Chapter 4 Part 1 Quantum Theory

The Planetary Model

Why a Quantum Theory? How do electrons move around the nucleus? Bohr/Rutherford model of the atom left questions…… How do electrons move around the nucleus? Why don’t electrons get pulled into the nucleus? If Newton’s Laws explain the motion of massive objects moving at ordinary speeds, what laws explain electron motion, almost massless particles moving at nearly the speed of light? What do light and electrons have in common?

Why a Quantum Theory? Bohr/Rutherford model of the atom left questions…… 4. When light from excited atoms is passed through a prism, what explains the unique pattern of colors that each produces?

Emission Line Spectrum The spectrum of brightly colored lines characteristic of the emitting substance subjected to some kind of excitation energy.

Emission Spectrum of hydrogen gas produces unique “fingerprint”

What is light? a form of electromagnetic radiation (EMR) that travels in waves

What is electromagnetic radiation? A form of energy that exhibits wave-like behavior as it travels through space. Has both electric and magnetic field components, which oscillate in phase perpendicular to each other AND perpendicular to the direction of energy propogation.

Electromagnetic Energy

What is electromagnetic radiation? Electromagnetic radiation is classified according to the frequency (and energy) of its wave. The electromagnetic spectrum arranges all forms of EMR in order of its frequency and wavelength. The spectrum consists of radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays

The electromagnetic spectrum

Speed Speed (c ) constant for all EM Radiation: c = 3.00 x 108 m s

Wavelength Wavelength ( ) The distance the wave travels in one full cycle measured in m, cm or nm 1cm = 1 x 10-2m 1nm = 1 x 10-9m visible light range 400-750nm

Frequency Frequency ( ) Number of wave cycles per second 1 wave cycle = 1 = s-1 = 1 Hertz 1 second s

Amplitude Amplitude (A) height of the wave from the rest position to the crest (intensity, brightness)

The wave equation Relates speed, frequency and wavelength. The Wave Equation: c =  Relates speed, frequency and wavelength. Since c is constant,  and  are inversely proportional

PARTICLE PROPERTIES OF LIGHT Some experimental results could NOT be explained by the wave theory of light!

The Photoelectric Effect: the emission of electrons from the surface of a metal when light of sufficient frequency (and energy) shines on the metal

The Photoelectric Effect

The photoelectric effect Einstein proposed that light has quantized “energy particles” called photons; quanta of radiant E PHOTON: A QUANTUM OF RADIANT ENERGY Radiation is absorbed or emitted only in whole numbers of photons. Einstein uses quantized energy to explain photoelectric effect and won Nobel Prize for this work

ELECTRON TRANSITIONS IN ATOMS

ELECTRON TRANSITIONS IN ATOMS Ground State: state of lowest E Excited State: states with more potential E Electrons cannot exist between the E levels!

The E of the e- increases as it absorbs a quantum of E and moves into higher orbits father from the nucleus Quantum: a discrete amount of electromagnetic energy.

When e- drops back to lower-energy orbit, the quantum of E returns in the form of EM radiation - a photon of light is emitted. Photon: particles of electromagnetic radiation (EMR) having zero mass & carrying a quantum of Energy. Radiation emitted has characteristic color() frequency () and energy (E) Energy of photon = ∆ E b/w the E levels

Quantum Leaps Max Planck proposed that energy absorbed or emitted by atoms is “quantized” with a fixed amount of energy. Quantum: minimum amount of energy that can be lost or gained by an atom Planck’s Law: E=h

Photon Energy

THE BOHR MODEL OF THE HYDROGEN ATOM Bohr connected Planck’s idea of quantized energy to the planetary model. Hydrogen’s one electron exists around the nucleus only in certain allowed orbits with definite energies. Used Planck’s equation (E=h ) to calculate all of the observed frequencies in hydrogen’s emission spectrum. First to see connection between the wavelengths an element emits and its atomic structure. Bright line spectra are evidence that E levels exist in atoms.

DeBroglie’s “matter waves” Light is now understand as having both the properties of waves (wavelength) and the properties of particles (mass). We call this wave-particle duality. Louis DeBroglie explored the idea of particles acting as waves and called them “matter waves”. He found that all matter has wave properties but only very small particles moving very fast will exhibit noticeable wave properties.

Heisenberg’s Uncertainty Principle Heisenberg discovered that it is impossible to know the position (or path) and momentum (mass x velocity) of an e-at the same time. This is called the Uncertainty Principle. The e- is so small that measuring it throws it off course and creates uncertainty in the second measurement. In other words, we can’t observe particle and wave properties in the same experiment.

Electron Configurations Chapter 4 Part 2 Electron Configurations

A new approach to the atom: The Quantum Mechanical Model Treats the electron as a wave that has quantized its energy. Their probable location is described by regions around the nucleus called orbitals. Orbital is the space occupied by two electrons. Orbitals have characteristic shapes, sizes & energies.

Bohr model has “orbits” – this implies a definite path Quantum Model has orbitals - give probable path

Electron Cloud Electrons can act As particles moving fast around a nucleus As waves spread around the nucleus Electron cloud is a good visual model.

Electron Cloud /Wave Model of the Atom

Electron Cloud /Wave Model of the Atom

Electron-Wave Erwin Schrodinger developed an electron-wave equation to describe electrons. The solutions to the his equations are called QUANTUM NUMBERS.

Quantum Numbers n = principal quantum number Indicates the main energy level occupied by the electron. n = 1 to 7

Quantum Numbers l = angular momentum (orbital) quantum number Indicates number of sublevels & shape of orbital. l = 0 to n-1

The orbital quantum number # sublevels which sublevels orbital shape 1 s sphere 2 s, p peanut 3 s, p, d double peanut 4 s, p, d, f flower

Quantum Numbers m = magnetic quantum number Tells the orientation of the orbital around the nucleus in three dimensions along x, y or z axis. m = -l to + l

Quantum Numbers S = spin quantum number Tells direction of electron spin, up or down, OR clockwise and counterclockwise. S = +½ or -½

Orbital Shapes

Giving atoms a stable home life… Think of quantum numbers like the address of the e-: two e- can’t occupy the same space. Two electrons in an orbital are paired and have opposite spins. Unpaired e- in equal-energy orbitals have parallel spins. The electron configuration of lowest E is the most stable and has the maximum number of unpaired e-… This is another way to state Hund’s Rule.

Writing Electron Configurations Electrons configurations are written for atoms in their ground state – the most stable configuration possible. Electron configurations are determined by distributing electrons in main energy levels, sublevels, and orbitals based on a set of principles or rules.

Rules for filling sublevels & orbitals The Aufbau Principle: e- go into orbitals from lowest E to highest E Hund’s Rule: e- are placed in equal-energy orbitals one at a time before pairing; this minimizes e- repulsion.

Rules for filling sublevels & orbitals The Pauli Exclusion Principle: Two e- per orbital maximum Two e- in the same orbital must have opposite spins; this prevents them from spinning out of their orbitals. Therefore: NO TWO ELECTRONS HAVE THE SAME SET OF FOUR QUANTUM NUMBERS!

Energy Level Overlap In the 3rd and 4th energy level, sublevels begin to overlap. There is even more overlapping when n=5 and n=6! The effect is : the atom has lower overall energy and is more stable. See energy level diagram or arrow diagram!

Aufbau (Arrow) Diagram Is easy to reproduce from memory AND Gives order of filling IF arrows are followed from their tails to their tips:

Aufbau Diagram

Exceptions to Aufbau Rule Chromium [Ar] 4s13d5 two half-filled sublevels = special stability Copper [Ar] 4s13d10 one full & one half-full = special stability Silver [Kr] 5s14d10 Gold [Xe] 6s14f145d10

Lewis electron dot diagrams A useful notation which shows the valence s and p electrons in an atom (and whether they are paired or unpaired) around the element symbol. Any e- that have a lower principal quantum number are not included! Valence e- are involved in bonding!!!

Procedure for drawing Lewis dot diagrams Write the electron configuration for the element. Select all the valence s and p electrons in the highest main energy level. (Ignore any that have a lower principal quantum number!) Draw dots around the four sides of the element symbol to represent the valence s and p orbitals.