics. Several experiments and observations around 1900 showed that there are some phenomenon which cannot be well-explained through the classical physics framework.
We will start with the Photoelectric Effect.
The Photoelectric Effect
Refer to your College Physics textbook Chap 28.2 (p. 927 – 930)
Background
1678 – Huygens published a work on the wave theory of light
1704 – Newton published his work, Opticks, based on a particle theory of light
1801 – Young’s double slit experiment
1818 – Poisson Spot
By the 1820s, the wave theory of light was widely accepted.
In 1887, Heinrich Hertz discovered the Photoelectric Effect – that when light shines on a freshly-polished Zinc plate, electrons are emitted. This effect was hard to explain based on the wave theory of light!
In 1905, Einstein once again proposed that light behaves as particles! He suggested that light behaves as if its energy is concentrated in discrete bundles, rather than as a continuous wave. He named these bundles light quanta. We now call them photons.
Einstein was building on the work of Max Planck. Planck’s constant, h, was derived when he was trying to explain the spectrum of blackbody radiation.
The energy of one photon is given by E= h f.
Example:
What is the energy of photons which have a wavelength of 500 nm?
A source emits monochromatic light of wavelength 500 nm at a power of 1.25 W. How many photons are emitted in one second?
Variables in the Photoelectric Effect
Refer to textbook for a description of the set-up and some characteristics of the effect
Magnitude of current (Saturation Current)
Kinetic energy of the ejected electrons (Stopping potential/voltage)
Graph of Photocurrent against Applied voltage
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Wave Theory
According to the wave model, electrons are ejected because being charged particles, the oscillating electromagnetic field will exert forces on them. The force can do work on the electrons and eject them from the surface of the metal.
The wave theory has a few predictions:
- Intensity of light – the greater the intensity of light, the greater the current and the KE will be.
- Applied voltage – if collector is positively charged, it will attract more photoelectrons and current will increase. If collector is negatively charged, current will decrease
- Type of metal – some electrons may be more tightly bound to the surface of some metals than others. This will affect the KE with which the electrons are ejected.
Problems with the Wave theory:
- Maximum KE is unaffected by intensity
- Cannot explain the existence of the threshold frequency (which is dependent on type of metal)
- There is no time delay even at very low intensities of light.
http://farm3.staticflickr.com/2565/3909285882_b61e74dd59_o.png
Einstein’s Interpretation
Einstein offered an explanation by assuming light is made up of photons. The release of electrons are caused by “collisions” of these photons with the electrons.
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- One photon “collides” with one electron
- In the “collision”, the photon transfers all its energy to the electron and disappears
- Some of the energy is used to overcome the binding energy of the electron (to the metal lattice)
- The remaining energy stays and becomes the electrons’ KE
Electrons can have different binding energies depending on their positions in the lattice. We consider those with the minimum binding energy. The minimum binding energy is called the work function of the metal. These electrons will then be ejected with the maximum possible KE.
Think!
By applying conservation of energy, write the equation for the Photoelectric Effect!
Einstein’s theory was put to the test by plotting the max KE against the frequency of incident light. The graph below shows the results:
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The gradient here agrees with what Planck derived as his constant based on another experiment!
Predictions of Einstein’s Model:
Greater intensity of light – larger saturation current but no change in stopping voltage
Low frequency of light – low stopping voltage, if f is too low, no current observed.
No time delay since photons transfer energy to the electrons in a single collision event.
Cleary, Einstein’s model resolved all the problems of the wave theory!
Photons
Refer to your College Physics textbook Chap 28.3 (p. 931 – 933)
Let’s discuss a bit about photons.
- E = h f
- Travel at the speed of light (only)
- No rest mass (can only exist in motion, cannot exist when not moving)
- When they are in motion, they have mass: E = m c^2
- Therefore, momentum of photon: p = m c
- Since c = f (lambda), p = h / (lambda)
Light exhibits particle-like behaviour sometimes and wave-like behaviour sometimes!
Superposition Principle of Waves
College Physics textbook Chap 16.1-16.3 (p. 508 – 516), Chap 17 (p. 548 – 567)
Two waves undergo superposition when they meet at the same point. The final displacement of a particle at that point where the wave meets is a vector sum of the displacements which would have arose due to each individual wave.
Standing waves are formed when waves reflect between two boundaries and overlap each other, travelling in opposite directions.
http://www.walter-fendt.de/ph14e/stwaverefl.htm
The interference and diffraction patterns are very simply and elegantly explained using a wave model.
If we consider the interference of two waves which are coherent, we end up with some nice results. If the waves are in phase at the point where the waves meet, there is constructive interference and the particle at that point oscillates with twice the amplitude. If the waves are completely out of phase where the waves meet, there will be destructive interference and the particle at that point would not oscillate.
To identify where will constructive or destructive interference take place, we need to make use of the path difference of the waves from the source. After analysing the path difference, it can be seen that constructive and destructive interference occurs at regular intervals, forming the distinct bright and dark fringes we can see for the case of light.
Wave-Particle Duality
The fact that light sometimes behave like a wave and sometimes behave like a particle is not contradictory because given the same circumstances, light always behave in the same way.
De Broglie then boldly proposed (with no experimental evidence yet) that the relationship between momentum and wavelength which was derived for photons actually applies to all particles.
Therefore, all particles have an associated de Broglie wavelength = h / momentum.
Matter Waves
College Physics textbook Chap 28.4 (p. 933 – 936)
In fact, electrons and neutrons have been found to be diffract! The interference diffraction of electrons was observed by Davisson and Germer and then G.P. Thomson. The pattern is exactly like that of X-rays.
In recent years, interference and diffraction of atoms have also been observed!
Why don’t we diffract as we walk through the door? The determining factor regarding when matter behaves like waves lie in their de Broglie’s wavelength. In order for wave patterns to be seen, we need to interact with objects which are of dimensions smaller than or similar to our wavelengths.
Quantization of Energy
College Physics textbook Chap 28.5 (p. 936 – 938)
De Broglie’s work also helped explain a phenomenon which classical physics did not manage to explain (see Activity below). In addition, he extended his work to further show that energy, as we know it, is quantized!
Uncertainty Principle
College Physics textbook Chap 28.7 (p. 940 – 942)
The wave-like behaviour of matter has some interesting complications. If a single electron going through a slit can diffract, it means that the electrons will gain a spread of velocities in the perpendicular direction after passing through the slit.
The smaller the slit, the wider the angle of spread, therefore, the wider the spread of velocities! This means that there is a lower limit to the product of an objects’ position and velocity.
Heisenburg’s uncertainty principle is one big blow to how we used to understand physical laws! Values for positions and velocity cannot be precisely determined both together!
Quantum Systems
Due to wave-like behaviours of particles, as well as the uncertainty principle, any measurement to a quantum system will also cause a halt in quantum evolution processes. Thus, a measurement / observation of a quantum system actually affects / changes a quantum system!
This is very different from how we understand measurements in the classical world! Measurements and observations of the system can be done without disturbing the classical system!
Here are some interesting (and famous) analogies to the quantum systems.
Schrodinger’s Cat
There are other interesting effects of quantum systems:
- Quantum Zeno Effect
- Quantum Tunneling
Quantum versus Classical Physics
So what about quantum physics makes it so different from all the other rules of physics? What exactly is the quantum-classical divide?
During the classical era, physicists dealth with laws, and deterministic relationships. However, the quantum era deals with probabilities! What is the chance of this outcome as opposed to another outcome?
However, does it mean that classical physicists are wrong and quantum physicists are correct? Why is the physical world such an oxymoron?
Physicists who are puzzled about the apparent contradiction are working on a unifying theory, which hopefully explains all these differences!
https://sites.google.com/a/nygh.edu.sg/2014-s4-physics-olympiad/quantum-physics