By the end of the 1800’s, classical physics had many successes. One prominent physicist even had suggested that all that remained was to further increase the significant digits for measurements. However, at this same time, several observations were directly in conflict with the classical understanding. We describe three of this first. The existence and behavior of absorption and emission lines in light spectra was one such observation. A very crucial one was the way light was emitted from a heated object, called ‘blackbody radiation’. Lastly, when light is incident on a conducting surface, electric charge was observed to be released which was impossible to understand classically. Understanding these observations led to a wholly different model of matter and energy we call ‘quantum mechanics. Atomic Spectra L4 A difficulty with the classical paradigm of physics arose when measurements of white light were passed thru gases. The spectrum of this light was observed to be missing very specific wavelengths, and the set of wavelengths missing (or 'absorbed') was unique to each chemical element in nature. Additionally, these elements could be made to emit light and the set of wavelengths of that emitted light was specific to each element and the same as the set of absorbed wavelengths. Since there was no model of an atom aside from a point-like particle, there was no way to understand the specificity of this behavior of light. • if you take a low pressure gas & cause an electric discharge (like a neon light) o You will observe bright narrow lines, and dark elsewhere  lines at specific λs  "emission spectrum" • if you pass white light through a gas  dark narrow lines on a bright continuum  "Absorption spectrum" • each element has unique set of lines o how Helium was discovered o lines of emission at same λs as those of absorption • no way to understand or predict patterns of lines classicallyBlack Body Radiation In attempting to understand the properties of light as emitted by matter, the concept of a 'blackbody' has become useful. Such an object absorbs all electromagnetic radiation that is incident on it and therefore heats up. The heated body then re-radiates this electromagnetic radiation in a characteristic spectrum called a 'blackbody spectrum'. The observed properties of this spectrum were that at small and large wavelengths, the intensity of emission were tiny. However, for some characteristic wavelength, the intensity of emission was a maximum. This 'peak wavelength' is correlated directly with the temperature of the blackbody – warm bodies radiate with a smaller peak wavelength than cooler bodies. Classically, the spectrum of blackbody radiation could only be calculated on the assumption that all wavelengths of light were possible in the emission. This led to the calculation that the observed intensity should be infinite when approaching wavelengths of 0 size. This unphysical result was a major blow to classical physics. • an object at temperature, T o emits thermal radiation. This is not reflected light, or light generated by chemical or nuclear reactions in the material. It is originating from the motion of the atoms in the material. o e.g. room temperature produces infrared light (i.e. longer wavelength than red)  characteristics depend on T o The object will emit λs from the whole spectrum but the intensity will peak at some λ o as the object gets hotter the peak moves to higher energies: IR-R-Y-G-B-V-UV classically o radiation from accelerated charged particles in atoms (vibrating) near surface of object  like small antennae o range of λs from range of energies of accelerating particles • A black body o ideal system absorbing all radiation incident on it Example: red glowing coals deep in a cooking grill is a decent approximation Observations • plot intensity of light vs. λ • as T up, peak λ down (Wien's Law) • total power, P o related to area under the curve o P ∝ T4 (Stefan's Law) which means total power increases very rapidly as temperature increases• classical expectation o have continuum of λs and energies for oscillation need to split energy evenly among all wavelengths Intensity of light emitted, I, is calculated classically to be infinite when λ near 0 (classically) - violates conservation of energy (can’t have infinite energy when put in finite amount of energy) - this is not what is observed “Quanta” L9p1 • M. Planck, 1900 • Assume radiation within the cavity is from “atomic oscillators” - remember, moving charge produces electromagnetic waves - also, heated objects have rapidly vibrating (oscillating) atoms - so oscillating atoms produce light we see as blackbody radiation - still no model of the atom, yet Then make 2 assumptions o The Energy of each oscillator can only have certain discrete values E = n h f n = quantum number; h = Planck’s constant, f = frequency  So each oscillator can have quantum states {0, 1hω, 2hω, 3hω, …} o Oscillators emit or absorb energy only when making transitions from one quantum state to another ΔE = m h f (m = n2-n1)  If we now calculate the energy emitted by a black-body o Don’t equally distributed Energy accross various λ bins (equipartition) o We must weight each λ bin according to a well-defined distribution that governs the occupation of higher energy states (This is the Boltzman distribution law) The weighting factor is (e-ε/kT). Classical Experiment Intensity wavelength 0 1 h fω 2 h f 3 h f 4 h f 5 h fEnergy level diagram L9p2 Short wave length  Large energy separation  Low probability of excited states  Few downward transitions Long wave length  Small energy separation  High probability of excited states  Many downward transitions Planck model L9p3 o Average energy is associated with a given λ  Product of E of transitions & factor related to probability of transition occurring  at low frequencies, close together energy levels - high probability to go thru transition - many contributions, but each generates low energy (long wavelength)  As energy levels are further apart - would correspond to larger energy released in transition from one level to next - a shorter wavelength, high frequency - probability of