Quantum mechanics is the set of scientific principles describing the behavior of energy and matter on the atomic and subatomatic scale. Much like the universe on the large and very vast scale (i.e., general relativity), so the universe on the small scale (i.e., quantum mechanics) does not neatly conform to the rules of classical physics. As such, it presents a set of rules that is counterintuitive and difficult to understand for the human mind, as humans are accustomed to the world on a scale dominated by classical physics. In other words, quantum mechanics deals with "Nature as She is—absurd."
Many elementary parts of the universe, such as photons (discrete units of light) have some behaviours which resemble a particle but other behaviours that resemble a wave. Radiators of photons such as neon lights have spectra, but the spectra are chopped up instead of being continuous. The energies carried by photons form a discontinuous and colour coded series. The energies, the colours, and the spectral intensities of electromagnetic radiation produced are all interconnected by laws. But the same laws ordain that the more closely one pins down one measure (such as the position of a particle) the more wildly another measure relating to the same thing (such as momentum) must fluctuate. Put another way, measuring position first and then measuring momentum is not the same as measuring momentum first and then measuring position. Even more disconcerting, particles can be created as twins and therefore as entangled entities -- which means that doing something that pins down one characteristic of one particle will determine something about its entangled twin even if it is millions and millions of miles away.
Around the turn of the twentieth century, it became clear that classical physics was unable to explain several phenomena. Understanding these limitations of classical physics led to a revolution in physics: the development of quantum mechanics in the early decades of the last century.
The first quantum theory: Max Planck and black body radiation
Thermal radiation is electromagnetic radiation emitted from the surface of an object which is due to the object's temperature. If an object is heated up sufficiently, it will start to emit light at the red end of the spectrum—it is "red hot". Heating it up further will cause the colour to change, as light at shorter wavelengths (higher frequencies) begins to be emitted. It turns out that a perfect emitter is also a perfect absorber. When it is cold, such an object will look perfectly black, as it will emit practically no visible light, but it will absorb all the light that falls on it. Consequently, an ideal thermal emitter is known as a black body, and the radiation it emits is also called black body radiation.
In the late 19th century, thermal radiation had been fairly well characterized experimentally. The wavelength at which the radiation is strongest is given by Wien's displacement law, and the overall power emitted per unit area is given by the Stefan–Boltzmann law. So, as temperature increases, the glow colour changes from red to yellow to white to blue. Even as the peak wavelength moves into the ultra-violet, enough radiation continues to be emitted in the blue wavelengths that the body will continue to appear blue. It will never become invisible—indeed, the radiation of visible light increases monotonically with temperature. Physicists were searching for a theoretical explanation for these experimental results.
The "answer" found using classical physics is the Rayleigh–Jeans law. This law agrees with experimental results at long wavelengths. At short wavelengths, however, classical physics predicts that energy will be emitted by a hot body at an infinite rate. This result, which is clearly wrong, is known as the ultraviolet catastrophe.
The first model which was able to explain the full spectrum of thermal radiation was put forward by Max Planck in 1900. He modelled the thermal radiation as being in equilibrium with a set of harmonic oscillators. To reproduce the experimental results, he had to assume that each oscillator had to produce an integral number of units of energy at its one characteristic frequency, rather than being able to emit any arbitrary amount of energy. In other words, the energy of each oscillator was "quantized". The quantum of energy for each oscillator, according to Planck, was proportional to the frequency of the oscillator; the constant of proportionality is known as the Planck constant. The Planck constant, usually written as h , has the value 6.63 × 10 −34 J s , and so the energy, E , of an oscillator of frequency f is given by
Planck's law was the first quantum theory in physics, and Planck won the Nobel Prize in 1918 "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta". At the time, however, Planck's view was that quantization was purely a mathematical trick, rather than (as we now know) a fundamental change in our understanding of the world.
Photons: the quantisation of light
In 1905, Albert Einstein took an extra step. He suggested that quantisation wasn't just a mathematical trick: the energy in a beam of light occurs in individual packets, which are now called photons. The energy of a single photon is given by its frequency multiplied by Planck's constant:
For centuries, scientists had debated between two possible theories of light: was it a wave or did it instead consist of a stream of tiny particles? By the 19th century, the debate was generally considered to have been settled in favour of the wave theory, as it was able to explain observed effects such as refraction, diffraction and polarization. James Clerk Maxwell had shown that electricity, magnetism and light are all manifestations of the same phenomenon: the electromagnetic field. Maxwell's equations, which are the complete set of laws of classical electromagnetism, describe light as wave: a combination of oscillating electric and magnetic fields. Because of the preponderance of evidence in favour of the wave theory, Einstein's ideas were met initially by great scepticism. Eventually, however, the photon model became favoured. One of the most significant pieces of evidence in favour of the photon model was its ability to explain several puzzling properties of the photoelectric effect, described in the following section. Nevertheless, the wave analogy remained indispensable for helping to understand other light phenomena, such as diffraction.
The photoelectric effect
Main article: Photoelectric effectIn 1887, Heinrich Hertz observed that light can eject electrons from metal. In 1902, Philipp Lenard discovered that the maximum possible energy of an ejected electron is related to the frequency of the light, not to its intensity. Moreover, if the frequency of the light is too low, no electrons are ejected. The lowest frequency of light which causes electrons to be emitted, called the threshold frequency, is different for every metal. This appeared to be at odds with classical electromagnetism, which was thought to predict that the electron energy would be proportional to the intensity of the radiation.
Einstein explained the effect by postulating that a beam of light is a stream of particles ( photons ), and that if the beam is of frequency f , each photon has an energy equal to hf . An electron is likely to be struck only by a single photon; this photon imparts at most an energy hf to the electron. Therefore, the intensity of the beam has no effect; only its frequency determines the maximum energy that can be imparted to the electrons.
To explain the threshold frequency, Einstein argued that it takes a certain amount of energy, called the work function , denoted by φ , to remove an electron from the metal. This amount of energy is different for each metal. If the energy of the photon is less than the work function then it does not carry sufficient energy to remove the electron from the metal. The threshold frequency, f 0 , is the frequency of a photon whose energy is equal to the work function:
If f is greater than f 0 , the energy hf is enough to remove an electron. The ejected electron has a kinetic energy E K which is at most equal to the photon's energy less the energy needed to remove the electron from the metal:
The relationship between frequency of radiation and the energy of each individual photon is why ultraviolet light can cause sunburn, but visible or infrared light cannot. A photon of ultraviolet light, which has a high frequency (short wavelength), will deliver a high amount of energy—enough to contribute to cellular damage such as a sunburn. A photon of infrared light, having a lower frequency (longer wavele
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