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Electrons!

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The nuclei of atoms (protons and neutrons) are NOT involved in chemical reactions, BUT ELECTRONS ARE! The first clue that early scientists had to the existence of electrons was ATOMIC SPECTRA.

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ATOMIC SPECTRA Continuous Spectrum – If white light is passed through a prism, a continuous spectrum (rainbow) can be observed. The order of the colors is ROY G BIV red, orange, yellow, green, blue, indigo, violet Red has the longest wavelength and the lowest energy. Violet has the shortest wavelength and the highest energy.

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Electromagnetic Spectrum The Atomic Spectrum produces visible light and is part of the Electromagnetic Spectrum. The Atomic Spectrum produces visible light and is part of the Electromagnetic Spectrum.

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Electromagnetic Radiation Visible light is one form of electromagnetic radiation. Some other examples are: Visible light is one form of electromagnetic radiation. Some other examples are: Gamma rays – highest energy Gamma rays – highest energy X-rays X-rays Ultraviolet rays Ultraviolet rays Visible light Visible light Infrared Infrared Microwaves Microwaves Radiowaves Radiowaves Electricity – lowest energy Electricity – lowest energy

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Atomic Spectra, continued Bright Line Spectrum – Compounds and metallic ions produce characteristic colors when placed in a flame. When these “flame tests” are passed through a prism, a bright line spectrum (black background with colored slits) can be seen. Bright Line Spectrum – Compounds and metallic ions produce characteristic colors when placed in a flame. When these “flame tests” are passed through a prism, a bright line spectrum (black background with colored slits) can be seen.

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Bright Line Spectrum A spectrum is produced when radiation from light sources is separated into different wavelength components. A spectrum is produced when radiation from light sources is separated into different wavelength components. The bright line spectrum contains radiation of only specific wavelengths of light. The bright line spectrum contains radiation of only specific wavelengths of light.

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Hydrogen example Spectral lines are the fingerprints of the elements!

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Atomic Spectra, continued Spectral Tubes – by passing an electrical current through a sealed tube containing a gas of an element, a bright line spectrum can be produced.

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The Modern Theory of Light Light has dual properties : Light has dual properties : Light has both wave and particle properties Light has both wave and particle properties Light is packets of energy called quanta or photons Light is packets of energy called quanta or photons The amount of energy in each quantum depends on the color of the light The amount of energy in each quantum depends on the color of the light light has the most energy. Violet light has the most energy.

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Equations to calculate the energy in light Wave properties:f = c / λ where:f = frequency (s) c = speed of light (or 3.0 x 10 8 m/s) λ = wavelength (m)

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Equations to calculate the energy in light Particle properties:E = h f whereE = Energy (J) h = Planck’s constant (6.63 x 10 -34 J · s) (6.63 x 10 -34 J · s) f = frequency (s)

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Bohr’s Model Since energy must be absorbed for an e- to move to a higher level and that energy is emitted when it jumps back to ground state, the total amount of energy can be determined by: Since energy must be absorbed for an e- to move to a higher level and that energy is emitted when it jumps back to ground state, the total amount of energy can be determined by: ∆E = E f – E i = E photon = hv Bohr states that only specific frequencies of light that satisfy this equation can be absorbed or emitted. Bohr states that only specific frequencies of light that satisfy this equation can be absorbed or emitted.

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Think About It! As an electron in a hydrogen atom jumps from the n=3 orbit to the n=7 orbit, does it absorb or emit energy? As an electron in a hydrogen atom jumps from the n=3 orbit to the n=7 orbit, does it absorb or emit energy? ABSORB ENERGY!

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Calculating light energy, cont. Since frequency is proportional to both wavelength and energy, there is a relationship between the wavelength of light and energy. This is the idea of “quantized energy” – a specific color of light that represents a specific energy or quantum of energy or photon. Since frequency is proportional to both wavelength and energy, there is a relationship between the wavelength of light and energy. This is the idea of “quantized energy” – a specific color of light that represents a specific energy or quantum of energy or photon.

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Ground State vs. Excited State The lowest energy state of an electron is called “ground state.” When an electron is in a higher energy state, it is called “excited state.”

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Ground State An electron in its lowest possible energy level An electron in its lowest possible energy level Ground state e - configuration: 12 Mg 2 – 8 – 2 Each electron energy level contains the maximum number of electrons that it can hold.

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Excited State An electron that has gained energy and moved to a higher energy level – it’s very unstable! An electron that has gained energy and moved to a higher energy level – it’s very unstable! Excited state e- configuration: 12 Mg 1 – 8 – 3 2 – 7 – 3 2 – 6 – 4

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n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 Hydrogen’s Line Emission Spectrum energyenergy UV wavelengths Wavelength (nm) 410 434 486 656

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Energy in Level Jumping The energy that an electron absorbs or emits as it jumps can be calculated using the following equation: ∆E = E f – E i = E photon = hv Using the Energy State constant, which is equal to E = (-2.18 x 10 -18 J) (1/n 2 ), it is possible to calculate the difference in energy.

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Energy Calculations ∆E = hv = hc/λ = (-2.18 x 10 -18 J) 1 1 ----- - ----- n 2 f n 2 i Example: If the electron moves from n i = 3 to n f = 1, the calculation is: (-2.18 x 10 -18 J) 1 1 ----- - ----- 1 2 3 2 8989 =-1.94 x 10 -18 J

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Knowing the energy of the emitted photon, we can calculate either its frequency or its wavelength. Wavelength: λ = c hc --- = ---- v ∆E (6.626 x 10 -34 J-s) (3.00 x 10 8 m/s) -1.94 x 10 -18 J = 1.03 x 10 -7 m

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Quantum Mechanics Where does this energy come from? Where does this energy come from? Quantum mechanics is a field of physics that answers this. Quantum mechanics is a field of physics that answers this. Electrons absorb a specific number of photons of energy when they are excited (heated or absorb some other form of energy). The electrons are not stable in that state and emit photons of energy (in the form of light or other forms of electromagnetic energy) when they return to normal states. Electrons absorb a specific number of photons of energy when they are excited (heated or absorb some other form of energy). The electrons are not stable in that state and emit photons of energy (in the form of light or other forms of electromagnetic energy) when they return to normal states.

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Electrons can act like waves and particles (DeBroglie, 1924.) He based this on the Bohr’s original model and used it to explain why electrons don’t fall into the nucleus. There are areas of an electron cloud where the electrons are most dense, and therefore, you would be most likely to find an electron.

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DeBroglie’s Theory He suggested that as the e- moves around the nucleus it is associated with a particular wavelength, and that this wavelength depends on its mass (m) and on its velocity (v) (where h = Planck’s constant.) He suggested that as the e- moves around the nucleus it is associated with a particular wavelength, and that this wavelength depends on its mass (m) and on its velocity (v) (where h = Planck’s constant.) h λ = ------ mv

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DeBroglie, continued mv is the momentum. mv is the momentum. DeBroglie also used the term matter waves to describe the wave characteristics of material particles. DeBroglie also used the term matter waves to describe the wave characteristics of material particles. This works only because the mass of an electron is so small. This works only because the mass of an electron is so small.

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Heisenberg’s Uncertainty Principle The dual nature of matter limits how precisely we can know the exact location and momentum of any electron because of its very small mass. The dual nature of matter limits how precisely we can know the exact location and momentum of any electron because of its very small mass.

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Schrodinger’s Wave Equation His equation incorporates both the wavelike behavior and the particle-like behavior of an electron, and involves complex calculus. His equation incorporates both the wavelike behavior and the particle-like behavior of an electron, and involves complex calculus. His work yields a set of wave functions and corresponding energies. These functions are called orbitals. His work yields a set of wave functions and corresponding energies. These functions are called orbitals.

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Orbitals and Quantum Numbers

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Orbitals Each orbital describes a specific distribution of electron density in space. Each orbital describes a specific distribution of electron density in space. Each orbital has a characteristic energy and shape. Each orbital has a characteristic energy and shape. The lowest energy orbital in Hydrogen has an energy of -2.18 x 10 -18 J and a specific shape as seen in the upcoming slides. The lowest energy orbital in Hydrogen has an energy of -2.18 x 10 -18 J and a specific shape as seen in the upcoming slides.

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Models Bohr model had a single quantum number, n, to describe an orbit. Bohr model had a single quantum number, n, to describe an orbit. The wave mechanical model uses three quantum numbers, n, l, and m to describe the orbitals. The wave mechanical model uses three quantum numbers, n, l, and m to describe the orbitals.

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Wave Mechanical Model Orbitals The first quantum number, the principal quantum number, n, can have positive integral values of 1, 2, 3, etc. The first quantum number, the principal quantum number, n, can have positive integral values of 1, 2, 3, etc. As n increases, the orbital becomes larger and the electron is farther from the nucleus. As n increases, the orbital becomes larger and the electron is farther from the nucleus. An increase in n also means that the electron has a higher energy and is less tightly bound to the nucleus. An increase in n also means that the electron has a higher energy and is less tightly bound to the nucleus.

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Second Quantum Number The second quantum number, the angular momentum quantum number, l, can have integral values from 0 to ( n-1 ) for each value of n. The second quantum number, the angular momentum quantum number, l, can have integral values from 0 to ( n-1 ) for each value of n. This quantum number defines the shape of the orbital. This quantum number defines the shape of the orbital. The value of l is generally designated by the letters, s, p, d and f, corresponding to l values of 0, 1, 2 and 3 respectively. The value of l is generally designated by the letters, s, p, d and f, corresponding to l values of 0, 1, 2 and 3 respectively.

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Third Quantum Number The third quantum number, the magnetic quantum number, m l, can have integral values between -l and l, including 0. The third quantum number, the magnetic quantum number, m l, can have integral values between -l and l, including 0. This quantum number describes the orientation in space. This quantum number describes the orientation in space.

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Quantum Number PrincipalAngular Momentum MagneticSpin Symbol nlmlml msms Possible Values 1, 2, 3... ∞0, 1, 2, 3, …n - 1 s, p, d, f -1...0...+1 ±½±½ Electron/Orbital Characteristic SizeShapeOrientationMagnetic Spin

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Electron Shells The collection of orbitals with the same value is called an electron shell. All orbitals that have n = 3, are said to be in the third shell. The collection of orbitals with the same value is called an electron shell. All orbitals that have n = 3, are said to be in the third shell. The set of orbitals that have the same n and l values is called a subshell. The set of orbitals that have the same n and l values is called a subshell.

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Orbital Shapes s Orbitals The electron density is spherically symmetric. The electron density is spherically symmetric. The electron density at a given distance from the nucleus is going to be the same no matter what direction from the nucleus. The electron density at a given distance from the nucleus is going to be the same no matter what direction from the nucleus. The most probable distance to find an electron in the s orbital, 0.529 Å, is identical to the orbit predicted by Bohr. The most probable distance to find an electron in the s orbital, 0.529 Å, is identical to the orbit predicted by Bohr.

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p Orbitals The electron density is not spherical. The electron density is not spherical. It is dumbbell-shaped and concentrated in 2 lobes separated by a node at the nucleus. It is dumbbell-shaped and concentrated in 2 lobes separated by a node at the nucleus. Starting with the n = 2 shell, each shell has 3 p orbitals in different spatial orientations (-1, 0, +1) Starting with the n = 2 shell, each shell has 3 p orbitals in different spatial orientations (-1, 0, +1)

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d and f Orbitals When n = 3 or greater, there are d orbitals. When n = 3 or greater, there are d orbitals. In each shell there are 5 possible values for m l. (-2, -1, 0, 1, 2) In each shell there are 5 possible values for m l. (-2, -1, 0, 1, 2)

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Principle nAngular Momentum l Magnetic m l Spin m s Sublevel designation Number of Orbitals 100±½1s1 20101 0 -1, 0, +1 ±½ 2s 2p 1313 3012012 0 -1, 0, +1 -2, -1, 0, +1, +2 ±½ 3s 3p 3d 135135 401230123 0 -1, 0, +1 -2, -1, 0, +1, +2 -3, -2, -1, 0, +1, +2, +3 ±½ 4s 4p 4d 4f 13571357

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Increasing energyIncreasing energy n = 1 n = 2 n = 3 n = 4 1s 2s2s 2p2p 3s3s 3p3p 4s4s 3d3d 4p4p 4d4d 4f4f 1 orbital x 2e - = 2 3 x 2e- = 6 8 1 x 2e- = 2 3 x 2e- = 6 5 x 2e- = 10 18 1 x 2e- = 2 3 x 2e- = 6 5 x 2e- = 10 7 x 2e- =14 32

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Many Electron Atoms The shapes of the orbitals for many- electron atoms are the same, but it greatly changes the energies of the orbitals. The shapes of the orbitals for many- electron atoms are the same, but it greatly changes the energies of the orbitals. In a many-electron atom, the electron- electron repulsion cause the different subshells to be at different energies. In a many-electron atom, the electron- electron repulsion cause the different subshells to be at different energies. For a given value of n, the energy of an orbital increases with a value of l. For a given value of n, the energy of an orbital increases with a value of l.

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Electron Spin Electron spin is a property that states that each electron is like a tiny sphere spinning on its own axis. Electron spin is a property that states that each electron is like a tiny sphere spinning on its own axis. This leads to a new quantum number, m s, the spin magnetic quantum number. This leads to a new quantum number, m s, the spin magnetic quantum number. The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of 4 quantum numbers. The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of 4 quantum numbers.

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Electron Configurations An electron configuration is a distribution of electrons among the various orbitals of an atom. An electron configuration is a distribution of electrons among the various orbitals of an atom. Paramagnetic – refers to an atom having one or more unpaired electrons. (Ex: Li, B, C, N, Na) Paramagnetic – refers to an atom having one or more unpaired electrons. (Ex: Li, B, C, N, Na) Diamagnetic – means that all the electrons in an atom are paired. Diamagnetic – means that all the electrons in an atom are paired.

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Quantum Theory and the Electronic Structure of Atoms Chapter 7.

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