Elements Periodic Table The periodic table of the

Elements

Periodic Table ] The periodic table of the elements was organized to explain chemical properties. • Quantum physics explained structure

Atoms ] Atoms are the smallest discrete unit of an element that has the same properties. ] • Nucleus: protons and neutrons • Electrons The atomic number of protons determines the type of element. • Total nuclear positive charge ] Atoms in a solid are typically separated by a few tenths of a nanometer. • Determined by electron orbits NIST

Mathematical Waves ] Newtonian mechanics is deterministic. ] De. Broglie’s work gave new direction to this thought. ] Schrödinger took the classical energy equation and made it into an abstract wave equation. ] The wave variable y was called the wavefunction. • Particles and trajectories ] Optics needed waves to account for interference. ] Theorists in the 1800’s wondered if there should be a wave version of mechanics as well.

Probability Waves ] The wavefunction cannot be directly measured and is an information wave. • Represents the state of a system ] The square of the wavefunction relates to the probability of a particular measurement. • Compare intensity to amplitude of an EM wave Rough one-dimensional form without time dependence

Electron Orbits ] The electron in the Bohr atom has a probability of being at a given radius. • Radius of Bohr equation most likely ] The average matches macroscopic results by the correspondence principle.

Quantum Numbers ] The Bohr model of hydrogen provided a single quantum number n. • Principal quantum number • One-dimensional solution ] Schrödinger’s equation for a real atom is 3 -D. • Two other quantum numbers • Orbital angular momentum • Orbital magnetic number (electron spin) 1 2 3 Shells for the principal quantum number n

Orbital Shells ] ] ] A. Clark, Chemical Computing Group ] Atomic quantum numbers were named for spectral lines. The Bohr shells have capital letters: 1=K, 2=L, 3=M, 4=N The orbital angular momentum shells have small letters: 0=s, 1=p, 2=d, 3=f, 4=g The electron spin is up or down: maximum two electrons per shell.

Electron Configurations ] Electrons in atoms populate the lowest energies first. • Two electrons per state for spin ] Atoms have unique ground states. • • Hydrogen has 1 1 s electron Helium adds another 1 s Lithium must start 2 s shell Boron starts 2 p shell which holds 6 electrons H He Li Be B C N O

Energy Levels ] ] Subshell: S G F D P Period • • 1 2 3 4 5 6 7 8 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 3 d 4 d 4 f 5 d 5 f 6 d 5 g 6 f 7 d 2 p 3 p 4 p 5 p 6 p 7 p 8 p ] The shells don’t fill up in exact order. • Patterns match the periodic table ] Exact energy levels are determined by quantum calculations.

Molecules ] Electron orbits can overlap between atoms. ] If the potential energy is lower a chemical bond is formed, creating a molecule. ] Energy is required to break bonds, sometimes releasing more energy as new bonds form.

Spontaneous Emission ] Atomic electrons can be excited by external radiation. • EM waves • Electrons in a field ] Atoms emit light when the electron returns to the ground state. • Random release time • Transition occurs spontaneously

Stimulated Emission ] Some atoms can be induced to emit light when they are excited. ] The triggering photon is not absorbed. • Continues after interacting • Triggering photon ] The emitted photon is coherent with the triggering photon. • • • Same phase Same direction Same polarization

Avalanche ] Many atoms can be pumped to an excited state at once. • Few begin discharge ] The light strikes other atoms and a coherent avalanche of light forms. • Semisilvered mirror amplifies the beam ] Light Amplification from Stimulated Emission of Radiation = LASER

Crystal Scattering ] Atoms in a crystal are arranged in uniform layers. • Spacing similar to x-ray wavelength. ] The layers can act as a reflection grating. ] ] The path difference for a reflection grating is twice the separation. The angles of the diffraction rings are used to determine the crystal spacing.

X-Ray Diffraction ] For crystals in random orientation the x-rays will diffract in circles. The angles of the diffraction rings are used to determine the crystal spacing.

Fermi Distribution ] Electrons in material are not all at the same energy. • Thermal motion increases some more than others ] ] Discrete energy states get filled up by available electrons. The last filled is the Fermi energy

Band Theory ] ] Real materials have gaps in the energy levels. Conductors have the Fermi energy away from a gap. ] Insulators have the Fermi energy in a gap. • Difficult for electrons to jump the gap

Semiconductors ] Semiconductors have a small gap that can be controlled with small amounts of impurities. • Parts per million or billion ] Electrons that jump between bands in a semiconductor may give off light. • Frequency based on energy f = E/h • Light Emitting Diode: LED