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Chapter 13 “Electrons in Atoms” Credits: Stephen L. Cotton Charles Page High School Mr. Daniel Olympic High School

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Section 13.3 Physics and the Quantum Mechanical Model l OBJECTIVES: Describe the relationship between the wavelength and frequency Distinguish between quantum mechanics and classical mechanics. of light. Identify the source of atomic emission spectra. Explain how the frequencies of emitted light are related to changes in electron energies.

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Light l Visible light is a type of electromagnetic radiation. l Electromagnetic radiation is a form of energy and includes many types: gamma rays, x-rays, radio waves, visible light… l Speed of light (c) = 3.00 x 10 8 m/s l All electromagnetic radiation travels at this same rate when measured in a vacuum

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Parts of a Wave Wavelength Amplitude Node Crest Trough

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- Page 373 “R O Y G B I V” Frequency Increases Wavelength Shorter

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Long Wavelength Low Frequency Low ENERGY Short Wavelength High Frequency High ENERGY Wavelength Table

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Wavelength and Frequency: l Are inversely related As one increases the other decreases. l Different frequencies of visible light are different colors. l There is a wide variety of frequencies l Spectrum: A whole range of electromagnetic wavelengths. (e.g. the visible light spectrum)

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Radio waves Micro waves Infrared. Ultra- violet X- Rays Gamma Rays Low Frequency High Frequency Long Wavelength Short Wavelength Visible Light Low Energy High Energy The Electromagnetic Spectrum

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So what is Energy? l All energy is quantized l A quantum is a “packet” of energy. Not all quanta (plural) are the same size. (eggs are not all the same size either, but all are eggs)

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So what is Light Energy? l Light is a form of energy. l Therefore, light must be quantized l A quantum of light energy is called a photon. Einstein determined that light is not only a wave, but is also a particle! He demonstrated it in an experiment that showed the photoelectric effect

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Photoelectric Effect

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Experiment demonstrates the particle nature of light.

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So what is Light Energy? (con’t) l Therefore, light has what is called wave- particle duality. It has characteristics of both waves and particles.

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Wave-Particle Duality (again) J.J. Thomson won the Nobel prize for describing the electron as a particle. His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron. The electron is a particle! The electron is an energy wave!

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Confused? You’ve Got Company! “No familiar conceptions can be woven around the electron; something unknown is doing we don’t know what.” Physicist Sir Arthur Eddington The Nature of the Physical World 1934

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The Physics of the Very Small l Quantum mechanics explains how very small particles behave Quantum mechanics is an explanation for subatomic particles and atoms as waves l Classical mechanics describes the motions of bodies much larger than atoms

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Section 13.1 Models of the Atom l OBJECTIVES: Identify the inadequacies in the Rutherford atomic model. Identify the new proposal in the Bohr model of the atom. Describe the energies and positions of electrons according to the quantum mechanical model. Describe how the shapes of orbitals related to different sublevels differ.

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Ernest Rutherford’s Model l Discovered dense positive piece at the center of the atom- “nucleus” l Electrons would surround and move around the nucleus l Atom is mostly empty space l It did not explain the chemical properties of the elements – a better description of the electron behavior was needed

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Niels Bohr’s Model l Why don’t the electrons fall into the nucleus? He agreed with Rutherford that electrons move around the nucleus, But: In specific circular paths, or orbits (like planets around the sun), at specific energy levels. An amount of fixed energy separates one electron energy level from another.

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The Bohr Model of the Atom Niels Bohr I pictured the electrons orbiting the nucleus much like planets orbiting the sun. However, electrons are found in specific energy levels around the nucleus, and can jump from one level to another.

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Bohr’s Model l Electrons occupy specific energy levels analogous to the rungs of a ladder l The electron cannot exist between energy levels, just like you can’t stand between rungs on a ladder l A quantum of energy is the amount of energy required to move an electron from one energy level to another (plural: quanta) l Since the energy of an atom is never “in between” there must be a quantum leap in energy.

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Changing the energy l Let’s look at a hydrogen atom, with only one electron, and in the first energy level.

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Changing the energy l Heat, electricity, or light can move the electron up to different energy levels. The electron is now said to be in an “excited state”

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Changing the energy l The electron is unstable at the higher energy level and as it falls back to the ground state, it gives the energy back in the form of light

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l They fall down in specific steps l Each step has a different energy (quantum) and results in a different color of light. Changing the energy

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Origin of Line Spectra Balmer series

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l The further electrons fall, the more energy is released and the higher the frequency of light emitted. l This is a simplified explanation! l Remember, the orbitals also have different sublevels within the principle energy levels Ultraviolet Visible Infrared

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Atomic Spectra 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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But not all light is 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 of light. l The colors can be used to identify the atom. l This is how we know what elements stars are made of.

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This is called a bright line spectrum Unique to each element, like fingerprints! Very useful for identifying elements

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Explanation of Atomic Spectra l ground state - the lowest energy level of the electron. l In summary. When an electron at ground state receives a quantum of energy it jumps directly to a higher energy level. The electron is unstable and immediately drops to a lower energy level. As it drops it gives off the same amount of

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The Quantum Mechanical Model Problems with Bohr’s theory : It was only successful for H- no other elements followed his predictions. It introduced the quantum idea artificially.

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Heisenberg Uncertainty Principle You can find out where the electron is, but not its energy OR… You can know how much energy it has, but not where it is! “One cannot simultaneously determine both the position and momentum of an electron.” Werner Heisenberg

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Heisenberg Uncertainty Principle l It is impossible to know exactly the location and velocity of a particle simultaneously. l The better we know one, the less we know the other. l Measuring one property, changes the other.

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Moving Electron Photon Before Electron velocity changes Photon wavelength changes After

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In 1926, Erwin Schrodinger derived an equation that described the energy and probable position of the electrons in an atom

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Schrodinger’s Wave Equation probability His equation determined the probability of finding a single electron along a single axis (x- axis) Erwin Schrodinger

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l Particles which are very small and travel very quickly (like electrons) behave very differently from objects big enough to observe. l The quantum mechanical model is a mathematical solution describing how those particles act. The Quantum Mechanical Model

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l Describes energy levels for electrons. l Electrons move in an unpredictable manner l We can only determine the probability of finding an electron a certain distance from the nucleus. The Quantum Mechanical Model

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l The electrons are probably located inside a blurry “electron cloud” l The area where there is the greatest chance of finding an electron. The Quantum Mechanical Model

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Atomic Orbitals l Principal Quantum Number (n) = the energy level of the electron: 1, 2, 3, etc. l Within each energy level, there are sub- levels (like theater seats arranged in sections): letters s, p, d, and f l The complex math of Schrodinger’s equation describes several shapes These are the atomic orbitals - regions where there is a 90% probability of finding an electron.

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Principal Quantum Number The Principle Quantum Number (n) denotes the shell (energy level) in which the electron is located. The maximum number of electrons that fit into an energy level can be calculated: 2n 2

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

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Types of Orbitals s orbital p orbital d orbital

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Types of Atomic Orbitals

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By Energy Level l First Energy Level l Has only an s sublevel l only 2 electrons l 1s 2 l Second Energy Level l Has s and p sublevels l 2 e - in s, 6 e - in p l 2s 2 2p 6 l 8 total electrons

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

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By Energy Level Beyond the fourth energy level, not all sublevels fill up. l You simply run out of electrons l So only the s, p, d and f sublevels are used l Because the energy levels overlap the orbitals do not fill up in a consistent pattern l However, the lowest energy orbitals fill first.

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Section 13.2 Electron Arrangement in Atoms l OBJECTIVES: Describe how to write the electron configuration for an atom. Explain why the actual electron configurations for some elements differ from those predicted by 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 … are the way electrons are arranged in various orbitals around the nuclei of atoms. Three rules tell us how: 1) Aufbau principle - electrons enter the lowest energy sublevels first. This becomes complex because of the overlap of orbitals of different energies – follow the diagram! 2) Pauli Exclusion Principle – there are at most 2 electrons per orbital - with opposite spins

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Pauli Exclusion Principle No two electrons in an atom can have the same four quantum numbers. Wolfgang Pauli To show the different direction of spin, a pair in the same orbital is written as:

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Electron Configurations 3) Hund’s Rule- When electrons occupy orbitals of equal energy, they don’t pair up until each orbital has one electron. l Let’s write the electron configuration for Phosphorus We need to account for all 15 electrons in phosphorus

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l The first two electrons go into the 1s orbital Notice the opposite direction of the 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 sublevel. They each go into separate orbitals (Hund’s) 3 unpaired electrons = 1s 2 2s 2 2p 6 3s 2 3p 3

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Orbitals fill in an order: l Lowest energy to higher energy. l Adding electrons can change the energy of the orbital. Full sublevels are the most stable arrangement. l Half filled sublevels have a lower energy than partially filled sublevels, and are next most stable.

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Write the electron configurations for these elements: lZlZirconium - 40 electrons [[Kr] 5s 2 4d 2 lTlTantalum - 73 electrons [[Xe] 6s 2 4f 14 5d 3 lClChromium - 24 electrons [[Ar] 4s 2 3d 4 (expected) BBut this is not what happens with Chromium

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Chromium is actually: l [Ar]4s 1 3d 5 l Why? l This gives us two half filled orbitals (the others are all still full) l Half full is 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: [Ar] 4s 2 3d 9 l But the actual configuration is: [Ar]4s 1 3d 10 l This change gives one more filled orbital and one that is half filled. l Remember these exceptions: Groups ending in d 4 and d 9

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Irregular configurations of Cr and Cu Chromium steals a 4s electron to make its 3d sublevel HALF FULL Copper steals a 4s electron to FILL its 3d sublevel

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