Quantum Physics

Quantum Theory Max Planck, examining heat radiation (ir light) proposes energy is quantized, or occurring in discrete small packets with a definite minimum value. (1901) All energy amounts were multiple of a certain constant, called Planck’s constant h with a value of 6.63 x Js Energy of radiation, E = hf

Max Planck

The Photoelectric Effect Hertz observed spark discharges improved with illumination (1898) Illumination of metal by electromagnetic radiation causes emission of electrons Could not be explained by wave theory Frequency of e-m radiation determines if emission occurs, not intensity

The Photoelectric Effect Each metal has minimum energy that must be supplied by light before emission occurs: called the work function of the metal. Each metal found to have cutoff frequency of incident light below which no emission occurs, no matter how intense the light Only particle theory of light could explain this

Einstein’s Explanation Light consists of stream of massless particles called photons having energy hf, moving along electromagnetic waves (1905) When photon strikes electron, it gives up all its energy to the electron If hf > w (work function of metal), emission occurs

Einstein’s Explanation Light intensity makes no difference if frequency is below a threshold frequency, f t Work function of metal = h f t Max. electron kinetic energy = hf - hf t Einstein won Nobel Prize for explanation

Albert Einstein

Laws of Photoelectric Emission Rate of emission is directly proportional to intensity of incident light Kinetic energy of photoelectrons is independent of intensity of incident light. Maximum kinetic energy of photoelectrons varies directly with difference between frequency of incident light and cutoff frequency of metal

Compton Shift Aurthur Compton sent X-rays into graphite X-rays scattered by collisions with electrons showed longer wavelength and lower energy Energy and momentum transferred from photon to electron Further support for particle nature of light

The Compton Shift Arthur Compton

The Quantized Atom Rutherford’s discovery of nucleus (1911) led to “solar system” model of atom Orbiting electrons contradicted e-m theory Niels Bohr (1913) proposed model of atom with electron orbits based on quantized energy states Difference between energy states always some multiple of Planck’s constant

Light Emission Electrons can absorb energy and “jump” to higher energy level When electrons fall to lower level, photon is emitted whose energy equals difference in the energy of the two levels Since frequency depends on energy, different energy changes cause different colors (frequencies) of light emitted

Niels Bohr Ernst Rutherford

Line Spectra Unique structure of each element results in unique pattern of emission lines for each element allowing identification by spectroscopy When light passes through the element (usually as a low pressure gas) same frequencies are absorbed from the spectrum

Continuous Spectrum When atoms are crowded together in a solid or dense gas, available energy levels are so numerous, all light frequencies are emitted White light is seen and when dispersed by a prism or diffraction grating, all colors are seen

The Hydrogen Spectrum Hydrogen spectrum first to be analyzed Visible emission lines predicted and observed by Balmer; called Balmer series. 6 uv emission lines (Lyman series) and 4 ir lines (Paschen series) discovered later.

Matter and Waves de Broglie proposed wave-particle duality applied to matter particles, photons must have momentum E = hf = mc 2 ; so mc = h/, photon momentum  h/mv, wavelength of particle with mass m and velocity v

Louis de Broglie

Matter and Waves All matter has wave properties but for large objects, wavelength is too small to be observed Wave nature of electron explains why only some orbits are stable: standing wave must fit in orbit Whole number of wavelengths must equal circumference of orbit

Matter Waves

X-Ray Production Reverse of photoelectric effect High energy electron beam strike metal causing emission of photons E K = hf max - w Frequency of photon depends on speed of electron

Werner Heisenberg

The Uncertainty Principle (Heisenberg, 1927) It is impossible to simultaneously measure particle’s position and momentum accurately Measurement of one quantity changes the other Electron’s location can only be described by probability

Erwin Schrödinger

The Wave Function Schrödinger (1926) proposed wave function (Ψ) that describes subatomic particles Probability of electron’s location can be found using the wave function Electron orbitals are probability distributions called electron clouds