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**ELECTRONIC STRUCTURE OF ATOMS**

Chapter 6 ELECTRONIC STRUCTURE OF ATOMS

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Electronic Structure Much of what we know about the energy of electrons and their arrangement around the nucleus of an atom comes from analysis of light emitted or absorbed by matter.

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**The Wave Nature of Light**

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**The Electromagnetic Spectrum**

<> c = l . n

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**Electromagnetic Radiation**

Relating frequency and wavelength c = l . n c = l . f c = speed of light = 3.00 x 108 m/s n or f = frequency in cycle per second or Hertz = wavelength in meters (1 nm = 1 x 10-9 m) Note: As wavelength increases, frequency (& energy) will decrease.

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**Limitations of the Wave Model of Light**

The prevailing laws of physics couldn’t explain: Blackbody Radiation – emission of light from hot objects Photoelectric Effect – emission of electrons from metal surfaces on which light strikes Emission Spectra – emission of light from excited gas atoms *Couldn’t relate temperature , intensity, & wavelength of light

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Max Planck 1900 Solved problem by stating energy can only be released or absorbed in discrete ‘chunks’ of some minimum size. He named this smallest quantity of energy a ‘quantum’. He said the minimum amount of energy that an object can gain or lose is related to its frequency. E = h . f E = Energy in Joules h = Planck’s Constant = x Joule-second f = frequency in cycles per second or Hertz

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Albert Einstein 1905 Used Planck’s Quantum Theory to explain the photoelectric effect. Photoelectric Effect - light shining on a clean metal surface causes the surface to emit electrons if the light is of a certain minimum frequency . He said light energy hitting a metal surface is not like a wave but like a stream of tiny energy packets called ‘photons’. He said the energy of a photon can also be found by: E = h * f 6. No matter the intensity, if the photons don’t have enough energy, no electrons are emitted.

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Dual Nature of Light Planck & Einstein are describing light as behaving like tiny particles of energy – just like matter is made of particles! We theorize light has both a wave like and a particle like nature. We refer to this as the DUAL NATURE OF LIGHT.

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Bohr Model of the Atom Ground State = when electrons are in the lowest energy state Excited State – when electrons absorb energy & move to a higher energy state Spectra – light energy given off when electrons return to lower energy states LIMITATION: Bohr couldn’t explain spectra of multi-electron atoms.

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**Red, Orange, Yellow, Green, Blue, Indigo, Violet**

Recall Hot objects give off light. When the light from a light bulb passes through a prism, a RAINBOW or CONTINUOUS SPECTRUM forms. Remember ROY G. BIV? Red, Orange, Yellow, Green, Blue, Indigo, Violet

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When the light from an element gas tube passes through a prism, only some colors are seen – called a BRIGHT-LINE SPECTRUM or LINE SPECTRA. Gas Tube Hydrogen gas gives off pink light Power Supply Hydrogen’s Bright Line Spectrum as viewed through a prism

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**This site shows the Line Spectra of Various Elements**

Often Shown This Way This site shows the Line Spectra of Various Elements

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**1/l = (RH)( 1/n12 - 1/n22 ) Johann Balmer**

Showed that the wavelengths of the four visible lines of hydrogen fit the following formula: 1/l = (RH)( 1/n /n22 ) Where RH = Rydberg Constant RH = x 107 m-1 n = energy level (n2 bigger than n1)

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**Niels Bohr explains Hydrogen’s Line Specta**

Bohr’s Postulates Electrons must be in specific energy levels An electron in an allowed energy state will not radiate energy & spiral into the nucleus Energy is emitted or absorbed by electrons as they move from one allowed energy state to another. The amount of energy: E = h . f

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**n is the energy level or principal quantum number**

How much energy? Bohr calculated the energy an electron possesses when in each energy state. E = (-2.18 x J) (1/n2) where n = 1, 2, 3, etc. n is the energy level or principal quantum number Note that the values are negative. The energy is lowest (most negative) for n = 1. When the electron is completely removed and an ion forms the energy = zero.

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E = (-2.18 x J) (1/n2)

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**And the Energy Change? DE = (-2.18 x 10-18 J) (1/nf2 - 1/ni2)**

Where the initial energy state = ni Where the final energy state = nf

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**Dual Nature of Light & Matter!**

Light has both particle (photon) & wavelike properties. Louis de Broglie suggested that matter is the same – called the de Broglie’s hypothesis. Matter has both particle like & wave like properties.

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**De Broglie’s Hypothesis**

For matter waves: = h / (m . v) Where: l = wavelength (meters) m v = momentum m = mass (kg) v = velocity (m/s) h = x Joule-second Recall: Joule = 1 kg-m2/s2 This wavelength only becomes significant when dealing with tiny high velocity particles such as electrons.

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**Heisenberg’s Uncertainty Principle**

Heisenberg’s Uncertainty Principle: It is inherently impossible for us to know simultaneously both the exact momentum of an object and its exact location in space. This becomes significant when dealing with the position of electrons within an atom.

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QUANTUM MECHANICS LIMITATION: Bohr couldn’t explain spectra of multi-electron atoms. It took Quantum Mechanics to explain the behavior of light emitted by multi-electron atoms. Quantum Mechanics is one of the most revolutionary discoveries of the 20th century – the ‘new’ physics.

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Quantum Mechanics Heisenberg & de Broglie set the stage for a new model of the electron that would describe its location not precisely, but in terms of probabilities - called Quantum Mechanics or Wave Mechanics.

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Erwin Schrodinger (1887 – 1961) Proposed a Wave Equation (wave functions - y) that incorporates the dual nature of the electron. Y2 provides info about the electron’s location. In the Quantum Mechanical Model, we speak of the probability (Y2) that the electron will be in a certain region of space at a given instant. We call it probability density or electron density.

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Con’t 4) The wave functions are called orbitals. 5) Orbitals differ in energy, shape, and size. 6) An orbital can hold up to TWO electrons. 7) Four numbers can be used to describe the location of an electron in an orbital.

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**Four Quantum Numbers 1st Quantum Number =**

The Principal Quantum Number (n) 2nd Quantum Number = The Azimuthal Quantum Number or The Angular Momentum Quantum Number (l) 3rd Quantum Number = The Magnetic Quantum Number (ml) 4th Quantum Number = The Spin Magnetic Quantum Number (ms)

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**Pauli Exclusion Principle**

Pauli Exclusion Principle states that no two electrons in an atom can have the same set of 4 quantum numbers. ( n, l, ml , ms )

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1st Quantum Number It tells the principal energy level (shell) – ‘n’ n = 1 for the 1st PEL n = 2 for the 2nd PEL , etc. As the value of ‘n’ increases, the electron has more energy, is less tightly bound to the nucleus, and it spends more time further away from the nucleus.

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2nd Quantum Number It tells the sublevel or subshell, which indicates the shape of the orbital – ‘l’ If ‘l’ = zero, the sublevel is s If ‘l’ = 1, the sublevel is p If ‘l’ = 2, the sublevel is d If ‘l’ = 3, the sublevel is f In terms of energy, s < p < d < f. The value of ‘l’ is always at least one less than the value of ‘n’.

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**3 rd Quantum Number ml ml ml ml ml**

It tells the orientation of the orbital in the sublevel - For the s sublevel, there is only one orientation: = 0 For the p sublevel, there are 3 possible orientations: = +1, 0, -1 For the d sublevel, there are 5 possible orientations: = +2, +1, 0, -1, -2 For the f sublevel, there are 7 possible orientations: = +3, +2, +1, 0, -1, -2, -3 ml ml ml ml ml

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4th Quantum Number It tells the electron spin within the orbital There are two possible values: + 1/2 or – 1/2 They indicate the two opposite directions of electron spin – which produce oppositely directed magnetic fields. (ms)

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Memorize

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The “s” orbital

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The “p” orbitals

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The “d” orbitals

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The “f” orbital

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**Atomic Orbitals: Putting Them Together**

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Be Able To: Assign a set of four quantum number to each electron in an atom. Recognize a valid set of quantum numbers Describe atomic orbitals using quantum numbers. Determine the # of orbitals and/or electrons in a given energy level or sublevel. State the order of orbital energies from highest to lowest.

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**Writing Electron Configurations**

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6 6f14 7d10

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**Table 7-2: Electron Configuration and Energy Levels for the Periodic Table of the Elements**

Group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Period s-Orbitals d-Orbitals p-Orbitals 1s1 1s2 2s1 2s2 2p1 2p2 2p3 2p4 2p5 2p6 3s1 3s2 3p1 3p2 3p3 3p4 3p5 3p6 4s1 4s2 3d1 3d2 3d3 3d4 3d5 3d6 3d7 3d8 3d9 3d10 4p1 4p2 4p3 4p4 4p5 4p6 5s1 5s2 4d1 4d2 4d3 4d4 4d5 4d6 4d7 4d8 4d9 4d10 5p1 5p2 5p3 5p4 5p5 5p6 6s1 6s2 * 5d1 5d2 5d3 5d4 5d5 5d6 5d7 5d8 5d9 5d10 6p1 6p2 6p3 6p4 6p5 6p6 7s1 7s2 ** 6d1 6d2 6d3 6d4 6d5 6d6 6d7 6d8 6d9 6d10 7p1 7p2 7p3 7p4 7p5 7p6 f-Orbitals * Lanthanoids 4f1 4f2 4f3 4f4 4f5 4f6 4f7 4f8 4f9 4f10 4f11 4f12 4f13 4f14 ** Actinoids 5f1 5f2 5f3 5f4 5f5 5f6 5f7 5f8 5f9 5f10 5f11 5f12 5f13 5f14

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Orbital Notation One way: Nitrogen Another way: Aluminum

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**Pauli Exclusion Principle**

Pauli Exclusion Principle states that no two electrons in an atom can have the same set of 4 quantum numbers. ( n, l, ml , ms ) NO! YES!

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Hund’s Rule Hund’s Rule – For degenerate orbitals, minimum energy is obtained when the number of electrons with the same spin is maximized. Degenerate – means same sublevel

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