PHYSICS 111 LASER AND LIGHT

CHAPTER 3

MODERN THEORIES OF LIGHT Blackbody radiation experiment was the first to generate a wide spread interest among physicists to reformulate the theory of light. Before this experiment, light was firmly established as a wave phenomenon, from the evidence drawn from Young's double slit experiment.

THE BLACKBODY RADIATION EXPERIMENT: The continuous spectrum of colors in the visible part of electromagnetic radiation, emitted by a hot solid body is often the practical example of an ideal blackbody radiation. A black body by definition emits and absorbs all wavelengths of electromagnetic radiation. In the experiment, the blackbody is kept at a constant temperature and, the power of electromagnetic radiation coming out of the blackbody is measured as a function of wavelength. If we look at the spectrum of a solid through a spectrometer, we find a continuous band of colors from blue to red. But the spectrum from a gas is discrete in nature. Different gases emit different discrete lines of colors, whereas the spectrum of a solid is almost the same for all solids.

BLACKBODY RADIATION: The continuous spectrum emitted by a hot solid is often approximated as the spectrum of a hot ideally blackbody. The spectrum of hot body shows that its power is not distributed evenly among all is wavelengths. It has a definite peak power for a certain wavelength of radiation if the temperature is constant. It is also found that its power decreases for both short and long wavelength regions.

Wavelength of maximum power of radiation is determined by the blackbody's actual temperature. This curve of radiation power versus wavelength obtained in blackbody radiation experiments, was the object of vigorous mathematical treatments by many scientists aimed at explanation.

The English scientists Lord Rayleigh (1842-1919) and James Jean (1877-1946) used classical ideas of electromagnetism and statistical mechanics to derive a mathematical formula to explain the curve obtained in blackbody radiation experiment. Their work known as Rayleigh-Jean's curve only partially explained the experiment. It failed to explain the short wavelength region of the radiation curve. Later, the German Physicist Max Planck (1858-1947) found the correct assumption to derive the mathematical formula that explained the blackbody radiation curve. The law bears his name as Planck's Radiation Formula. The correct assumption Planck made, was the definition of energy. A blackbody emits energy in quanta. This energy of radiation is proportional to frequency. The constant of proportionality is a universal constant, called Planck's constant and is denoted by "h".

Energy, E=hf

Later on, Einstein made it more inclusive by stating that the blackbody absorbs and emits energy of radiation in quanta. The blackbody radiation curve was the pioneer of quantum physics.

A series of further investigations with light produced a large evidence for Quantum nature of light. The foundations of the quantum physics are based in the quantum nature of light that came out of experiments and related theoretical investigations. These are Rutherford Scattering, photoelectric effect, Compton effect, Mosley's law, Franck-Hertz experiment, Bragg's law, de Broglie's theory of matter-waves, Schrodinger's wave mechanics and Bohr's theory of an atom. Of these we shall discuss photoelectric effect, Bohr model of an atom and de Broglie's matter-wave concept.

PHOTOELECTRIC EFFECT: First discovered in 1887 by Heinrich Hertz. He found negative charges are released from the metal when its surface is irradiated with electromagnetic waves in the ultraviolet or visible.

Results of photoelectric effect:

a) Energy of the emitted electrons is independent of the intensity of radiation

b) There exists a threshold frequency of the incident energy, below which no electrons are emitted, no matter how intense the beam of radiation is. If the frequency of radiation is greater than the threshold frequency, the extra energy seems to increase the energy of emitted electrons.

c) No time lag between the irradiation and production of emitted electrons

d) Number of the emitted electrons is proportional to the intensity of radiation falling on the metal surface. Maximum energy of the emitted electrons for a fixed incident energy of one frequency, is the same.

e) Different metals have different threshold frequencies.

In 1905 Einstein explained photoelectric effect which fetched him the Nobel Prize in physics in 1921. He explained, assuming light or electromagnetic wave as a particle, which collides with the atom of the metal while irradiated, and in the process knocks out an electron from the atom. It requires certain minimum amount of energy of light to produce emitted electron. This minimum energy is related to the threshold frequency. This is because emitted electrons are slightly bound to the solid before emission. The process is like an inelastic collision between a photon and the electron. In modern theory light considered particles are called PHOTONS.

Photoelectric effect cannot be explained by wave theory of light. In quantum theory, light is absorbed and emitted in quanta as assumed by Planck.

THE NUCLEAR ATOM: Rutherford model of an atom. Earnest Rutherford and his coworkers used a thin gold foil as target that was bombarded by positively charged Alpha particles (a Helium atom stripped off its two electrons). They found most of the Alpha particles to pass without hindrance. But some were scattered at various angles. A few were back scattered which led Rutherford to formulate the result of the experiment assuming an atom to made up of tiny massive center called nucleus and orbiting electrons surrounding it. But, this model failed to explain the discrete spectra obtained in the gas discharge lamps.

BOHR MODEL OF AN ATOM: Neils Bohr gave the first successful model of an atom, which explained the discrete spectra observed through a spectrometer.

He made the following bold hypothesis,

1. Electrons revolve around the nucleus in certain discrete orbits, not in any orbit at any distance from nucleus.

2. Electron in the atom does not radiate any energy while in those discrete fixed orbits. Electron in the atom absorbs energy if it jumps from lower to a higher orbit. Electron emits energy if it jumps from higher to a lower orbit. The emitted energy or the absorbed energy is equal to the difference in the electron energy between the two orbits.

3. Angular momentum of the orbiting electron is proportional to an integer value. Constant of proportionality is Planck's constant "h".

Bohr was able to point out that energy emitted or absorbed by an electron in the atom is discrete. Because electron orbit and its energy in such orbits are fixed. The energy difference of the two orbits is equal to the discrete energy emitted or absorbed by the electron in the atom. This results in the discrete spectra of discharge lamps.

de BROGLIE'S MATTER WAVES: Louis de Broglie predicted the wave character of any particle. He showed that the momentum of a particle is related to particle's wavelength (called de Broglie wavelength). The wavelength of a particle is given by,

l= h/mv, where mv is the momentum of the particle.

Hence, quantum physics was formulated on the basis of matter waves. Wave and matter are compatible with each other. He pointed out that waves have particle properties just as particles have wave properties.