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LECTURE 14 ATOMIC STRUCTURE: ELECTRONS, PROTONS and NEUTRONS The above figure displays a cathode-ray tube (CRT). Today, a CRT is described as a vacuum tube  that contains one or more electron guns  and a  phosphorescent  screen, and is used to display images.  It modulates, accelerates, and deflects electron beams onto a screen to create the images. The images may represent electrical waveforms (in an oscilloscope ), pictures (a television screen,  computer monitor ),  radar  targets, or other phenomena.  We now know that cathode rays are streams of electrons observed in discharge tubes. If an evacuated glass tube (upper image) is equipped with two electrodes and a voltage is applied, glass behind the positive electrode is observed to glow (lower image), due to electrons emitted from the negative cathode. The above “official” account presupposes that one knows what an electron is and what are its physical properties (mass and charge). The discovery of the electron opened up a whole new chapter in the understanding of matter. This led to the realization that light and matter could not be fully understood using the classical laws of physics, and that a totally different way of understanding nature was needed. Thus emerged, beginning in the last years of the 19th century, a completely new description of light and matter. This new description became known as quantum mechanics, and resulted in the quantum theory of atoms, molecules and the chemical bond. This is the historical journey on which we shall embark in this Lecture. Cathode rays were discovered by  Julius Plücker  (1801-1868) and  Johann Wilhelm Hittorf (1824-1914).  Their experimental apparatus depended on two earlier inventions: 1) Volta’s battery; and, 2) a sealed glass tube in which a partial vacuum was maintained. The latter was invented by a  German  physicist and glassblower,  Heinrich Geissler , in 1857.

Hittorf observed that some unknown rays were emitted from the  cathode  (negative electrode) which could cast shadows on the glowing wall of the tube, indicating the rays were traveling in straight lines. In 1890,  Arthur Schuster  demonstrated cathode rays could be deflected by  electric fields , and  William Crookes  showed they could be deflected by magnetic fields. It was these experiments on cathode rays inside the cathode ray tube that drew the attention of Röntgen. After repeating the above experiments, he began to study the radiation emitted outside the cathode ray tube, using fluorescent chemical sensors, e.g., barium platinocyanide, to detect radiation. His discovery of x-rays on November 8, 1895 was communicated to the Physico-Medical Society of Würzburg later in November, 1895. A translation of his paper appeared two months later on January 23, 1896 in the English journal, Nature.   (You can dial up this article on Gallica and read it for yourself). Paraphrasing Louis XV (1710 – 1774) of France, were he not such a humble, unassuming man, Röntgen might have said " Après nous, le déluge " A controversy sprang up surrounding the interpretation of cathode rays. Most German physicists believed that cathode rays were some form of light (electromagnetic radiation). Thomson, a British physicist and head of the Cavendish Laboratory at Cambridge University (Newton’s alma mater), believed otherwise on the grounds that cathode rays could be deflected by both electric and magnetic fields, whereas electromagnetic radiation could not.

Thomson believed that cathode rays were a stream of charged particles and designed a variation on the earlier design of the cathode ray tube in which the cathode ray was subjected to combined electric and magnetic fields. See his apparatus below. In 1897, he showed that the cathode ray consisted of negatively charged particles smaller than atoms, the first " subatomic particles ", which were later named  electrons .  In the 19th century, the charge-to-mass ratios of ions were measured by electrochemical methods, using an apparatus first introduced by Faraday. In measuring the charge-to-mass ratio, Thompson showed that charged particles in the cathode ray were characterized by a charge-to-mass ratio much smaller than the ion of the smallest element, the hydrogen ion H+, by a factor of nearly 2000. Importantly, he realized that the previously-held view that the atom was the smallest, elemental “building block” of Chemistry could not be correct. He concluded that there must exist a subatomic structure of matter.

Thomson realized that the accepted model of a neutral atom did not account for negatively or positively charged particles. Therefore, he proposed a new model of the atom which he likened to English plum pudding. The negative electrons represented the raisins in the pudding and the dough contained the positive charge. Thomson's model of the atom did explain some of the electrical properties of the atom due to the electrons, but it failed to account correctly for the positive charges in the atom .

Over the years, I realized that a better metaphor than “plum pudding” for students is the watermelon. The black seeds are electrons, and the delicious red “stuff” the uniform background (cloud) of positive charge. .

The Nobel Prize in Physics 1906 was awarded to Joseph John Thomson "in recognition of the great merits of his theoretical and experimental investigations on the conduction of electricity by gases." At this point, the storyline takes an unexpected twist. While Thompson was undertaking his experiments, Röntgen, on New Years Day, 1896, mailed his manuscript (together with the photograph of his wife’s hand), to five scientists, one of whom was the celebrated French theoretical physicist, engineer, and philosopher of science, Jules Henri Poincaré, at that time President of the Académie française  (French Academy). Poincaré took Röntgen’s manuscript to the next meeting of the Académie, sharing its contents with those that attended. Poincaré was fascinated with the results of Röntgen’s study, and speculated that the unknown radiation might be similar to the kind emitted by fluorescent rocks and minerals. One of the members of the Académie who showed up that day was Henri Becquerel. Reports of that meeting comment that Becquerel was dozing off during the meeting, but woke up when Poincaré mentioned fluorescent minerals. Becquerel, following in the footsteps of his Dad and Grandfather, had been studying these interesting minerals for years. There is a great display of fluorescent minerals at Chicago’s Field Museum. Becquerel went back to his lab and began using naturally fluorescent minerals intending to determine whether the radiation emitted by these materials was, in fact, the  x-rays discovered by Röntgen. He exposed potassium uranyl sulfate to sunlight and then placed it on photographic plates wrapped in black paper, believing that the uranium absorbed the Sun’s energy and then emitted it as x-rays. His hypothesis was disproved on the 26th-27th of February, when his experiment "failed" because it was overcast and rained in Paris on those days. But, for some reason, Becquerel decided to develop his photographic plates anyway. To his surprise, the images were strong and clear, proving that the uranium emitted radiation without an external source of energy (such as the Sun). Becquerel had discovered radioactivity.

Becquerel used an apparatus similar to that displayed below to show that the radiation he discovered could not be x-rays. X-rays are neutral and can not be bent in a magnetic field. The new radiation was bent by the magnetic field so that the radiation must be charged and different from x-rays. When different radioactive minerals were put in the magnetic field, they deflected in different directions or not at all, showing that there were three classes of radioactivity: negative, positive, and electrically neutral.

The term radioactivity was actually coined by Marie Skłodowska Curie (1867-1934), born in Warsaw, Poland and later a  naturalized French  citizen. Together with her husband Pierre, she began investigating the phenomenon discovered by Becquerel. The Curies extracted uranium from ore and to their surprise, found that the leftover ore showed greater radioactivity than the pure uranium. They concluded that the ore contained radioactive elements other than uranium. This led to their discoveries of the elements polonium and radium. It took four more years of processing tons of ore to isolate enough of each element to determine their chemical and physical properties. BTW, if you discover a new comet or a new element, you can name it whatever you please. The first element discovered by the Curies was polonium, named after the country of Marie’s birth. If you go to the oldest quarter in Warsaw where she grew up, on the front of the apartment building where she lived, there are two large discs, one inscribed with the chemical symbol for polonium (Po) and the other for radium (Ra).

Together with Becquerel, they received the 1903 Nobel Prize in Physics "in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel." Later she was awarded the Nobel Prize in Chemistry in 1911 "in recognition of her services to the advancement of chemistry by the discovery of the elements radium and polonium, by the isolation of radium and the study of the nature and compounds of this remarkable element." Following is the press release of her visit to Chicago: June 3, 1921–Marie Curie, on her first trip to the United States, visits Chicago for two hours and is “besieged by newspaper men and women anxious to get her ideas on the fashions, the war, radium, woman suffrage, the political situation.” [Chicago Daily Tribune, June 4, 1921]. All Curie, the winner of two Nobel Prizes in Physics, wants to discuss, though, is Lake Michigan.  The Tribune reports, “To her the engineering feat of reversing the flow of the Chicago river to dispose of the city’s sewage was a problem far more interesting than a comparison of American styles with French creations.”  By nightfall she is off to Colorado with a topographical map of the western states in hand, a gift of Mrs. W. Lee Lewis of Northwestern University.

So, what are the mysterious rays emitted from radioactive minerals? Enter the story, Ernest Rutherford (1871-1937), a New Zealand-born British  physicist  who came to be known as the father of  nuclear physics . Einstein considered Rutherford to be the greatest experimentalist since  Michael Faraday  (1791–1867). In the years 1899 and 1900, physicists  Rutherford  (working in McGill University in Montreal, Canada) and  Paul Villard  (working in Paris) separated radiation into three types: eventually named alpha (α), beta(β) , and gamma (γ) rays by Rutherford, based on their penetration of objects and deflection by an electric field. A sketch of his experimental apparatus is shown below. Alpha rays were defined by Rutherford as those having the lowest penetration of ordinary objects.

Rutherford's work also included measurements of the ratio of an alpha particle's charge to mass ratio, which led him to hypothesize that alpha particles were doubly charged helium ions (later shown to be “bare” helium nuclei).  In 1907, Ernest Rutherford  and  Thomas Royds  finally proved that alpha particles were indeed ions of Helium, the second element in the Periodic Table of elements. To do this they allowed alpha particles to penetrate a very thin glass wall of an evacuated tube, thus capturing a large number of the hypothesized helium ions inside the tube. They then caused an  electric spark  inside the tube, which provided a shower of electrons that were taken up by the ions to form neutral atoms of a gas. Subsequent study of the spectra of the resulting gas showed that it was Helium and that the alpha particles were indeed the hypothesized helium ions. During this period, Rutherford also identified a signature of radioactive elements, the  half-life , and discovered the radioactive element Radon. This work was performed at  McGill University  in  Montreal , Quebec, Canada. It was the basis for the  Nobel Prize in Chemistry which he was awarded in 1908 (at age 37) "for his investigations into the disintegration of the elements, and the chemistry of radioactive substances.” Today, you can visit a museum on the McGill campus which displays his experimental equipment. In contrast to the Röntgen museum in Würzburg, you can benefit from a guided tour by a most enthusiastic and engaging curator.

The next piece in the puzzle was provided by Robert Millikan (1868-1953), an American experimental  physicist . Millikan graduated from  Oberlin College  in 1891 and obtained his doctorate at  Columbia University  in 1895. In 1896 he became an assistant professor at the  University of Chicago . In 1909 Millikan began a series of experiments to determine the  electric charge  carried by a single electron. His apparatus is shown below.

He began by measuring the downward trajectory of charged  water  droplets in an  electric field . The results suggested that the charge on the droplets is a multiple of an elementary electric charge, but the experiment was not accurate enough to be convincing. He obtained more precise results in 1910 with his famous “ oil-drop” experiment  in which he replaced water (which tended to evaporate too quickly) with  oil (which was “heavier”).

Since Thomson had already determined the charge-to-mass ratio of the electron,  q/m = −1.75882001076(53)×1011 C⋅kg−1 where q is the charge measured in Coulombs (C) and m is the mass measured in kilograms (kg). Once Millikan had determined the charge on a single electron, 1.602 x 10-19 C, he could calculate the mass m of the subatomic particle, the electron, 9.109×10−31 kg, and compare this with the mass of the smallest atom, Hydrogen, 1.67377 10-27 kg, the difference a factor of 1838.  The 1923 Nobel Prize in Physics was awarded to Robert Andrews Millikan "for his work on the elementary charge of electricity and on the photoelectric effect." Later, Millikan left the University of Chicago to become President of the newly founded Throop University in Pasadena, CA, known today as California Institute of Technology (Caltech), arguably the best university in the World (according to the Chinese).

Now, back to Rutherford. Rutherford designed an experiment to use alpha particles  emitted by a radioactive element as probes to the unseen world of atomic structure. See a sketch of his experimental apparatus below.

The target was a gold foil, hence the name, “gold foil” experiment. From Lecture 2, you recall that Gold is the most malleable of elements. It can be hammered into sheets of such thinness that you can see light passing through. If Thomson was correct, the beam of alpha radiation should go straight through the gold foil. Indeed, most of the beams went through the foil, but a few were deflected at wide angles, even backwards. This was crazy! If, in Thomson’s model, you had electrons embedded in a uniform background of positive “stuff,” and the electron has a mass ~1/2000 the mass of the smallest element (H), given that the mass of Helium is four times greater than the mass of H, how on Earth could an electron scatter an alpha particle that was ~ 8000 times heavier?

Rutherford presented, eventually, a new physical model for subatomic structure to interpret this unexpected experimental result. In this model, the atom is made up of a central charge (this is the modern  atomic nucleus ) surrounded by a cloud of orbiting  electrons . For definiteness, consider the passage of a high speed α particle through an atom having a positive central charge N e, and surrounded by a compensating charge of N electrons.

From purely energetic considerations of how far charged particles of known speed would be able to penetrate toward a central charge, Rutherford was able to calculate that the radius of the  gold  central charge (later called the nucleus of the atom) would have to be less than 3.4 × 10−14 meters. The radius of a single gold atom is ~ 10−10 meters or so. Comparison of these two radii revealed the astonishing result that the nucleus was a factor less than 1/3000 the diameter of the atom. Today, Rutherford’s model of the atom is (sometimes) called the “Solar System” model of the atom, representations of which you probably saw in grade school.

While the Rutherford model concentrated the atom's positive charge and a great deal of the mass in a very small core (the nucleus), thus counterbalancing negatively-charged electrons, so that the atom was electrostatically neutral, it did not account for the atomic mass.

Rutherford (and others) believed that there must be an elementary particle with a charge exactly opposite the charge on the electron, but having a (much) heavier mass. In a series of experiments performed by Rutherford and his student James Chadwick, they were able to change one element into another by hitting atoms with high energy alpha particles. They noticed that nitrogen (N), oxygen(O), and aluminum(Al), when hit with an alpha particle, disintegrated and emitted a fast particle of positive charge. To be more specific, hydrogen nuclei were always emitted in the process. In a dark room, they were able to observe flashes of light when alpha particles hit a florescent screen. They realized that the positive charge of any nucleus could be accounted for by a whole (integer) number of positively charged hydrogen nuclei, which were named protons by Rutherford in 1920.

Knowing the mass of the Hydrogen atom (essentially the mass of the proton, since the electron mass is ~ 2000 times smaller) poses a problem. Helium, the second element in the Periodic Table, has a mass four times the mass of a single proton. So, the Helium atom, must have more than “just” protons to account for the factor of four in mass. This conundrum was solved by a student of Rutherford, James Chadwick, with the discovery in 1932 of a new elementary particle, distinct from the proton, the neutron. The neutron has no charge, and a mass slightly greater than the mass of the proton. The conclusion reached was that the Helium nucleus has two protons and two neutrons, and is orbited by two electrons.

Further, it was this discovery that opened up the understanding of isotopes: two or more forms of the same element that contain equal numbers of protons but different numbers of neutrons in their nuclei, and hence differ in relative atomic mass but not in chemical properties. This point will be crucial in understanding nuclear chemistry, nuclear medicine, radiography, nuclear power plants and the atomic bomb. See Lecture 16. The Nobel Prize in Physics 1935 was awarded to James Chadwick "for the discovery of the neutron."

Two additional experiments, both involving the electron, need to be discussed before we can take up the quantum theory of the chemical bond, molecular structure, and chemical reactivity. The first deals with the “spin” of the electron. This involves consideration of a quantity called angular momentum. Angular momentum is the rotational equivalent of linear momentum, the latter defined as mass x velocity.  In physics, mass is given the symbol m, velocity v, linear momentum p, and angular momentum the symbol L.

Spin is one of two types of angular momentum in quantum mechanics (the other being orbital angular momentum). The existence of spin angular momentum was  inferred  from experiments, such as the  Stern–Gerlach experiment (see below), in which silver atoms were observed to possess two, discrete values of the angular momenta and no orbital angular momentum. The effect was attributed to “electron spin.” Electrons have an intrinsic angular momentum characterized by a (soon to be called) quantum number s. In Rutherford’s “Solar System” model of the atom, planets circling the Sun correspond to electrons orbiting the nucleus. Just as the Earth revolves on its axis, some describe electron spin as electrons spinning on their axis. Note that you can only spin in two directions, clockwise and counterclockwise. The spin quantum number s can take on only two values, s = +1/2 and s = − 1/2. In textbooks, these two values of the spin are shown as arrows, ↑↓ .

Stern–Gerlach experiment: Silver atoms travelling through an inhomogeneous magnetic field, and being deflected up or down depending on their spin; (1) furnace, (2) beam of silver atoms, (3) inhomogeneous magnetic field, (4) classically expected result, (5) observed result.

Otto Stern was a German-American physicist, awarded the Nobel Prize in Physics 1943 "for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton."

The second experiment is the Davisson-Germer experiment.

Between 1923 and 1927, Clinton Davisson  and  Lester Germer  at  Western Electric (later Bell Labs) , discovered that electrons scattered by the surface of a crystal of nickel (Ni) metal displayed a diffraction pattern. This confirmed the  hypothesis , advanced by  Louis de Broglie  in 1924, that an electron can “behave” like a wave or a particle, a foundational concept of quantum mechanics called wave-particle duality.

At the same time  George Paget Thomson  independently demonstrated the same effect firing electrons through metal films to produce a diffraction pattern. Davisson and Thomson shared the Nobel Prize in Physics in 1937.

Given the avalanche of unexpected experimental results, starting with Röntgen’s discovery of x-rays in 1895 and the demonstration of wave-particle duality in the 1920’s, the natural question is: What does this tell us about atoms, molecules and the chemical bond? Everything. The theoretical understanding of these phenomena sprang from analyzing two, apparently unrelated, experiments, both involving radiation. The first experiment centered on Black-body radiation,   thermal   electromagnetic radiation emitted by a  black body  (an idealized opaque, non-reflective body). It has a specific spectrum of wavelengths, inversely related to intensity, that depend only on the body's temperature.

As the temperature (in degrees Kelvin, K) decreases, the peak of the intensity of black-body radiation (vertical axis) moves to lower intensities and longer wavelengths. Conversely, when the temperature increases the radiation curve moves to higher frequencies. Theories to explain the behavior of the radiation curve using classical physics worked perfectly well at long wavelengths (lower frequencies) but failed completely at higher frequencies. The failure of classical theories in the regime of high frequencies was called the ultraviolet catastrophe. In 1900, the German physicist Max Planck (1858–1947) explained the ultraviolet catastrophe by proposing that the energy of electromagnetic waves is quantized rather than continuous. This means that for each temperature, there is a maximum intensity of radiation that is emitted in a blackbody object, corresponding to the peaks in the above figure, so the intensity does not follow a smooth curve as the temperature increases, as predicted by classical physics. Rather, Planck hypothesized that energy could only be gained or lost in integral multiples of some smallest unit of energy, a quantum (the smallest possible unit of energy). Energy can be gained or lost only in integral multiples of a quantum. Recall that in Lecture 13, we noted that in the classical theory of waves, the energy is given by E = ½ k A2 ( k = a constant, A = amplitude ) In Planck’s quantum theory of radiation, the energy is given by E = h ν ( h = a constant, ν = frequency) The constant h in the above equation is now called Planck’s constant. The Nobel Prize in Physics 1918 was awarded to Max Karl Ernst Ludwig Planck "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta."

The second experiment is called the photoelectric effect. The photoelectric effect is the emission of  electrons  or other  free carriers  when  electromagnetic radiation , like  light , hits a material.  According to  classical electromagnetic  theory, the photoelectric effect can be attributed to the transfer of  energy  from the light to an electron. From this perspective, an alteration in the  intensity  of light should induce changes in the kinetic energy (Kinetic Energy = ½ mv2, where m is mass and v is velocity) of the electrons emitted from the metal. According to classical theory, a sufficiently dim light is expected to show a time lag between the initial shining of its light and the subsequent emission of an electron.

Sadly, the experimental results did not correlate with either of the two predictions made by classical theory. Instead, experiments showed that electrons are dislodged only by the impingement of light when it reached or exceeded a threshold  frequency ν. Below that threshold, no electrons are emitted from the material, regardless of the light intensity or the length of time of exposure to the light. In 1905, Albert Einstein (1879-1955) solved this apparent paradox by describing light as composed of discrete quanta, now called photons, rather than continuous waves. By assuming that light actually consisted of discrete energy packets, with the energy given by Planck’s E = h ν , Einstein wrote an equation for the photoelectric effect that agreed with experimental results.

Albert Einstein in 1904 (age 25)

The Nobel Prize in Physics 1921 was awarded to Albert Einstein "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect."  In 1911 the  Belgian   industrialist   Ernest Solvay organized an invitation-only meeting at the Hotel Metropole in Brussels. Considered a turning point in physics, in the following year Solvay founded Conseil Solvay, the International Solvay Institutes for Physics and Chemistry and, after WW I, sponsored a series of historic meetings in Physics, Chemistry and Biology. In the iconic photograph below, you will recognize a few of the physicists and chemists noted in Lectures 13 and 14. Madame Curie is seated next to Henri Poincaré, Rutherford is standing just behind them, Einstein is second from the right in the second row, Planck and de Broglie are at the other end of the row.

Photograph of the first conference in 1911 at the  Hotel Metropole . Seated (L–R):  W. Nernst ,  M. Brillouin ,  E. Solvay ,  H. Lorentz ,  E. Warburg ,  J. Perrin ,  W. Wien ,  M. Curie , and  H. Poincaré . Standing (L–R):  R. Goldschmidt ,  M. Planck ,  H. Rubens ,  A. Sommerfeld ,  F. Lindemann ,  M. de Broglie ,  M. Knudsen ,  F. Hasenöhrl ,  G. Hostelet ,  E. Herzen ,  J. H. Jeans ,  E. Rutherford ,  H. Kamerlingh Onnes ,  A. Einstein  and  P. Lan gevin.