Chapter 32: The Atom & The Quantum (Or, the Evolution of the Model of the Atom)

Evolution of the Atomic Model Democritus was a Greek philosopher (470-380 B.C.) who is the father of modern atomic thought. He claimed that matter was made of small, hard particles that he called “atomos” He proposed that matter could NOT be divided into smaller pieces forever.

Evolution of the Atomic Model John Dalton (1808) created the very first atomic theory. It had 4 statements: Dalton viewed atoms as tiny, solid balls. He was an English school teacher who performed many experiments on atoms. His atomic theory had 4 statements…

Evolution of the Atomic Model Atoms are tiny, invisible particles. Atoms of one element are all the same. Atoms of different elements are different. Compounds form by combining atoms. Dalton viewed atoms as tiny, solid balls. He was an English school teacher who performed many experiments on atoms. His atomic theory had 4 statements…

Evolution of the Atomic Model J.J. Thomson (1897) discovered electrons. He also proposed the existence of a (+) particle. How did he discover electrons?

Discovery of the Electron Electrodes in a cathode-ray tube under low pressure are connected to a voltage source, causing the gas to glow due to a “ray” emerging from the negative terminal (the cathode). Electrodes in a cathode-ray tube under low pressure are connected to a voltage source, causing the gas to glow due to a “ray” emerging from the negative terminal (the cathode). Slits could make the ray narrow and plates could prevent the ray from reaching the positive terminal (the anode).

Discovery of the Electron When electric charges were brought near the tube, the ray bent toward positive charges and away from negative charges. The ray was also deflected by the presence of a magnet. When electric charges were brought near the tube, the ray bent toward positive charges and away from negative charges. The ray was also deflected by the presence of a magnet. These findings indicated that the ray consisted of negatively charged particles. Thomson reasoned that the amount of the beams’ deflection depended on the mass of the particles and their electrical charge. The greater each particle’s mass, the greater the inertia and the less the deflection. The greater each particle’s charge, the greater the force and the greater the deflection. The greater the speed, the less the deflection.

Discovery of the Electron After the discovery of the electron, Milikan did an experiment and determined the charge on a single electron. Millikan sprayed tiny oil droplets into a chamber between electrically charged plates—into an electric field. He adjusted the field so that droplets hovered motionless, i.e., when downward force of gravity was balanced by upward electrical force. He found that the charge on each drop was always some multiple of a single value – the charge of each electron.

Evolution of the Atomic Model These experiments gave rise to a new model. Thompson’s atomic model was known as the “raisin bun model” or the “plum pudding model … Atoms are made mostly out of (+) charged material, like dough in a bun. The (-) charged electrons are found inside the (+) dough.

Evolution of the Atomic Model Along came Earnest Rutherford in 1911 Rutherford discovered protons and the nucleus. He showed that atoms have (+) particles in the center, and are mostly empty space. He called these (+) particles protons. He called the center of atoms the nucleus.

Discovery of the Atomic Nucleus In Rutherford’s experiment, a beam of positively charged alpha particles was directed through a thin gold foil. Nearly all alpha particles passed through with little or no deflection. Some particles were deflected from their straight-line paths. A few alpha particles were widely deflected, and a very small number were even scattered backward! These alpha particles must have hit something relatively massive—but what? Rutherford reasoned that the undeflected particles traveled through empty space in regions of the gold foil, While the small number of deflected particles were repelled from extremely dense, positively charged central cores. Each atom, he concluded, must contain one of these cores, which he named the atomic nucleus. Ernest Rutherford’s famous gold-foil experiment showed that the atom is mostly empty space with most of its mass concentrated in the central region – the atomic nucleus.

Atomic Spectra: Clues to Atomic Structure An important sequence of lines in the hydrogen spectrum starts with a line in the red region, followed by one in the blue, then by several lines in the violet, and many in the ultraviolet. Spacing between successive lines becomes smaller and smaller from the first in the red to the last in the ultraviolet, until the lines become so close that they seem to merge. An important sequence of lines in the hydrogen spectrum starts with a line in the red region, followed by one in the blue, then by several lines in the violet, and many in the ultraviolet. Spacing between successive lines becomes smaller and smaller from the first in the red to the last in the ultraviolet, until the lines become so close that they seem to merge. Balmer first expressed the wavelengths of these lines in a single mathematical formula. He was unable to provide a reason why his formula worked so successfully. Rydberg noticed that the frequencies of lines in certain series in other elements followed a formula that the sum of the frequencies of two lines in such series often equals the frequency of a third line. This relationship was later advanced as a general principle by Ritz and is called the Ritz combination principle.

Bohr’s Model of the Atom [Bohr reasoned in 1913 that electrons occupy “stationary” states (of fixed energy, not fixed position) at different distances from the nucleus. Electrons can make “quantum jumps” from one energy state to another. Light is emitted when such a quantum jump occurs (from a higher to a lower energy state). Frequency of emitted radiation is determined by E = hf where E is the difference in the atom’s energy when the electron is in the different orbits.] We’ve learned about atomic excitation and how excited electrons jumping down from higher energy states emit photons whose frequency correspond proportionally to the energy drop. Here we see three of many energy levels in an atom. An electron jumping from the third level to the second emits a red photon (DRAW). An electron jumping from the second energy level to the first (ground state) emits a green photon (DRAW) And finally, an electron jumping from the third energy level down to ground state emits a blue photon (DRAW). The sum of the energies of this jump equal the sum of the energies from the red and green photons. Eblue = hf (=Ered + Egreen) And it follows that (=hred fred + hgreen fgreen) and so fblue = fred + fgreen Niels Bohr

Bohr’s Model of the Atom Yet it was very perplexing to him and other early investigators. It was perplexing because the electron, at the time, was thought to be a particle whirling around a small nucleus like a planet whirls around the sun. Just like any satellite can orbit at any distance from the sun, it seems as if an electron should be able to orbit at any distance around the nucleus, depending, of course, like the satellite on its speed. If electrons moved randomly among ALL orbits, they’d emit photons of ALL frequencies, but this DOESN’T happen. Niels Bohr

Bohr’s Model of the Atom According to classical theory, an electron accelerating around its orbit should continuously emit radiation. This loss of energy should cause it to spiral rapidly into the nucleus. But this does not happen. Also, according to classical theory, an electron accelerating around its orbit should continuously emit radiation. This loss of energy should cause it to spiral rapidly into the nucleus. But this does not happen.

Bohr’s Model of the Atom Why the electron occupies only discrete levels is understood by considering the electron to be not a particle but a WAVE.

Explanation of Quantized Energy Levels: Electron Waves Louis de Broglie hypothesized that a wave is associated with every particle. Louis de Broglie

Explanation of Quantized Energy Levels: Electron Waves The wavelength of a matter wave is inversely related to a particle’s momentum. de Broglie showed that a Bohr orbit exists where an electron wave closes on itself constructively. The electron wave becomes a standing wave, like a wave on a musical string. These matter waves behave just like other waves. They can be reflected, refracted, diffracted, and caused to interfere. Using the idea of interference, de Broglie showed that the discrete values of radii of Bohr’s orbits are a natural consequence of standing electron waves. A Bohr orbit exists where an electron wave closes on itself constructively! In this view, the electron is thought of not as a particle located at some point in the atom but as if its mass and charge were spread out into a standing wave surrounding the atomic nucleus with an integral number of wavelengths fitting evenly into the circumferences of the orbits. Louis de Broglie

Explanation of Quantized Energy Levels: Electron Waves (a) An orbiting electron forms a standing wave only when the circumference of its orbit is equal to a whole-number multiple of the wavelength. (b) When the wave does not close in on itself in phase, it undergoes destructive interference. Hence, orbits exist only where waves close in on themselves in phase. (a) An orbiting electron forms a standing wave only when the circumference of its obit is equal to a whole-number multiple of the wavelength. (b) When the wave does not close in on itself in phase, it undergoes destructive interference. Hence, orbits exist only where waves close in on themselves in phase. The electron wave becomes a standing wave, like a wave on a musical string. In this view, the electron is thought of not as a particle located at some point in the atom, but as if its mass and charge were spread out into a standing wave surrounding the atomic nucleus – with an integral number of wavelengths fitting evenly into the circumference of the orbits.

Explanation of Quantized Energy Levels: Electron Waves The electron orbits in an atom have discrete radii because the circumferences of the orbits are whole-number multiples of the electron wavelength. This results in a discrete energy state for each orbit. The circumference of the innermost orbit, according to this picture, is equal to one wavelength. The second, two wavelengths. And so on. For each orbit, the electron has a unique speed which determines its wavelength. This is similar to a chain necklace made of paper clips. No matter what size necklace is made, its circumference is equal to some multiple of the length of a single paper clip. This figure is, of course, greatly oversimplified, as the standing waves make up spherical and ellipsoidal shells rather than flat, circular ones.

Explanation of Quantized Energy Levels: Electron Waves This model explains why electrons don’t spiral closer and closer to the nucleus, causing atoms to shrink to the size of the tiny nucleus. If each electron orbit is described by a standing wave, the circumference of the smallest orbit can be no smaller than one wavelength. No fraction of a wavelength is possible in a circular (or elliptical) standing wave. As long as an electron carries the momentum necessary for wave behavior, atoms don’t shrink in on themselves. This model explains why electrons don’t spiral closer and closer to the nucleus, causing atoms to shrink to the size of the tiny nucleus. If each electron orbit is described by a standing wave, the circumference of the smallest orbit can be no smaller than one wavelength. As long as an electron carries the momentum necessary for wave behavior, atoms don’t shrink in on themselves. VIDEO: deBroglie….

Quantum Mechanics In the still more modern wave model of the atom, electrons move not only around the nucleus but also in and out, toward and away from the nucleus. The electron wave is spread out in three dimensions, leading to the picture of an electron “cloud”.

Quantum Mechanics This is a cloud of probability, not a cloud made up of a pulverized electron scattered over space. The electron, when detected, remains a point particle.

Quantum Mechanics Erwin Schrödinger An Austrian physicist, named Erwin Schrödinger, formulated an equation that describes how matter waves change under the influence of external forces. Erwin Schrödinger

Quantum Mechanics The fundamental equation of quantum mechanics is Schrödinger’s wave equation, which is: (Details of this equation are beyond the scope of this course.)

Quantum Mechanics Quantum Mechanics In Schrödinger’s wave equation, the thing that “waves” is the nonmaterial matter wave amplitude—a mathematical entity called a wave function, represented by the symbol  (the Greek letter psi). All the information about the matter waves is contained in the wave function. Schrödinger's equation plays the same role in Quantum Mechanics that Newton’s equation (a = F/m) plays in classical physics. For now, just realize that the Schrödinger equation cannot tell us where an electron can be found in an atom at any moment, but only the likelihood of finding it there.

Quantum Mechanics Progression from the Bohr model of the atom to the modified model with de Broglie waves to the Schrödinger model Progression from the Bohr model of the atom to the modified model with de Broglie waves to the Schrödinger model When an electron’s position in its Bohr energy level (state) is repeatedly measured and each of its locations is plotted as a dot, the resulting pattern resembles a sort of electron cloud. An individual electron may, at various times, be detected anywhere in this probability cloud; it even has an extremely small but finite probability of momentarily existing inside the nucleus. It is detected most of the time, however, close to an average distance from the nucleus, which fits the orbital radius described by Niels Bohr. Don’t expect the same clear understanding of quantum mechanics that you may enjoy with classical mechanics….

Quantum Mechanics Richard Feynman Even though QM is extremely well supported with experimental evidence and is one of the most successful theories in physics. many of the greatest minds in QM, have struggled with it. Read the quote. Actually, what I think he said was a bit closer to the following: Richard Feynman: "Anyone who claims to understand quantum theory is either lying or crazy." MOST physicists view QM as a fundamental theory of nature. Richard Feynman

Quantum Mechanics But not all of them. Einstein himself, one of the founders of QM, was troubled by it though and never accepted it as fundamental. He considered the probabilistic nature of quantum phenomena as the outcome of deeper yet undiscovered physics. This is what he had to say: READ The treatment we have given QM here has only scratched the surface. But it is a beginning for those of you who wish to go further into the world of the quantum.

Quantum Mechanics Let’s see if what I’ve taught here has settled with you. Think about this question and then lets discuss.

Correspondence Principle The correspondence principle says that in order for a new theory to be valid, it must account for the verified results of the old theory. New theory and old must correspond; that is, they must overlap and agree in the region where the results of the old theory have been fully verified. When the techniques of quantum theory are applied in classical situations, the results are identical. First introduced by Bohr in 1913. READ IT. It is satisfying to know that quantum theory and classical theory, which make such completely different predictions at the level of the single atom, blend smoothly into a description of nature that extends from the smallest to the largest things in the universe. So why don’t we throw out classical theory? Simplicity!