The Birth of the Quantum Theory

1. The Birth of the Quantum Theory Classically: Mechanics (Newton), Electromagnetism (Maxwell), Thermodynamics (Carnot, mayer, Helmholtz, Clausius, Kelvin), Statistical Mechanics (Maxwell, Clausius, Blotzmann, Gibbs). Start of Quantum Theory: A problem in classical Statistical Mechanics: Calculate the intensity of radiation at a given wavelength from a heated cavity. Planck solution: Only certain (discrete, quantized) energy levels are allowed. Einstein: Extended the quantization of energy to light (photoelectric effect). Compton: Light carries momentum as well as kinetic energy.

2. Maxwell theory of electromagnetism Alternating currents set up fluctuating electric and magnetic fields in the region surrounding the original disturbance. These waves have frequency equal to the frequency of the current oscillations. The radiated waves would behave in every way like light: reflection, refraction, polarization, interference and speed. “light wave also a type of Maxwell’s wave, created by extremely high frequency electric oscillators in matter”. AT that time the nature of these oscillators was not known, but they can emit light with frequency equal to the oscillator frequency. Need Proof !!

3. Hertz Experiment Seeking experimental evidence to establish the equivalence between light and the EM waves. Hertz (1883) verified experimentally that an oscillating electric current does indeed send out electromagnetic waves that posses every characteristic of light except wavelength. Oscillator: spark gap terminated in two small metal spheres with air gap of half inch. High voltage pulses produce high E oscillations Receiver: Simple loop antenna to detect radiation even at distances 100’s of meters. He showed that these waves could be reflected, refracted, …

4. Blackbody Radiation Can we use Maxwell equation of light to solve the following puzzle? Problem: Predict the radiation intensity at a given wavelength emitted by a glowing solid at a specific temperature. History Wedgwood (maker of china): in 1972 he observed that all objects in his oven, regardless of their chemical nature, size, or shape become red at the same temperature. Mid-1800: It was know by spectroscopy that glowing solids emit continuous spectra rather than the bands or lines emitted by heated gases. Kirchhoff (1859): Showed based on thermodynamics that for any body in thermal equilibrium with radiation, the emitted power is proportional to the power absorbed. Balckbody: an object that absorbs all the EM radiation falling on it and consequently appears black. (ideal radiator)

5. Stefan and Wien Laws Stefan (1879): He found experimentally that the total power per unit area emitted at all frequencies by a hot solid was proportional to the fourth power of its absolute temperature. Non-ideal radiator. Five years later, Boltzmann derived Stefan’s law from combination of thermodynamics and Maxwell’s equations. What about Energy !!! Wien’s Law: spectral energy density or energy per unit volume per unit frequency Experimental Verification: Paschen: Confirmed Wien’s law in the infrared range of 1-4 micro-m and for T=400-1600 K Lummer and Pringsheim/ Rubens and Kurlbaum (1990): Extended measurements to 18 micro-m and 60 micro-m: Wien’s law FAILED.

6. Planck: Birth of Quantum Theory Planck knew the following: Wien’s Exponential law agreed with experiment at low wavelength (high f) Rubens experiment proved that at high wavelength (low f), the spectral energy is proportional to T. He came up with his famous law for spectral energy density. Planck was convinced that blackbody radiation was produced by submicroscopic electric oscillators which he called resonators. He assumed that the walls of the glowing cavity were composed of billions of these resonators, all vibrating at different frequencies. Each should emit radiation with a frequency corresponding to its vibration frequency. Planck had to assume that the total energy of a resonator with frequency f should be multiple integer of hf. Emission of radiation of frequency f occurred when a resonator dropped to the next lowest energy state.

7. The Photoelectric Effect What is it? Electrons are emitted from metallic surfaces when exposed to light. Hertz (1883)Clean metal surfaces emit charges when exposed to UV light. Hallwachs (1888) the emitted charges were negative Thompson (1899) emitted charges were electrons Lenard (1902) electrons are emitted from the metal with a range of velocities and the maximum kinetic energy of the electrons Kmax does not depend on the intensity of the exciting light. Kmax increases with light frequency. This was unexpected classically. Also unexpected: The linear relationship between and Kmax frequency The existence of a threshold frequency (work function) There is no time lag between the start of illumination and the start of photocurrent. Conclusion: classical EM theory has major difficulties explaining the above.

8. Einstein’s Explanation Maxwell’s theory is successful in describing the propagation of light through space but not its interaction with matter. The energy of light is not distributed evenly over the classical light wave front, but is concentrated in discrete regions called quanta, each containing energy hf. Light quantum (photon) was so localized that it gives all its energy directly to a single electron in metal. The maximum kinetic energy is Kmax =hf – phi For fixed f, increase in intensity increase the number of photons and this gives more photoelectrons. Light of threshold frequency which has just enough energy to knock an electron out of the metal surface, cause the electron to be released with zero Kmax The variation of the threshold frequency for different metals is because of the different work functions. Kmax should vary linearly with frequency and the slope is h Millikan (1916) reported photoelectric measurement and found h with a precision of 0.5%.

9. Einstein: Photons Carry Momentum Einstein (1905): Introduced the concept that light consists of pointlike quanta of energy Einstein (1906): Concluded that a light quantum of energy E travels in a single direction and carries a momentum directed along its line of motion of E/c=hf/c. ”If a bundle of radiation causes a molecule to emit or absorb an energy packet hf, the momentum of quantity hf/c is transferred to the molecule directed along the line of motion of the bundle for absorption and opposite the bundle for emission”. Photon-particle collision Debye/Compton (1923): Scattering of x-ray photons from electrons could be explained by treating photons as pointlike particles with energy hf and momentum hf/c and conserving relativistic energy and momentum of the photon-electron pair in a collision. Particle picture of light: by showing that photons in addition to carrying energy hf, carry momentum hf/c, and scatter light particles. X-rays Roentegen (1895): discovered that a beam of high-speed electrons striking a metal target produced a new and extremely penetrating type of radiation.

10. The Compton Effect (1922) Experimental confirmation that x-ray photons behave like particles with momentum hf/c. They showed that the classical wave theory failed to explain the scattering of x-rays from free electrons. Classical theory predicted that incident radiation of frequency f0 should accelerate an electron in the direction of propagation of the incident radiation, and should cause forced oscillations of the electron and re-radiation at frequency f’, where f’<f0. Also, the frequency (or wavelength) of the scattered radiation should depend on the length of time the electron was exposed to the incident radiation as well as on the intensity of the incident radiation. Experimentally Compton found that the wavelength shift of x-rays scattered at a given angle is absolutely independent of intensity of radiation, and the length of exposure, and depends only on the scattering angle. Compton effect is evidence that when light interact with matter it behaves as if it is composed of particles with energy hf and momentum h/lambda. If the photon is a particle then what is the meaning of frequency and wavelength? What is its mass? Quantum theory: different experimental conditions gives the waves properties or the particle properties of light.