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Electrons in Atoms

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Models of the Atom OBJECTIVE: l Summarize the development of atomic theory.

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Models of the Atom OBJECTIVES: l Explain the significance of quantized energies of electrons as they relate to the quantum mechanical model of the atom.

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Greek Idea l Democritus and Leucippus l Matter is made up of solid indivisible particles l John Dalton - one type of atom for each element

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J. J. Thomson’s Model l Discovered electrons l Atoms were made of positive stuff l Negative electron floating around l “Plum-Pudding” model

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Ernest Rutherford’s Model l Discovered dense positive piece at the center of the atom- nucleus l Electrons would surround it l Mostly empty space l “Nuclear model”

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Niels Bohr’s Model l He had a question: Why don’t the electrons fall into the nucleus? l Move like planets around the sun. l In circular orbits at different levels. l Amounts of energy separate one level from another. l “Planetary model”

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Bohr’s planetary model l Energy level of an electron l analogous to the rungs of a ladder l electron cannot exist between energy levels, just like you can’t stand between rungs on ladder l Quantum of energy required to move to the next highest level

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The Quantum Mechanical Model l Energy is quantized. It comes in chunks. l A quanta is the amount of energy needed to move from one energy level to another. l Since the energy of an atom is never “in between” there must be a quantum leap in energy. l Erwin Schroedinger derived an equation that described the energy and position of the electrons in an atom

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l Things that are very small behave differently from things big enough to see. l The quantum mechanical model is a mathematical solution l It is not like anything you can see. The Quantum Mechanical Model

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l Has energy levels for electrons. l Orbits are not circular. l It can only tell us the probability of finding an electron a certain distance from the nucleus. The Quantum Mechanical Model

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l The atom is found inside a blurry “electron cloud” l A area where there is a chance of finding an electron. l Draw a line at 99 % l Think of fan blades The Quantum Mechanical Model

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Atomic Orbitals l Principal Quantum Number (n) = the energy level of the electron. l Within each energy level, the complex math of Schroedinger’s equation describes several shapes. l These are called atomic orbitals - regions where there is a high probability of finding an electron. l Sublevels- like theater seats arranged in sections

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Summary s p d f # of shapes Max electrons Starts at energy level

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By Energy Level l First Energy Level l only s orbital l only 2 electrons l 1s 2 l Second Energy Level l s and p orbitals are available l 2 in s, 6 in p l 2s 2 2p 6 l 8 total electrons

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By Energy Level l Third energy level l s, p, and d orbitals l 2 in s, 6 in p, and 10 in d l 3s 2 3p 6 3d 10 l 18 total electrons l Fourth energy level l s,p,d, and f orbitals l 2 in s, 6 in p, 10 in d, ahd 14 in f l 4s 2 4p 6 4d 10 4f 14 l 32 total electrons

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By Energy Level l Any more than the fourth and not all the orbitals will fill up. l You simply run out of electrons l The orbitals do not fill up in a neat order. l The energy levels overlap l Lowest energy fill first.

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Electron Arrangement in Atoms OBJECTIVES: l Apply the aufbau principle, the Pauli exclusion principle, and Hund’s rule in writing the electron configurations of elements.

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Electron Arrangement in Atoms OBJECTIVES: l Explain why the electron configurations for some elements differ from those assigned using the Aufbau principle.

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Increasing energy 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 3d 4d 5d 7p 6d 4f 5f Aufbau diagram

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Electron Configurations l The way electrons are arranged in atoms. l Aufbau principle- electrons enter the lowest energy first. l This causes difficulties because of the overlap of orbitals of different energies. l Pauli Exclusion Principle- at most 2 electrons per orbital - different spins

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Electron Configuration l Hund’s Rule- When electrons occupy orbitals of equal energy they don’t pair up until they have to. l Let’s determine the electron configuration for Phosphorus l Need to account for 15 electrons

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l The first two electrons go into the 1s orbital l Notice the opposite spins l only 13 more to go... Increasing energy 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 3d 4d 5d 7p 6d 4f 5f

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l The next electrons go into the 2s orbital l only 11 more... Increasing energy 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 3d 4d 5d 7p 6d 4f 5f

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The next electrons go into the 2p orbital only 5 more... Increasing energy 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 3d 4d 5d 7p 6d 4f 5f

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The next electrons go into the 3s orbital only 3 more... Increasing energy 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 3d 4d 5d 7p 6d 4f 5f

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Increasing energy 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 3d 4d 5d 7p 6d 4f 5f The last three electrons go into the 3p orbitals. They each go into separate shapes 3 unpaired electrons = 1s 2 2s 2 2p 6 3s 2 3p 3

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The easy way to remember 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s 2 2 electrons

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Fill from the bottom up following the arrows 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s 2 2s 2 4 electrons

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Fill from the bottom up following the arrows 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s 2 2s 2 2p 6 3s 2 12 electrons

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Fill from the bottom up following the arrows 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 20 electrons

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Fill from the bottom up following the arrows 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 38 electrons

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Fill from the bottom up following the arrows 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 56 electrons

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Fill from the bottom up following the arrows 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 14 5d 10 6p 6 7s 2 88 electrons

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Fill from the bottom up following the arrows 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 14 5d 10 6p 6 7s 2 5f 14 6d 10 7p electrons

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Exceptional Electron Configurations

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Orbitals fill in order l Lowest energy to higher energy. l Adding electrons can change the energy of the orbital. l Half filled orbitals have a lower energy. l Makes them more stable. l Changes the filling order

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Write these electron configurations l Titanium - 22 electrons 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 2 l Vanadium - 23 electrons 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 3 l Chromium - 24 electrons 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 4 expected But this is wrong!!

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Chromium is actually: l 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 5 l Why? l This gives us two half filled orbitals. l Slightly lower in energy. l The same principal applies to copper.

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Copper’s electron configuration l Copper has 29 electrons so we expect: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 9 l But the actual configuration is: l 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 10 l This gives one filled orbital and one half filled orbital. l Remember these exceptions: d 4, d 9

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Physics and the Quantum Mechanical Model OBJECTIVES: l Calculate the wavelength, frequency, or energy of light, given two of these values.

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Physics and the Quantum Mechanical Model OBJECTIVES: l Explain the origin of the atomic emission spectrum of an element.

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Light l The study of light led to the development of the quantum mechanical model. l Light is a kind of electromagnetic radiation. l Electromagnetic radiation includes many kinds of waves l All move at 3.00 x 10 8 m/s = c

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Parts of a wave Wavelength Amplitude Origin Crest Trough

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Parts of Wave l Origin - the base line of the energy. l Crest - high point on a wave l Trough - Low point on a wave l Amplitude - distance from origin to crest l Wavelength - distance from crest to crest Wavelength is abbreviated by the Greek letter lambda =

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Frequency l The number of waves that pass a given point per second. l Units: cycles/sec or hertz (hz or sec -1 ) Abbreviated by Greek letter nu = c =

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Frequency and wavelength l Are inversely related l As one goes up the other goes down. l Different frequencies of light are different colors of light. l There is a wide variety of frequencies l The whole range is called a spectrum,

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Radio waves Micro waves Infrared. Ultra- violet X- Rays Gamma Rays Low energy High energy Low Frequency High Frequency Long Wavelength Short Wavelength Visible Light

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Prism l White light is made up of all the colors of the visible spectrum. l Passing it through a prism separates it.

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If the light is not white l By heating a gas with electricity we can get it to give off colors. l Passing this light through a prism does something different.

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Atomic Spectrum l Each element gives off its own characteristic colors. l Can be used to identify the atom. l How we know what stars are made of.

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These are called discontinuous spectra, or line spectra unique to each element. These are emission spectra The light is emitted given off

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Light is a Particle l Energy is quantized. l Light is energy l Light must be quantized l These smallest pieces of light are called photons. l Photoelectric effect? l Energy & frequency: directly related.

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Energy and frequency E = h x l E is the energy of the photon is the frequency l h is Planck’s constant l h = x Joules x sec. l joule is the metric unit of Energy

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l 2 equations so far: c = E = h

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Examples l What is the wavelength of blue light with a frequency of 8.3 x Hz? l What is the frequency of red light with a wavelength of 4.2 x m? l What is the energy of a photon of each of the above?

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Explanation of atomic spectra l When we write electron configurations, we are writing the lowest energy. l The energy level, and where the electron starts from, is called it’s ground state- the lowest energy level.

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Changing the energy l Let’s look at a hydrogen atom

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Changing the energy l Heat or electricity or light can move the electron up energy levels (“excited”)

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Changing the energy l As the electron falls back to ground state, it gives the energy back as light

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l May fall down in steps l Each with a different energy Changing the energy

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{ { {

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l Further they fall, more energy, higher frequency. l This is simplified l the orbitals also have different energies inside energy levels l All the electrons can move around. Ultraviolet Visible Infrared

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What is light? l Light is a particle - it comes in chunks. l Light is a wave- we can measure its wavelength and it behaves as a wave If we combine E=mc 2, c=, E = 1/2 mv 2 and E = h We can get: = h/mv l called de Broglie’s equation l Calculates the wavelength of a particle.

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Sample problem l What is the approximate mass of a particle having a wavelength of meters, and a speed of 1 m/s? Use = h/mv = 6.6 x (Note: 1 J = N x m; 1 N = 1 kg x m/s 2

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Matter is a Wave l Does not apply to large objects l Things bigger than an atom l A baseball has a wavelength of about m when moving 30 m/s l An electron at the same speed has a wavelength of cm l Big enough to measure.

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The physics of the very small l Quantum mechanics explains how the very small behaves. l Classic physics is what you get when you add up the effects of millions of packages. l Quantum mechanics is based on probability

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Heisenberg Uncertainty Principle l -It is impossible to know exactly the location and velocity of a particle. l The better we know one, the less we know the other. l Measuring changes the properties. l Instead, analyze interactions with other particles

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More obvious with the very small l To measure where a electron is, we use light. l But the light moves the electron l And hitting the electron changes the frequency of the light.

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Moving Electron Photon Before Electron changes velocity Photon changes wavelength After

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