Quantum Physics

Quantum TheoryMax 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 10-34 JsEnergy of radiation, E = hf

Max Planck1858-1947

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 EffectEach 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 lightOnly 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 electronIf hf > w (work function of metal), emission occurs

Einstein’s Explanation

Light intensity makes no difference if frequency is below a threshold frequency, ft

Work function of metal = h ft

Max. electron kinetic energy = hf - hft

Einstein won Nobel Prize for explanation

Albert Einstein

1879-1955

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 ShiftAurthur 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

1892-1962

The Quantized AtomRutherford’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 EmissionElectrons can absorb energy and “jump” to higher energy levelWhen electrons fall to lower level, photon is emitted whose energy equals difference in the energy of the two levelsSince frequency depends on energy, different energy changes cause different colors (frequencies) of light emitted

Niels Bohr

1885-1962

Ernst Rutherford

1871-1937

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 = mc2 ; so mc = h/ , photon momentum

h/mv , wavelength of particle with mass m and velocity v

Louis de Broglie

1892-1987

Matter and Waves

All matter has wave properties but for large objects, wavelength is too small to be observedWave nature of electron explains why only some orbits are stable: standing wave must fit in orbitWhole 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

EK = hfmax - w

Frequency of photon depends on speed of electron

Werner Heisenberg

1901-1976

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

1887-1961

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