CHAPTER 6: ATOMS & STARLIGHT

Chapter in brief:

6-1. ATOMS
Rutherford-Bohr Planetary Model of an Atom, electrons, nucleus, protons, neutrons, mass and dimensions
 
Different kinds of atoms: 114 kinds called chemical elements, stable and unstable atoms, isotopes, ionization, ion, molecule
 
Electron Shells: Coulomb's force, binding energy, quantum physics, permitted orbits, atom and the ion of the same element have different sizes and permitted orbits.
 
6-2. THE INTERACTION OF LIGHT AND MATTER
Excitation of atoms, energy levels, excited atoms, ground state, emission and absorption processes
Radiation from a heated object: black body radiation, bell shape curve, wavelength of maximum intensity, discrete and continuous spectrum, absolute zero.
 
Formation of a spectrum: Absorption and emission spectrum, dark line spectrum, absorption lines and emission lines, bright line spectrum, Kirchhoff's 3 laws,
Law 1: hot solid or liquid or dense gas produces continuous spectrum
Law 2: low density excited gas atoms produce emission line spectrum
Law 3: light comprising of continuous spectrum passing through a low density hot gas, produces absorption line spectrum.
 
Hydrogen spectrum: electron transition, Lyman series, Balmer series, Paschen series and Pfund series
 
6-3. STELLAR SPECTRA
The Balmer thermometer: second energy level, surface temperature of stars - 2,000 to 40,000 oK,

weak Balmer lines in stars cooler than sun - because of lack of atomic collisions,

weak Balmer lines in hotter (more than 2,000 oK) stars - because of violent collisions - at times knocking off electrons, this means ions are produced and not much Balmer lines, at intermediate temperatures (near 10,000 oK), regular collisions produce strong Balmer lines,
strength of Balmer lines depends on the temperature of the star's surface layer.
Other thermometers- ionized calcium or ionized iron or titanium oxide for hotter stars and ionized helium for cooler stars.
 
Spectral Classification: Astronomer Annie Cannon observed and classified 250,000 stars. Seven Spectral Classes or types are O, B, A, F, G, K and M.
 
Spectral sequence is a temperature sequence - O stars are hottest and M stars are coolest - sub-classification into 10 more divisions for each class of stars, example of naming a star is A1 or B4, numbers showing finer temperature scale - larger number signifies lower temperature
 
The Doppler effect: It is a phenomenon in which an observer at rest hears high or low pitch sound from a passing siren in an ambulance or a police car. This effect is used to measure the radial velocity of the moving object.

Chemical composition: The chemical composition of most stars is found from the data of the spectra of the stars. Sodium D-lines - wavelength at 589 and 589.9 nm.

 
NEW TERMS
nucleus, proton, neutron, electron, isotope, ionization, ion, molecule and Coulomb's force, binding energy, quantum physics, permitted orbits, energy level, excited atom, ground state, black body radiation, wavelength of maximum intensity, continuous spectrum, absolute zero, joule, absorption line, absorption spectrum (dark line spectrum), Kirchhoff's 3 laws, electron transition, Lyman series, Balmer series, Paschen series, spectral class or type, spectral sequence, Doppler effect, radial velocity
 

CHAPTER DETAIL
The question to be answered in this chapter is, "How atoms interact with light?" So far, in the last 5 chapters, we studied what we see with our eyes and these observations are explained by use of theories and models. This chapter begins with a new subject called "Astrophysics". The subject area of Astrophysics relates to the applications of physics in the studies of Astronomy or sky. The secrets of stars are not made clear by naked eye observations alone. We explore other scientific methods in the studies of the stars starting with this chapter. This chapter is treated as a tool for understanding the chapters ahead.
In 19th century, the Munich optician Joseph von Fraunhofer found as many as 600 dark lines that exist in the spectrum of sunlight. These dark lines were later explained as absorbed light by atoms in the surface of the star. It provided information about the constituent elements of the sun's surface. Spectral measurements can be analyzed to find out the temperature of the star.
Spectral wavelength is measured to find the speed of the star relative to earth.

 

Model of an Atom: The planetary model of the atom consists of a tiny massive nucleus at the center and orbiting electrons surrounding the nucleus. Atom as a whole is electrically neutral. The nucleus contains protons that are positively charged, the electrons that are negatively charged and the neutrons that are electrically neutral particles. Size of an atom is measured in Angstorm (one of 10 billions parts of a meter) while that of the nucleus is 10,000 times smaller than Angstorm. Protons and neutrons are the particles that make up most of the mass of an atom. 

So, we may say that a typical atom is 1x10-10 m. The size of the nucleus is 1x10-15 m. Protons and neutrons are the particles that reside inside the nucleus. An atom that has lost one (may also gain one) or more electrons, is called ion. The process of converting a neutral atom into ion is called "ionization."

Isotopes of an element have the same atomic number (equal to number of protons in the nucleus) but possess different mass because of deficiency or excess mass of neutrons.

A molecule is formed by two or more atoms bound together. Hot stars seldom permit atoms to form chemical bonds resulting in the formation of a molecule. Exceptions are the cool stars where Titanium oxide (TiO) is known to be present. Collisions among atoms in hot stars produce ions.

QUANTUM PHYSICS: When particles are small (e.g., atoms, electrons) and sizes are not large, the physical properties can be described by a set of rules different from everyday familiar notions. These rules or laws are what constitute the branch of physics called "Quantum Physics." One of the laws of quantum physics states that the location and speed of a particle can be simultaneously determined only with limited accuracy. The product of the uncertainties of location and its motion (momentum relating to speed) is always greater than a number called Planck's constant. This law challenges the REALITY of our ability to perform. What follows in these notes will use ideas of quantum nature and behavior of atoms and subatomic particles.

Electron shells: The ancient Greek scholars believed the motion of a planet to be generated by the rotating crystalline spherical shell. It was the model of the universe. In case of an atom, the picture is similar. The negatively charged electrons orbit around the center called the nucleus of an atom. The nucleus is massive containing positively charged protons and electrically neutral particles called neutrons. The electron and the positively charged nucleus are bound by an attractive electric force known as Coulomb's force. The energy needed to free the orbiting electron from the nucleus is called binding energy. The orbit radius of anyone electron is fixed in this model called Bohr model of an atom. This means that all orbits are not permitted for anyone electron. When an atom accepts a quantum of energy (called photon), the outer electron jumps from its stable orbit to a permitted higher orbit. This process is called absorption of a photon. When an atom releases a quantum of energy (called photon), the outer electron jumps from higher orbit to a permitted lower orbit. This process is called emission of a photon. The permitted orbits of the electrons in an atom depend on the charge of the nucleus or type of the atom.

Interaction of light and matter: Each permitted orbit in the atom has a specific amount of binding energy associated with it. This fixed energy of each orbit is referred to as energy level. When an atom moves from one energy level to another, the energy difference between the two levels, is the energy either absorbed photon or emitted photon. In the normal state of an atom, the outer electron stays in the lowest possible orbit. Such a state of an atom is called ground state. Whenever an atom absorbs a quantum energy the outer electron moves to higher orbit and, the atom is said to be in an excited state. This happens when the electron leaves its ground state. An atom may move to an excited state if it collides with another atom as in a hot gas. A photon may be absorbed by an atom, triggering an electron transition to a higher orbit or excited state.

Black body radiation: About one hundred years ago, the outcome of a simple experiment with heated object resulted in a break through or revolution in physics, called the quantum revolution. When a piece of iron is heated, it begins to glow with a color of deep dull red initially. When the heating is intense, the color changes to bright red, to orange, to yellowish white and finally to white color. This is because the electron in the iron atom makes transition to higher energy levels. Initially, the amount of energy absorbed is small resulting in deep dull red color (lower frequency). As the iron atom begins to absorb greater chunk of energy, it emits photon of higher energy such as yellow or green and blue photon. The final mixture of it seems like white color in our eye.

Radiation from a hot body. Wavelength of maximum intensity given by Wien's Displacement law.

Hydrogen spectrum: Characteristic spectral lines produced by heated hydrogen gas and viewed through a prism.

Balmer series: The series of discrete color lines in the visible from heated hydrgen gas.

STELLAR SPECTRA: The 21cm radio frequency radiations from outer space suggest concentration of hydrogen atoms in the stars. The Balmer thermometer.

DOPPLER EFFECT: Everyone is familiar with the change in the intensity of siren from a moving Ambulance. This is called Doppler effect in sound. Similar effect is also detected in the case of light of certain wavelength.

Photons, Discrete Nature of Light:

Max Planck (1858-1947) argued emission of radiant energy by ideal radiators (blackbodies) is not continuous.

Energy transported by EM wave is not continuously distributed over wavefront defined by crests. Energy is actually located at discrete points, photons, along wavefront

Photons - discrete representation of electromagnetic radiation which carrys discrete or definite amounts of energy 1905, Einstein used Planck's idea of discrete nature for emission of light to explain a phenomenon discovered in 1887 known as photoelectric effect. Photon concept rests on extensive body of experimental and theoretical evidence. Conclusion today is that light does indeed exhibit a discrete nature

Properties of Photons: Energy content in photon inversely proportional to its wavelength. Shorter wavelength, more energetic is photon Longer wavelength, less energetic is photon. Equation for energy content:

Energy of photon = hc/l        
where h = Planck'sconstant                                       
c = velocity of light
l = wavelength
Photons move with velocity of light in straight lines
Photons are massless and electrically neutral
Photons Interaction With Matter

A hot body emits photons of discrete amounts of energy in all directions. Photons are created inside atoms of radiating body from which they receive their energy content. Photon energy content remains constant while traveling through space. Photons may be absorbed by atoms when they encounter matter; they lose their identity by transferring their energy to atom. Creation and destruction of photons by atoms is a classic example of conservation of energy.

Paradox of Light: Concept of light as being either particle or wave is quite possible. Light behaves as discrete photonsin some experiments and also, behaves as continuous waves in other experiments.

              This concept seems self-contradictory and contrary to experience. When we think of discrete entities, marbles or pebbles, applicable concepts, such as size, precise location, etc, come to mind. For massless photons, such concepts have no meaning.

Max Born said, "The ultimate origin of the difficulty lies in the fact (or philosophical principle) that we are compelled to use the words of common language when we wish to describe a phenomenon, not by logical or mathematical analysis, but by a picture appealing to the imagination. Common language has grown by everyday experience and can never surpass these limits."

              Laboratory experiments designed to inquire about either light's wave nature or its corpuscular nature. No experiment will simultaneously yield discrete and wave properties of light.

Max Born said, "We can therefore say that the wave and corpuscular descriptions are only to be regarded as complementary ways of viewing one and the same objective process, a process which only in definite limiting cases admits of complete pictorial interpretation...."

              Mathematical resolution of paradox

              Wavelength characterizes wavelike properties of light

              Energy content refers to its discrete nature of light

              Fact that wavelength and energy content can be linked in mathematical equation

(Energy of a photon = hc/l) strongest argument for duality ~ light cannot be simultaneously wave and photon.

The Balmer thermometer: The intensity in the Balmer series of visible spectral lines is related to the temperature of the gas body emitting the lines.

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Updated 01/14/2014