Quantum physics is the theoretical basis of modern physicsthat explains the nature and behavior of matter and energy on the atomic andsubatomic level. Quantum physics is sometimes referred to as quantum mechanics.The development of quantum physics began many years ago thatis to say as early as the fifth century B.
C by Greek philosophers who put up anidea that everything around as contained invisible and indivisible particles whichare now called atoms. Although quantum physics was createdto describe an atomic world far from our daily life, its impact on our dailylives could hardly be greater. The spectacular advances in chemistry, biology,and medicine and in essentially every other science could not have occurredwithout the tools that quantum physics made possible. Without quantum mechanicsthere would be no development in electronics because the electronics revolutionthat brought us the computer age is a child of quantum mechanics. The followingare some of the spectacular highlights in the development of quantum physics:In 1895, WilliamRoentgen, a German physicist, discovered invisible rays which can fogphotographic plates even when materials like wood, paper and other materialsare placed between the tube and the photographic plates. He also observed thatthe rays were not cathode rays since they were not deflected by electromagneticradiation and hence called the unknown rays X-rays, X meaning unknown.
This isone of the most important discoveries of mankind which is most essential in themedical field today.In 1896, AntoineHenri Becquerel, a French scientist placed a piece of Uranium metal in front ofa photographic plate and after sometime he discovered that a clear strong imagehad formed on the plate and concluded that the piece of Uranium producedradiations like the X-rays which led to the formation of the image on thephotographic plate hence leading to the development of the theory ofradioactivity.In 1897 – J. J. Thomson, an English physicist, conducts aseries of experiments on cathode rays and demonstrates that they consist of astream of small, electrically charged particles which have a mass over athousand times less than that of a hydrogen atom based on the highcharge-to-mass ratio.
This particle was initially called the “corpuscle” butlater named as the electron hence making it increasingly clear that atoms aremade up of smaller particles. He also concluded that electrons must be commonto all atoms and that all electrons must be the same.In 1899, Ernest Rutherford investigatesradioactivity. He names the terms alpha and beta rays in 1899 to describe the twodistinct types of radiation emitted by thorium and uranium salts through a process of nuclear decay.In1900, German physicist MaxPlanck presents a paper to the German Physical Society in which he derivesthe blackbody formula.
A black body is a body which allows all incidentradiation to pass into it and internally absorbs all the incident radiation.Hence a black body is a perfect absorber for all incident radiation. In 1902 -Philipp Lenard, a French physicist, investigates the photoelectric effect. Hediscovers that the photoemission of electrons from a metal has a strangeproperty: the frequency of the light, not its intensity, determines whetherthere is emission.
That is, if the frequency is above a certain threshold, thenelectrons are immediately emitted, no matter how weak the light is. Conversely,if the frequency is below the threshold, then no electrons are emitted,regardless of how strong the light is.1905 – Albert Einstein, a clerk in the Swiss Patent Office andsometime physicist, publishes a paper in which he outlines a possibleexplanation for the photoelectric effect. Suppose that light does not carryenergy in a continuous fashion, as would be expected for a classical wave, butinstead carries it in bundles, which come later to be called photons. (Einstein did not invent that term.) Suppose further that the energies ofthese photons are given by the Planck formula, E = hf.
Then one cansee why the photoelectric effect depends on the frequency of the light: theelectrons will not be detached from the material unless they receive a largeenough “bundle” of energy, and since the size of the”bundle” depends on the frequency, only light above a certainfrequency will generate the photoelectric effect.By no means was Einstein saying that light is a particle. He wasonly saying that the energy in the wave, for some reason, can only be deliveredin bundles rather than continuously. He predicts that measurements of theenergy of the electrons emitted by the photoelectric effect will be given bythe equation E = hf – , where is the amount of energyneeded to initially remove the electron from the metal.
Since the constant”h” is already known from blackbody measurements (a seemingly muchdifferent phenomena), this is a strong prediction. For technical reasons, dueto the considerable difficulty of generating variable-frequency ultravioletlight and of accurately measuring electron energies in a vacuum, thisprediction cannot be verified for some years.1909 – Eugene Marsden and Hans Geiger (who will later invent theGeiger counter) are two graduate students working with nuclear physicist ErnestRutherford in Manchester, England. They perform a series ofexperiments in which gold foil is bombarded by heavy, fast-moving subatomicparticles known as “-particles”. (See the Particle & NuclearTimeline for more details about -particles.) Matter at this timeis generally thought to be smooth, even if it does consist of atoms.
A popularmodel is J. J. Thompson’s “plum pudding” model, in whichpositively-charged matter is thought of like a pudding, and electrons arethought to be embedded in the goo like raisins. Rutherford is investigatingwhat happens when bullets are fired into the pudding. Several physicists immediately point out a serious problem withthis model: an orbiting electron must be accelerating, and an acceleratedcharge must radiate electromagnetic energy, according to Maxwell’s equations.Therefore, the electron should quickly lose all its kinetic energy and spiralinto the nucleus, causing the atom (and thus all matter) to collapse.1911 – Robert Millikan, aphysicist at the University of Chicago, measures the charge on the electron towithin 1%. He does this by spraying very fine oil droplets into a chamber witha perfume atomizer, then watching the droplets with a tele-microscope to see ifany of them have happened to pick up a static electric charge from the frictionof being sprayed in.
Millikan could tell if the droplets were charged or notbecause he’d set up things such that he could put an electric field (i.e., avoltage differential) across the chamber. The uncharged droplets would fall tothe bottom, but the charged droplets would be attracted by the electric fieldand float. Millikan could measure the charge on the oil droplet by carefullyadjusting the voltage to exactly balance the force of gravity, thus making thedroplet float in one spot. Millikan works on this experiment for elevenyears(!) and eventually has enough data to prove that the charge on theelectron is fixed at 1.6 X 10-19 coulomb.He also shows that he has never seen a charge of any size which would involve afraction of an electron’s charge; he has only seen charges that are evenmultiples of the electron’s charge.
He thus provides strong evidence that thecharge on the electron is the smallest, most fundamental unit of charge in theUniverse.This near-legendary experiment is considered to be one of the mostlaborious ever carried out by one man. The University of Chicago has preservedthe chamber where Millikan sat staring through his tele-microscope, year afteryear, waiting patiently for stray electrons to float into view so that he couldpainstakingly balance them by hand with a variable voltage source. Millikan wonthe 1923 Nobel Prize, mostly for this work.1913 – The Danish physicist Neils Bohr has been working on themost critical problem with Rutherford’s “solar system” atom, which isthat a rotating electric charge should quickly radiate away all its energy (see1909). As a way out of this, he hypothesizes that an orbiting electron can onlyradiate or absorb energy in quantized packets, similar to the ideas proposed byEinstein for the photoelectric effect and by Planck for the black-body formula.
This would automatically stabilize the atom against the energy-radiationproblem, and even better, finally provide a good reason for why atoms exhibitspectral lines when they are excited.If an electron can only be in certain energy levels, then it canonly give up or absorb energy by moving between those levels. The energydifferences between these levels must correspond to specific frequencies (usingE = hf), thus only those frequencies (colors) of light can be emitted. In thefigure at left, we are shown six quantized energy levels in a hypotheticalatom. There are four arrows, representing quantum transmissions (electronjumps) from levels 6, 5, 4, and 3 down to level 2. When the electron jumps froma higher energy level to a lower energy level, then it loses energy and thathas to go somewhere. Where it goes is into a single photon whose energy exactlyequals the energy left over after the electron has jumped to a lower level. Inthe spectrum at the top, we are shown that the violet line corresponds to thephotons emitted as electrons jump from level 6 to level 2.
Likewise, the bluishline represents the transition from level 5 to level 2, and so forth.Note that the transition 3 to 2 gives a red line (longerwavelength, lower frequency, lower-energy photons), whereas the transition 6 to2 gives a violet line (shorter wavelength, higher frequency, more energeticphotons). This is the way it must be, because level 6 is above level 3 inenergy, so when the electron drops to level 2 it must give up more energy inthe 6 to 2 transition than in the 3 to 2. So the photons given off by the 6 to2 transition are violet (higher energy), and the 3 to 2 photons are red (lowerenergy).. Arnold Sommerfeld (left) and Niels Bohr (right) at a conference in 1919.
Bohr is able to derive the Balmer formula theoretically (see 1885)and show that the fo in Balmer’s formula (which is anexperimentally measured quantity) should be equal to:where m = mass of the electron, k = the electrostatic forceconstant, e = the charge on the electron, and h = Planck’s constant. When oneputs in the values for all these constants, one does indeed get fo.It was clear that there had to be something “real” in this idea, butBohr was unable to explain finer details of the hydrogen spectrum, or to extendthe theory to other atoms.1915 – The German physicist Arnold Sommerfeld extends Bohr’sideas about the hydrogen atom by including elliptical orbits as well ascircular ones. He also incorporates relativity into the model. In this way heis able to explain considerably more details in the hydrogen spectrum than Bohrdid – but the theory still cannot be extended to other atoms.1915 – Robert Millikan, after nearly ten years of work onimproved vacuum chambers, has finally completed his research on Einstein’sprediction for the photoelectric effect (see 1905) — which, by the way,Millikan is completely certain is total nonsense. (Legend has it that when oneof Millikan’s assistants took some preliminary data that seemed to verifyEinstein’s equation, Millikan decided to do all of the rest of the workpersonally, to be certain it was correct.
) But after two years of experiments,Millikan is reluctantly forced to admit that E = hf. In announcing his results,Millikan writes, “Einstein’s photoelectric equation appears in every caseto predict exactly the observed results. Yet the physical theory of which itwas designed to be the symbolic expression is found so untenable that Einsteinhimself, I believe, no longer holds it.”Ha. Einstein was actually moving ahead with the quantum idea, andby 1916 had concluded that his “photons” not only carried discreteamounts of energy, but also carried momentum, given by the formula p = hf / c. Millikan is rather famous (or infamous) as theclassic example of how many of the older physicists of this period simply neverbelieved in quantum mechanics. Millikan lived until 1953, when he was 85, andeven as late as 1948 he was still saying “I spent ten years of my lifetesting that 1905 equation of Einstein’s, and contrary to all my expectations,I was compelled in 1915 to assert its unambiguous verification in spite of itsunreasonableness, since it seems to violate everything we know about theinterference of light.
“Not that Millikan didn’t admit that there had to be something tothis Einstein-Bohr-Planck quantum stuff. It worked too well to be completelywrong. But he, and many other physicists of his generation, always believedthat quantum mechanics was fundamentally wrong, somehow. The gap betweenquantum uncertainty and Newtonian mechanics was just too much for them toaccept. Towards the end of his life, Max Planck commented that the new ideas inphysics had gradually taken over only because everyone who believed in the oldones had died.
If there is an epitome for this remark, Millikan is it.1916 – American chemist Gilbert Lewis proposes (correctly) thatthe arrangement of electrons into quantum “shells” around atoms isthe basic mechanism responsible for chemistry.1923 – French physicist Louis de Broglie presents theoreticalarguments which indicate that everything should obey theEinstein formula for the momentum of a photon. Using the fact that c = f , we have: p = hf / c = h / , where h is Planck’sconstant and is the wavelength of either aphoton or a particle. In other words, not only should lightbehave like a particle, in certain ways, but particles should also behave likewaves, in certain ways. Planck’s constant is so small, however, that even awavelength of a nanometer is only going to have a momentum of 6.6 X 10-34 J-sec/ 10-9 m = 6.
6 X 10-25 kgm/s2. Which is a very small amount of momentum. This means thatonly very small particles will show the wave phenomena to any appreciabledegree, and de Broglie realizes that only electrons are likely to showwave-particle duality clearly enough to be observed. He predicts that electronscan be diffracted like X-rays, with their wavelength and momentum connected by:(de Brogliewavelength equation) p = h / 1925 – German physicist Werner Heisenberg (whois only 24 years old) concludes that the astronomical-oriented ideas of Bohrand Sommerfeld and others – who describe spectral lines in terms of electronsin elliptical orbits, tilted orbits, rotation around an axis, and so forth -are totally useless.
He develops matrix mechanics, in which pure numbersrepresenting the energy and momentum of electron orbitals are manipulatedwithout any regard for what they might mean in terms of a physical picture.This is the beginning of modern quantum mechanics.1926 – Austrian physicist Erwin Schrodinger develops atheory of electron motion which also discards the astronomical-orbits ideas ofBohr and Sommerfeld. His theory, however, becomes known as wave mechanicsbecause in this theory the electron is visualized as a wave-type entity whichis literally everywhere at once, and only “collapses” to a point whenit interacts with other matter. Schrodinger works out possibly the most usefulequation in modern physics, the Schrodinger wave equation, which says that theabsolute position of matter is almost a meaningless question. All that one cando is calculate a relative probability that it might be somewhere as comparedto somewhere else. Schrodinger’s equation is actually a general formulationthat must be tailored to each specific problem, so its exact form variesdepending on the circumstances.
A particularly simple version is the one forthe hydrogen atom:(Schrodinger wave equation for the hydrogenatom)