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Light and Atoms

The almost sole source of information of the Universe outside the immediate vicinity of the Earth is light that is borne to us from the source located in some distant corner of the Universe. Visible light for the most part of human history, but also other kinds of light (like X-ray and Infra red) over the last couple of decades. In order to understand the story the light we receive tells us we need to understand the process by which light is emitted and absorbed by material. This route to this understanding is nearly as circuitous as the path to the understanding of Gravitation and dynamics.

Pre-History

The history of light seems to have been at least as confusing as that of astronomy. People knew of the use of curved mirrors as weapons to burn using the Sun for a long time. Still there remained confusion as to the correct theory of sight. Pythagoras suggested we saw because our eyes irradiated light that reached out (like a cockroach's antennae) and touched things that we then saw. Epicurus, however suggested (300 years later) that light emanated from a source (like the Sun) and reached our eyes on reflection from objects that we then saw. Euclid, who lived during the same time however continued to accept the Pythagorean hypothesis. It wasn't until 1000 A.D., when under the influence of the Arab physicist, Alhazen, that the Pythagorean hypothesis was dropped.

It was accepted that light propagated rectilinearly, in rays. Euclid knew that on reflection off a mirror the angle of incidence was equal to the angle of reflection. Ptolemy knew that when light passed from a lighter to a denser material (as from air into water) the direction of the ray bent towards the normal to the bounding surface between the two materials. Snell introduced the Snell's law (or the Sine law) that states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant. When one of the material is vacuum then the constant is called the index of refraction of the other material. Fermat could explain these phenomenon using the Fermat's principle which stated that rays of light traveled the path of least time. This meant that the velocity of light was less in dense media than in lighter media.

This was the situation until diffraction, the transmission of light around corners (like sound), was observed. This lead Christiaan Huygens to propose that light consisted of waves. This was strengthened by observations of the interference of light resulting in, for example, colors in a thin film of oil on a wet surface. Newton however discounted these small deviations from rectilinear motion and stated that light was made of small projectiles (or packets of energy). Subsequent work by a large number of physicists resulted in the acceptance of the Huygens' picture of the wave nature of light, with one modification. Huygens had light waves as longitudinal, i.e., oscillating in the direction of motion (like sound waves), whereas the newer wave theory had the light waves to be transverse oscillating normal to the direction of motion (like ocean waves). Correspondingly there was felt a need for some material to fill the parts of the Universe that was previously thought to be empty, like between the Sun and Earth. This Universal material was referred to as Ether. This theory was made more elegant and placed on a proper footing by Maxwell who stated the laws of electromagnetism with mathematical rigor and generalized the concept of electric current. He could then predict the existence of electromagnetic waves. These waves had a constant speed (regardless of frequency, i.e., color) in vacuum called c. This constant could be measured from electrical circuits. However measurements of the speed of light indicated it to be close to the value of c. This lead to the understanding of the connection of electromagnetism and light. That these two were connected had already been shown by Michael Faraday.

The wave theory of light held the imagination of the people until Plank showed that light as radiated by matter behaved like it was a stream of corpuscles. Einstein showed through the photoelectric effect that light when absorbed by matter also behaved like corpuscles. A proper understanding of these phenomenon together with the wave like properties of light observed through diffraction and interference led to quantum mechanics that properly explained the interactions of light and matter.

The Indivisible Atom

Since Lucretius atoms were thought of as indivisible bits of matter. Actually Lucretius was stating the philosophy of Epicurus in the form of poetry. Not much is known of Lucretius other than that he wrote this poem and he is alleged to have committed suicide, having been driven insane by a love potion. Epicurus on the other hand led a life of serenity and repose, opening a school that admitted (unlike any other then) women and at least one slave. Water and barley bread was the usual repast and he saved the lives of the school members by rationing out beans during a famine. Contrary to suggestions by jealous Stoics life in his school, although by no means monastic, was not full of irregularities. Even in his extremely painful death throes from prostatitis his last act was to dictate a very affectionate letter to all his students.

The Atom divided

In 1897 Sir Joseph John Thomson discovered the electron and changed this long standing view of the atom. It was known that when an electric discharge was passed through air or any gas enclosed in a chamber, rays emanated from the air or gas. These were called cathode rays. Thomson showed that these rays were streams of particles, he called electrons. He concluded that these electrons were bits of the atoms of the gas loosened by the electric discharge. And thus managed to do the impossible and broke the atom. He hypothesized that the atom was a sphere of positive charge with electrons (possessing negative charge) embedded in them. This is referred to as the plum pudding model. One of Thomson's students, Ernest Rutherford, a New Zealander, brought about the next revolution in atomic physics. He joined McGill University in Montreal for a salary of 500 pounds that while small he felt was enough to get married on and have a child. There he proceeded on his work with radioactivity and found how to measure the electric charge and mass of the daughter products of radioactive materials like thorium. One of these daughter products was the alpha particle, which was a positively charged heavy particle. When he shot these at thin sheets of gold most went straight through, but a few were deflected by small angles. His students Gieger and Marsden found that a very few were even scattered all the way back in the direction they were shot from. Rutherford concluded that the positive ions in atoms occupied a very small region (contrary to the plum pudding model) with the electron somehow distributed around it. This had been suggested earlier by a Japanese physicist Hantaro Nagaoka. But the model found it hard to gain acceptance because it was hard to imagine how one could hold up the negatively charged electrons without it falling back to the positively charged nucleus. If you tried to think of the electrons around the nucleus like a solar system, it doesn't work as well, because unlike planets, electrons possess electric charge. This means that if set in circular motion, they radiate light. This means they lose energy (as if they had a friction acting on it) and gradually reduce the radius of their orbits and fall into the nucleus.

Quantum Mechanics

Light Quanta

A black body is a perfect absorber. Kirchoff had defined it as an object that absorbed all light shining on it and re-emitted it all back when the source of light was switched off. The distribution of energy radiated by a light source at different colors is called its spectrum. Light of a specific color is associated with electromagnetic waves of a specific wavelength or frequency. So a spectrum can be quantified as the intensity of light of a specific wavelength. In the case of a blackbody the spectrum has a specific form that depended only the temperature of the blackbody and not on its constitution. Max Planck found a form that fitted the spectrum of a blackbody very accurately. This form is called the Planck's law. But he went beyond that. He assumed energy of light was proportional to its frequency (color). Further he assumed that the blackbody absorbed and re-emitted radiation energy in little packets. Then he could derive the Planck's law. Soon after this Einstein also argued that light appeared to behave as little packets in certain circumstances.

The Bohr Atom

One of Thomson's students, Niels Bohr was interested in the problem of electrons and atoms. However finding Thomson not very interested in his work he moved to work with Rutherford who had moved back to Manchester from McGill. He solved the problem of the stability of the Rutherford atom by introducing the new laws of quantum mechanics on the atom. He postulated that the atom could only exist in a distinct set of states each characterized by a specific energy. He postulated that while the atom was in a specific state it would not radiate. Only when it made a transition from one state to the next could it radiate. And the energy radiated equaled the difference of the energies characterizing the two states. As a corollary an atom in a specific state could only absorb light of a certain energy and make a transition from one state to another separated by the same energy. This tied in wonderfully with Planck's law and his postulates of absorption and emission of discrete packets of energy as well as Einstein's work on absorption of light by matter in discrete packets of energy.

The Astronomical Spectra

Long before all this, Joseph Von Fraunhoffer had already observed that if he looked at the Sun through a prism there were dark lines. These came to be called Fraunhoffer lines. In view of the Bohr atom these could now be understood. The sun radiates light with a certain spectrum. This is called the continuum because there are no gaps in the spectrum. But when the light passes through thinner, colder material in the outer parts of the Sun some of the light gets absorbed by the atoms and molecules. As Bohr stated, atoms in a specific energy state absorb light of only one energy (i.e., color or frequency). Of course the atom re-emits the light but there are many other directions for the light quanta to go to other than in its original direction. So very little light of that particular color will reach us. This will appear as a dark line in the Sun's spectrum. Then knowing the spectrum we should expect from the Sun and that we see we can say a lot about the constituency of the outer regions of the Sun and of the material between the Sun and Earth. Or for that matter anything between any source in the Universe and us. Of course this is complicated by the fact that we don't always know what the spectrum expected from an astronomical object should be like. But we can observed similar stars in different direction in the sky. Presumably they will have different amounts and composition of intervening material. So the shared characteristics of the spectrum tells us about the intrinsic spectrum of the stars. As a corollary the characteristics not shared by the spectra says something about the intervening material. It was in this identification and classification of the stellar spectra that the some of the first female scientists started making inroads into Astronomy.


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