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# Energy as wave and particle

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Energy as wave and particle
The Quantum Model Energy as wave and particle

Bohr Model Electrons are a HUGE deal in chemistry
Responsible for chem rxns Today: How many are there Where do they reside

Periodic Table

Electron Configurations
Electron configurations are...

Electron Configuration Vocab
Principle Energy Level correlates to the period (1-7), periods go from left to right across the periodic table Sublevel are located in the principle energy level. There are 4 that we will talk about s, p, d and f. Orbital located in the sublevel. Where electrons are most likely to be found 1 ORBITAL HOLDS 2 ELECTRONS

Writing Electron Configurations
Principle Energy Level[sublevel]number of electrons OR a[b]c Get your periodic table! Start from left to right!

Orbital Diagrams Tool for creating electron configurations
2 dimensional representation of where electrons are in an atom

Aufbau Principle electrons are added to the lowest available energy level. Hydrogen as an example:

Pauli Exclusion Principle
each orbital can hold two electrons those electrons must have opposite spins spin is represented by the arrow facing up or down.

Hund’s Rule Orbitals of equal energy are occupied by one electron before 2 electrons occupy 1 orbital. The second electron is added after all orbitals have one electron

Aufbau Diagram

Noble Gas Configuration – Short cut
Locate the element on the PT Trace backward to the nearest noble gas Put that noble gas in [] (brackets) Fill in remaining electrons

Principle Quantum Numbers
Quantum numbers define the characteristics of a particular electron. Work as an address for the electron electrons repel each other, no two electrons can have the same address. Pauli Exclusion principle

Quantum Numbers – electron Address
State City Street Number of your home n - principle energy level 1, 2, 3, l – sublevel “shape” of the region of space (s, p, d, f) m - orbital orientation axes of the magnetic moment. s – spin Can be +1/2 or –1/2 for electrons

Valence Electrons Electrons in the HIGHEST energy level (n)
Electrons that interact during chem rxns Always in the s & p sublevels

Finding Valence Electrons
Locate the highest energy level Count the electrons present Orbital diagrams SUPER helpful Example: Sulfur How many valence e’s?

Shapes of s orbitals s orbital

s orbitals

Shapes p orbitals Nodal plane

P orbitals in more detail
p sublevel 3 orbitals x, y & z Work like a coordinate plane Atoms are 3-D

Shapes of d orbitals

Heisenberg Uncertainty Principle
An electron’s location and speed cannot be determined at the same time. If we cause change to find one variable, we are no longer looking at the actual e- situation. If we need to slow or stop it to locate it or if we need to locate it to find its speed, then we allow the chance of change. So quantum mechanics can tell us the probability that an electron is somewhere, but it does not tell us how it got there.

Nodal Surfaces A nodal surface is a region that defines the border of an orbital. This is where the probability function equals zero. Electrons CAN NOT exist in this area. Nodal surfaces are NOT spherical for other orbitals. Nodal surfaces are spherical for the “s” orbitals. 2p orbital 3s orbital

The Electromagnetic Spectrum

What is light? Wave Particle

Wave Comparison Red Light Low frequency Long wavelength Violet Light
nm = 1 x 10-9 m Red Light Low frequency Long wavelength Violet Light High frequency Short wavelength

Waves & Wavelength How many wavelengths are represented in each figure below?

C= It stands to reason that if energy is constant then  (wavelength) is inversely proportional to  (frequency). OR As wavelength increases frequency decreases

Max Planck Max Planck mathematically determined “h” that could be multiplied by  to solve for energy (E) every time an electron gave off light as it fell. (This simply means that all wavelengths are proportional) E = h Thus E will tell us the relative distance apart of each energy level in a given atom based upon the spectral lines.

C= Remember that Einstein told us that matter and energy are the same thing. Matter is simply frozen energy. From Einstein we were able to come up with several more equations to understand quantum mechanics. C=  = wavelength Ex: yellow orange = 580 nanometers So as in the lab, using a spectroscope we can determine the wavelength of the color of light (). We can solve for frequency () mathematically.

De Broglie De Broglie argued that as particles (i.e.electrons) drop back to lower energies, photons of energy are given off in “packets” or specific amounts called quanta. His doctoral board scoffed and was ready to deny his degree but changed their minds when Einstein supported him fully. His model changed the Bohr model so that all elements could be explained according to their frequencies of energy. Remember that energy is constant and that standing waves are quantized as well (they only increase by multiples of ½)

De Broglie Essentially the model went from de Broglie Bohr to

Spectra With the de Broglie Model, it became possible to explain the spectral lines of all models. Each wavelength would allow electrons to fall back to lower energy levels emitting various energies which translate to frequencies thus defining a wavelength

Hydrogen Emission Spectrum

Some Atomic Emission Spectra
Hydrogen Mercury Argon Helium

de Broglie and Wave Model
An electron in its path is associated with a wavelength. The wavelength depends on the mass:

Example Problem What is the characteristic wavelength of an electron with a velocity of 5.97 x 106 m/s? (Use 9.11 x kg for the mass of an e-)

Bright-line Spectra Atoms are quantized, existing only in definite energy states so an atom absorbs a specific quanta of energy pushing electrons to higher energy levels. An “EXCITED” electron jumps from its ground state to a higher energy level. The energy cannot be maintained so it falls back to where it came from losing exactly the same amount of energy that it absorbed.

Energy of Electrons We can calculate the energy the electrons of a hydrogen atom emit when they fall by using the Balmer equation So if an electron falls from the 6th energy level to the 2nd energy level then – Note: energy levels are not actually distances between electrons and the nucleus. n = 3,4, k = constant = 2.179x10-18

Excited atoms

Quantum or Wave Mechanics
Schrodinger applied idea of e- behaving as a wave to the problem of electrons in atoms. He developed the WAVE EQUATION Solution gives set of math expressions called WAVE FUNCTIONS,  Each describes an allowed energy state of an e- E. Schrodinger

Waves: standing, travelling
Q1 - A standing wave is the combination of two waves (travelling in opposite directions). It has nodes, where a portion of the wave remains stationary (spring demonstration) W = 0.5 W = 1.5 W = 1 W = 2 Notice that a standing wave (which is what an electron is) can only have certain wavelengths (0.5, 1, etc.) because the ends are fixed as nodes

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