How Do You Know if Its Classical or Quantum
THREE FAILURES OF CLASSICAL PHYSICS
one. Blackbody Radiation
Any object with a temperature to a higher place absolute aught emits light at all wavelengths. If the object is perfectly blackness (and then it doesn't reflect whatsoever light), then the light that comes from it is called blackbody radiation.
The energy of blackbody radiation is not shared evenly by all wavelengths of calorie-free. The spectrum of blackbody radiation (below) shows that some wavelengths get more energy than others. Three spectra are shown, for three different temperatures. (1 of the curves is for the surface temperature of the Sun, 5770 Thou.)
Here are some experimental facts well-nigh blackbody radiations:
a. The blackbody spectrum depends just on the temperature of the object, and not on what it is made of. An iron horseshoe, a ceramic vase, and a piece of charcoal --- all emit the same blackbody spectrum if their temperatures are the same.
b. As the temperature of an object increases, information technology emits more blackbody energy at all wavelengths.
c. As the temperature of an object increases, the peak wavelength of the blackbody spectrum becomes shorter (bluer). For example, blue stars are hotter than red stars.
d. The blackbody spectrum always becomes minor at the left-hand side (the short wavelength, high frequency side).
The explanation of classical physics: Calorie-free is an electromagnetic wave that is produced when an electrical charge vibrates. (Strictly speaking, "vibrates" means any alter in how the charge moves --- speeding up, slowing downward, or changing direction.) Now call up that heat is just the kinetic energy of random motion. In a hot object, electrons vibrate in random directions and produce low-cal as a outcome. A hotter object means more energetic vibrations and and then more lite is emitted past a hotter object --- it glows brighter. Then far, so good. But classical physics could not explain the shape of the blackbody spectrum.
The electrons in a hot object tin vibrate with a range of frequencies, ranging from very few vibrations per second to a huge number of vibrations per second. In fact, there is no limit to how swell the frequency can be. Classical physics said that each frequency of vibration should have the same free energy. Since there is no limit to how swell the frequency can exist, there is no limit to the energy of the vibrating electrons at loftier frequencies. This ways that, according to classical physics, there should be no limit to the energy of the calorie-free produced by the electrons vibrating at high frequencies. Wrong!! Experimentally, the blackbody spectrum e'er becomes small at the left-paw side (short wavelength, loftier frequency).
At about 1900, Max Planck came up with the solution. He proposed that the classical idea that each frequency of vibration should have the aforementioned energy must exist wrong. Instead, he said that free energy is not shared equally by electrons that vibrate with different frequencies. Planck said that energy comes in clumps. He called a dodder of free energy a breakthrough. The size of a clump of free energy --- a quantum --- depends on the frequency of vibration. Here is Planck's rule for the a quantum of free energy for a vibrating electron:
energy of a quantum = (a calibration constant) x (frequency of vibration)
or
East = hf
where h, the calibration constant, is today called Planck's constant. Its value is most 6 x 10 -34 , very tiny!
And so how does this explain the spectrum of blackbody radiation? Planck said that an electron vibrating with a frequency f could only have an energy of 1 hf, 2 hf, 3 hf, four hf, ... ; that is,
energy of vibrating electron = (any integer) x hf
But the electron has to have at least one quantum of energy if information technology is going to vibrate. If it doesn't take at least an energy of 1hf, information technology volition not vibrate at all and tin can't produce whatever light. "A ha!" said Planck: at high frequencies the amount of free energy in a breakthrough, hf, is so big that the high-frequency vibrations can never get going! This is why the blackbody spectrum always becomes pocket-size at the left-hand (high frequency) side.
2. The Photoelectric Issue
When low-cal shines on the surface of a metallic substance, electrons in the metallic blot the free energy of the light and they can escape from the metal's surface. This is chosen the photoelectric effect, and it is used to produce the electric electric current that runs many solar-powered devices. Using the idea that light is a wave with the free energy distributed evenly throughout the wave, classical physicists expected that when using very dim light, it would take some time for enough light free energy to build up to eject an electron from a metallic surface. Wrong!! Experiments show that if light of a certain frequency tin can eject electrons from a metal, it makes no difference how dim the light is. At that place is never a time delay.
In 1905, Albert Einstein came up with the solution. If Max Planck's idea that free energy comes in clumps (quanta) is correct, then light must consist of a stream of clumps of energy. Each clump of light free energy is called a photon, said Einstein, and each photon has an free energy equal to hf (Planck'south abiding times the frequency of the light). Therefore the energy of light is non evenly distributed forth the moving ridge, but is concentrated in the photons. A dimmer lite means fewer photons, but just turning down the light (without changing its frequency) does not alter the free energy of an individual photon. And so for a specific frequency light, if a single photon has plenty energy to eject an electron from a metallic surface, so electrons will e'er exist ejected immediately afterward the light is turned on and the photons hitting the metal.
three. The Hydrogen Atom
When a small tube of hydrogen gas is heated, it begins to glow and emit low-cal. Unlike the blackbody radiations that comes from a hot dense solid or gas, this light consists of just a few colors (wavelengths): a ruby-red wavelength, a turquoise, and several violets. Classical physicists at the showtime of the century thought they should certainly be able to understand hydrogen, since information technology is the simplest atom. Hydrogen consists of a positively charged proton at the center, with a negatively charged electron orbiting around it. The electrical allure between the positive proton and the negative electron keeps the electron in orbit, just similar the gravitational attraction between the Sun and the Earth holds the World in orbit. There was just one problem. Classical physics said that considering the orbiting electron is constantly irresolute direction, it should emit electromagnetic radiation --- light. Every bit a result, the electron should exist continually losing energy. In fact, physicists calculated that the electron should lose all of its energy and spiral down into the proton in only about 0.000000000001 second! In other words, atoms should non exist longer than a mere 10 -12 seconds. WRONG!!
Niels Bohr provided an explanation in 1913. In the Bohr model of the hydrogen atom, the electron can't orbit the proton in any size orbit information technology pleases. There are just certain immune orbits, and each allowed orbit has a certain radius and a certain energy. Bohr invented a rule that immune him to summate the size and energy of each orbit. If you are curious, Bohr's rule said that
iiπ x (electron mass) x (electron orbital speed) x (orbit radius) = (whatsoever integer) x h
which is not too obvious, to say the least! (The integer would be 1 for the smallest orbit, 2 for the adjacent orbit out, and so on.) Bohr too made up a new dominion to explain the stability of the hydrogen cantlet --- why information technology could final longer than 0.000000000001 second. He said that when an electron is in an allowed orbit, the electron will not produce electromagnetic radiation. Bohr did not explain why, he merely proposed a new police force of nature. And nature agreed with Niels Bohr. His new model of hydrogen gave wavelengths for hydrogen gas that precisely agreed with what was measured.
Question: If the electrons do not produce light when they are in their allowed stable orbits, where is the source of the light that comes from hydrogen? Respond: According to Bohr, electrons have more than energy when they are in larger orbits. If an electron falls from a larger orbit down to a smaller orbit, it loses energy. According to the law of conservation of energy, the energy lost by the electron must become somewhere. Bohr explained that a photon carries abroad the lost free energy from the hydrogen cantlet; that is,
photon energy = (electron energy in larger orbit) - (electron free energy in smaller orbit)
Information technology works the other way, likewise. If a photon strikes an atom, the atom can absorb the photon and its energy if (and simply if) the photon's energy is exactly equal to the difference between 2 orbital energies. In this instance, an electron uses the photon's energy to bound from the smaller orbit upwards to the larger orbit. This is chosen a quantum bound.
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WAVES OR PARTICLES? BOTH!
When light passes through a double-slit, an interference pattern consisting of bright bands and dark bands is seen on a screen. This is produced when the moving ridge from one slit combines with the wave from the other slit. If two wave crests meet at the screen, the waves add and y'all become a bright band. If a wave crest from ane slit meets a wave trough from the other slit, the waves cancel and you get a dark band. This proves that calorie-free is a wave.
On the other hand, the photoelectric effect proves that low-cal consists of massless particles chosen photons.
So which is information technology? Is light a moving ridge or a stream of particles? The answer is "Yep!"
Light acts similar a moving ridge if y'all desire to know how it propagates, how it travels from 1 identify to some other. To describe how light travels from the double slits to the screen, yous have to apply the moving ridge characteristics of lite.
Light acts like particles (photons) if you want to know how low-cal interacts with matter. To describer how light interacts with the electrons in a metal and how it ejects them from the metal's surface, you take to employ the particle characteristics of light.
Nosotros say that light exhibits a wave-particle duality. It tin can deport like either waves or particles (just not both at the same fourth dimension), depending on the situation.
Thinking nigh the photoelectric effect again, how can a photon (which has no mass) knock an electron well-nigh? Einstein used his theory of relativity to evidence that even massless photons have momentum. Newton defined momentum = (mass) ten (velocity) for a particle with mass, but Einstein was able to show that the momentum of a massless photon depends on its wavelength:
The smaller the wavelength, the greater the momentum of the photon.
In 1923, Prince Louis de Broglie of France had an idea. Maybe the wave-particle duality applies to everything in nature. He proposed that everything propagates like a moving ridge, and that everything interacts like a particle. Say what?? What do you hateful by the wavelength of an electron, or the wavelength of a baseball? De Broglie rewrote Einstein'southward formula for the momentum of a photon and applied it to a particle with mass:
Planck's constant, h, is then tiny that nosotros don't notice the wavelength of a thrown baseball game, which is only about 10 -35 meters! But an electron's mass is likewise tiny, and so information technology has a wavelength near 10,000 times shorter than the wavelength of visible light. This is useful, because microscopes that utilise electron waves instead of light waves can run across several thousand times more than detail!
The proof that electrons propagate like a wave came when electrons were passed through a double slit and counted as they striking a screen. If the electrons traveled like a stream of particles, they would have only piled upwardly at two locations behind the two slits. Merely they didn't. They showed a double-slit interference pattern, bright bands and night bands but similar the ones produced by light waves. Without a doubt, electrons exhibit the wave-particle duality of nature. In fact, every massive object exhibits the wave-particle duality of nature. It just isn't noticeable on the big calibration of our everyday world.
SUMMARY
If y'all look at nigh of the "equations" above, you will find Planck's abiding, h. This is the trademark of "modernistic physics." The failure of classical physics to explicate blackbody radiation, the photoelectric effect, and the hydrogen atom ultimately demolished the foundations of classical physics.
Max Planck, Albert Einstein, Niels Bohr, and Louis de Broglie made inspired guesses about how nature works. Other people of their fourth dimension made different guesses. Nature agreed with Planck, Einstein, Bohr, and de Broglie, but not with the others whose names are at present forgotten. Like Arcadia's Thomasina, these were intuitive geniuses who went beyond mere mathematics to make creative conjectures almost how the world operates. Those who came later calculated the consequences of the new physics, simply this was just mathematics (sometimes vivid mathematics, only mathematics all the same). It is those rare intuitive geniuses who courageously discard the sometime rules and invent new ones who are in the start rank of physicists.
Finally, It is important to remember that Planck's constant is very tiny, only about six x x -34 . Roughly speaking, this means that in our everyday globe, quantum effects like the wave-particle duality make a difference only in the 34th decimal identify when predicting the behavior of a moving baseball. Big objects obey Newton's laws. But the behavior of large object reflect the average beliefs of their component atoms, so it is fair to say that Newton'southward laws work only "on boilerplate." The beliefs of small systems is radically different than what classical physics predicts. Ultimately, the whole idea of prediction --- that the same conditions should always produce the aforementioned results --- was overthrown. This is explained in Affiliate 6 of Richard Feynman's The Character of Physical Police.
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Final modified: Sunday, May 08, 2005 06:03 PM
Source: https://physics.weber.edu/carroll/honors/failures.htm
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