C. Johannesson Ch. 4 - Electrons in Atoms

Section 1 The Development of a New Atomic Model Objectives Explain the mathematical relationship among the speed, wavelength, and frequency of electromagnetic radiation. Discuss the dual wave-particle nature of light. Discuss the significance of the photoelectric effect and the line-emission spectrum of hydrogen to the development of the atomic model. Describe the Bohr model of the hydrogen atom.

Properties of Light LOWENERGYLOWENERGY HIGHENERGYHIGHENERGY zThe Wave Description of Light Electromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space. Together, all the forms of electromagnetic radiation form the electromagnetic spectrum.

Properties of Light, continued zWavelength ( ) - length of one complete wave zFrequency ( ) - # of waves that pass a point during a certain time period yhertz (Hz) = 1/s zAmplitude (A) - distance from the origin to the trough or crest

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C. Johannesson Waves A greater amplitude (intensity) greater frequency (color) crest origin trough A

on EM Spectrum LOWENERGYLOWENERGY HIGHENERGYHIGHENERGY ROYG.BIV redorangeyellowgreenblueindigoviolet LONG WAVELENGTHLONG WAVELENGTH

EM Spectrum zFrequency & wavelength are inversely proportional c = c:speed of light 3.00  10 8 m/s (in a vacuum) :wavelength (m, nm, etc.) :frequency (Hz)

EM Spectrum GIVEN: = ? = 434 nm = 4.34  m c = 3.00  10 8 m/s WORK : = c = 3.00  10 8 m/s 4.34  m = 6.91  Hz zEX: Find the frequency of a photon with a wavelength of 434 nm.

Quantum Theory zEinstein (1905) yPhotoelectric effect- emission of electrons from a metal when light shines on the metal (causing an electric current) yA photon is a particle of electromagnetic radiation having zero mass and carrying a quantum of energy.

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Click below to watch the Visual Concept. Visual Concept Energy of a Photon

The Particle Description of Light zA quantum of energy is the minimum quantity of energy that can be lost or gained by an atom. zrelationship between a quantum of energy and the frequency of radiation: E = hν * E is the energy, in joules, * ν is the frequency, in s −1 * h is a fundamental physical constant now known as Planck’s constant; h = × 10−34 J s.

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Development of a New Atomic Model Day 2

Line-Emission Spectrum zEach element has a unique bright-line emission spectrum. yHydrogen always produced same line- emission spectrum so releases (emission) energy of only certain values y“Atomic Fingerprint” Helium

Line-Emission Spectrum Cont… ground state- lowest energy state of an atom excited state- state in which an atom has a higher potential energy than its ground state ENERGY IN PHOTON OUT yLine –emission spectrum is caused by energy released when electrons “jump from higher energy to lower energy

Bohr Model of the Hydrogen Atom Niels Bohr proposed a hydrogen-atom model that linked the atom’s electron to photon emission. According to the model, the electron can circle the nucleus only in allowed paths, or orbits. Electrons are allowed to exist in any one of a number of energy levels (lowest energy state is closest to the nucleus)

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Bohr Model of the Hydrogen Atom, continued When an electron falls to a lower energy level, a photon is emitted, and the process is called emission. Energy must be added to an atom in order to move an electron from a lower energy level to a higher energy level. This process is called absorption. Only worked for Hydrogen (1 electron) 

zPlanck (1900) yObserved - emission of light from hot objects yConcluded - energy is emitted in small, specific amounts (quanta) not continuously as expected by energy in the form of waves yQuantum - minimum amount of energy that can be lost or gained by an atom

Quantum Theory zPlanck (1900) vs. Classical TheoryQuantum Theory

zEinstein (1905) yConcluded - light has properties of both waves and particles “wave-particle duality” yPhoton - particle of light that carries a quantum of energy

Day3

Electrons as Waves zLouis de Broglie (1924) yApplied wave-particle theory to e -: suggested that electrons be considered waves confined to the space around an atomic nucleus. yIt followed that the electron waves could exist only at specific frequencies ye - exhibit wave properties as well as particle

Electrons as Waves, continued Electrons, like light waves, can be bent, or diffracted. Diffraction refers to the bending of a wave as it passes by the edge of an object or through a small opening. Electron beams, like waves, can interfere with each other. Interference occurs when waves overlap.

Electrons as Waves EVIDENCE: DIFFRACTION PATTERNS ELECTRONS VISIBLE LIGHT

Quantum Mechanics zHeisenberg Uncertainty Principle yImpossible to know both the velocity and position of an electron (small particle) at the same time zQuantum theory describes mathematically the wave properties of electrons and other very small particles.

Quantum Mechanics Electrons do not travel around the nucleus in neat orbits, as Bohr had postulated. Instead, they exist in certain regions called orbitals. Orbital (“electron cloud”) yRegion in space where there is 90% probability of finding an e - three- dimensional space Orbital

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Day4

C. Johannesson Quantum Numbers UPPER LEVEL zFour Quantum Numbers: ySpecify the “address” of each electron in an atom ySpecify properties of the atomic orbitals and properties of electrons in it

Quantum Numbers 1. Principal Quantum Number ( n ) yEnergy level ySize of the orbital yn 2 = # of orbitals in the energy level yAs n increases, e- energy and distance from nucleus increases

Quantum Numbers s p d f 2. Angular Momentum Quantum # ( l ) yEnergy sublevel yShape of the orbital yNumber of orbital shapes possible equal to n

Quantum Numbers zn=# of sublevels per level zn 2 =# of orbitals per level zSublevel sets: 1 s, 3 p, 5 d, 7 f

Electrons Accommodated in Energy Levels and Sublevels

Quantum Numbers 3. Magnetic Quantum Number ( m l ) yOrientation of orbital xS-1, p-3,d-5, f-7  Specifies the exact orbital within each sublevel

Quantum Numbers zOrbitals combine to form a spherical shape. 2s 2p z 2p y 2p x

Quantum Numbers 4. Spin Quantum Number ( m s ) yElectron spin  +½ or -½ yAn orbital can hold 2 electrons that spin in opposite directions. yAs it spins creates a magnetic field

Quantum Numbers zPauli Exclusion Principle yNo two electrons in an atom can have the same 4 quantum numbers. yEach e - has a unique “address”:

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Day 5

Electron Configuration zArrangement of electrons in an atom zAtoms of different elements have different numbers of e-, a distinct electron configuration exists for atoms of each element ze- in atoms tend to assume arrangements that have lowest possible energies (ground-state)

Relative Energies of Orbitals

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General Rules zPauli Exclusion Principle yEach orbital can hold TWO electrons with opposite spins.

General Rules zAufbau Principle yElectrons fill the lowest energy orbitals first. y“Lazy Tenant Rule” yEnergies of sub-levels begin to overlap x4s is lower in energy than 3d

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RIGHT WRONG General Rules zHund’s Rule yWithin a sublevel, place one e - per orbital before pairing them. ySeparating unpaired electrons into as many orbitals as possible minimizes the repulsion between electrons

O 8e - zOrbital Diagram zElectron Configuration 1s 2 2s 2 2p 4 Notation 1s 2s 2p

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zShorthand Configuration S 16e - Valence Electrons Core Electrons S16e - [Ne] 3s 2 3p 4 1s 2 2s 2 2p 6 3s 2 3p 4 Notation zLonghand Configuration

Writing Electron Configurations

Periodic Patterns zShorthand Configuration/Nobel Gas Notation yCore e - : Go up one row and over to the Noble Gas. yValence e - : On the next row, fill in the # of e - in each sublevel.

[Ar]4s 2 3d 10 4p 2 Periodic Patterns zExample - Germanium

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