 Welcome to Quantum Mechanics 4, atoms. Until now we've been concerned exclusively with light. We saw that Max Planck was able to describe the variation of thermal radiation intensity versus frequency, but only by proposing that energy is transferred in discrete quanta, thus giving birth to quantum theory. Soon it became clear that these chunks of energy correspond to momentum carrying particles of light that we call photons. The wave nature of light places fundamental limits on the precision with which we can simultaneously know related quantities, such as photon momentum and position. This uncertainty principle is one aspect of the so-called wave particle duality that characterizes photons. Starting with this video we want to turn our attention to matter, specifically the atom. The concept of atoms has been around since antiquity. We put, matter is either infinitely divisible or it is not. And if it isn't then there must be a smallest indivisible unit of a substance that we call the atom. Democrates and Lucretias were two of the ancients who argued philosophically for this idea. The scientific basis for atomic theory can arguably be said to begin with John Dalton. He proposed that the fundamental substances, the elements, are composed of identical atoms. Scientific numbers of atoms of different elements can combine to form molecules characteristic of a compound substance. For example, two hydrogen atoms and one oxygen atom combine to form one water molecule. Consequently, any quantity of water will always be exactly two parts hydrogen and one part oxygen. Chemical reactions between compounds are then simply the rearrangement of their constituent atoms. All atoms are bound into molecules and why different atoms have different chemical properties remain a mystery. In addition to displaying unique chemical properties, different materials often display distinctive colors when they burn. By the late 19th century this idea had been refined with great precision through the study of atomic spectra. In place of a flame an electric current can be discharged through a pure gas sealed in a glass tube. The emitted light can be resolved into a spectrum of constituent colors using a prism or for more precision a so called diffraction grating. Each element is found to emit a unique spectrum. The reason for this was another mystery of the atomic realm. When an incandescent light bulb is viewed through a diffraction grating we observe a continuous rainbow spectrum. A graph of light intensity versus wavelength shows a continuous spectrum of the type Planck's law describes. But when electric current is passed through a gas, helium in this case, the spectrum displays a distinctive pattern of colors. It's characterized by discrete spectral lines at specific wavelengths instead of a continuous spectrum. Why does helium only emit light at these wavelengths? And why do different elements emit different spectra? What physical process gives rise to these emissions? These questions were topics of intense research near the end of the 19th century. As the first element in the periodic table and the lightest gas, hydrogen was presumably the simplest atom. So it became a focal point for atomic research. Hydrogen displays a series of spectral lines that are named after the different researchers who first studied them. In the ultraviolet, near 100 nanometers is the Lyman series. In the visible region is the Balmer series and so on. Empirically it was found that these spectral lines follow a simple pattern described by the so-called Rydberg formula. The inverse of any of these wavelengths equals the Rydberg constant R times 1 over n squared minus 1 over k squared, where n and k are integers with k greater than n. Each n value corresponds to a particular series while the k values correspond to the lines in that series. For example, n equals 2 is the Balmer series in the visible region, k equals 3 is a red line, k equals 4 is blue and larger values of k are in the violet end of the spectrum. Any theory of the hydrogen atom must be able to explain the Rydberg formula. A key piece of the puzzle fell into place with the discovery of the electron in 1897 by J.J. Thompson. He used an early cathode ray tube, the device that evolved into the TV picture tube. Inside an evacuated glass tube are metal plates connected to a voltage source. There's a negative plate called the cathode and two positive anode plates with slits cut in their centers. It's found that for a high enough voltage something is emitted from the cathode and moves towards the anodes. Some of that emission passes through the slits and forms a so-called cathode ray which travels to the end of the tube, strikes a phosphorous screen and produces a visible dot. Thompson put two more metal plates inside the tube parallel to this beam. Applying a voltage to those plates created an electric field between them and by varying this electric field Thompson found he could bend the beam thereby moving the dot on the screen. The direction of the bending showed that this beam carried a negative electrical charge. Thompson also placed wire coils on either side of the tube. Passing electric current through the coils produced a magnetic field and an electric charge moving through this magnetic field is subject to a force. By varying the magnetic field Thompson could also bend the beam and move the visible dot. The electric and magnetic fields can be combined and adjusted so their effects on the cathode ray precisely cancel. Thompson assumed the ray was composed of particles of mass M and charge minus E moving with velocity V all three of which were unknown. The magnitude of electric force is charge times the known electric field E and the magnetic force magnitude is charge times velocity times the known magnetic field B. These had been adjusted to cancel out so Thompson knew that the force magnitudes were equal although they pointed in opposite directions. This gave him an equation from which the velocity V is the ratio of the known electric field E to the known magnetic field B. Thompson found that the cathode ray was traveling very fast more than one tenth the speed of light. Now he turned off the magnetic field and observed the effect of the electric field alone. The electric field exists only in a region of length L between the charged plates. The ray is moving to the right with velocity V. Between the plates the electric force will accelerate it upward. When it exits the plates it will be traveling at an angle determined by the original rightward velocity V and the added upward velocity. The latter is the electric force divided by the electron mass that is the upward acceleration times the time spent between the plates which is the distance L over the velocity V. By measuring this angle Thompson could determine the charge to mass ratio E over M. He found this was about a thousand times as large as the estimated value for a positively charged hydrogen ion, what we now call a proton, as obtained by electrochemical methods. Since a proton and an electron together form an electrically neutral hydrogen atom they must have opposite charges. So the difference in their charge to mass ratio must be due to a difference in mass. Thompson concluded that the electron is only about one thousandth the mass of a proton. Following the discovery of the electron Thompson proposed an atomic model in which atoms consist of positively and negatively charged components. For hydrogen the bulk of the atomic mass is contained in a cloud of positive charge E. In this floats a much smaller and lighter electron of negative charge minus E. This model was very appealing because it seemed to unlock one of the mysteries of the atom, the existence of discrete spectral lines. If the positive charge is uniformly spread out through a sphere of radius A and the electron is displaced from the sphere's center a distance R, then the electron feels a net force only from the positive charge inside the radius R, the dark blue region. The forces from charge in the light blue region pull in different directions and cancel out. The charge Q in the dark blue region is the total charge E times the fraction of the volume occupied by the dark blue region, namely R over A cubed, because the volume of the sphere varies as its radius cubed. The force pulling the electron back towards the center is the product of charges E times Q divided by the distance R squared. When you put in the expression for Q you end up with a force which is a constant times the displacement R. A force that varies proportional to displacement is characteristic of a spring. So in the Thompson model the electron is bound to the atom by a type of electric spring. A mass on a spring oscillates with a single definite frequency. Calculating this for hydrogen gives a frequency and wavelength of ultraviolet light near the Lyman spectral series. The radiation produced by an oscillating electron is precisely described by electromagnetic theory, which in Thompson's day had already been known for decades. Here we show two views of the electric field of an electron. When the electron is at rest the field is unchanging. As the electron begins to oscillate its electric field peels off in waves which radiate away at the speed of light. These waves carry away energy so the oscillation energy of the electron will decrease. This gives us a picture of how passing electric current through a gas produces light. Suppose a hydrogen atom with its electron at rest at its center suffers an intense collision which transfers energy to the atom and displaces the electron. The atom's electric spring then causes the electron to oscillate. As it does it produces radiation which carries the energy away causing the electron to come back to rest and the radiation to stop. Another collision can restart the process. Now a major shortcoming of this simple model is that it predicts only a single radiation frequency when we know that real atoms emit series of spectral lines. Still, we seem to be headed in the right direction. The discovery of the electrons show that atoms were not fundamental particles but built from more elementary objects. However, Thompson's experiment measured only the electron charged the mass ratio and did not determine charge or mass independently. Because of this, it did not definitely establish the electron as a specific particle. For example, in a given electric field one could conceivably have a series of particles with different charges and masses but all having the same charge to mass ratio. Maybe they were different sized pieces of the same stuff. Yet their behavior in the electric field would be identical. To rule this out one needed to establish the charge of a single electron. The fundamental charge was measured in 1909 by Robert Millican. Millican achieved this in his so-called oil drop experiment. Here's the idea. A chamber was formed between two parallel metal plates. The top plate had a hole in the middle. The distance between the plates was d. You could look through the chamber, using a microscope actually, at a ruler. An oil mist was sprayed above the top plate and occasionally a tiny oil drop would fall through the hole into the chamber. Millican wanted to know the mass of the oil drop. In principle you could measure the radius of the drop directly with the ruler but it's so small that precise measurement isn't practical. Instead, Millican timed the oil drop falling with its terminal velocity, which is very small, over a relatively long distance, which could be measured accurately. And it gave him the value of the terminal velocity. When something is falling at terminal velocity, the downward pull of gravity, m times g, is balanced by the upward air drag, Fd. There's a formula called Stokes law that gives the drag, in terms of known properties of air, the radius of the oil drop and the terminal velocity. Knowing the effective density of the oil, you could relate the radius to the volume and hence to the mass. The equation mg equals Fd then has a single unknown, the radius r, which can be solved for. Thus Millican determined the size, mass, and weight of the oil drop. Knowing the oil drop's weight, he then applied a large voltage between the plates. This created an electric field. If the oil drop carried any static electricity, this produced an upward force that could be adjusted to just balance the weight, causing the oil drop to stay suspended in the chamber. Millican knew the electric field in terms of the voltage and plate separation, so he could solve for the static electrical charge. He did this many times and always found that the charge was an integer number of a fundamental charge, which he identified as the charge of a single electron. Thus Millican was able to see the effects of single electrons, and to show that these were identical in all cases. And together with Thompson's results, this established the electron as a unique particle with known charge and mass.