Download Chapter 6. Electronic Structure of Atoms

C H A P T E R 6 . E L E C T R O N I C S T RU C T U R E O F A TOM S
Student LEARNING OUTCOMES
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Realize that using the unit s–1 for frequency makes the units cancel more easily
Be able to convert between various labels
Be aware that quantum theory laid foundations for such areas as spectroscopy and nanotechnology
Know the difference between the Bohr model and orbitals
Be able to know what spectral lines represent
Be able to distinguish between an emission or absorption spectrum
Be able to calculation various Energy transitions between two energy levels.
Be able to write electronic structure both long & short-cut forms, Energy level diagram, and identifications
by structures including atoms and ions
Be able to recognize valence electrons, those mostly involved in gain & lose in chemical reactions
Be able to know what are core (inner) electrons
Be able to understand the difference between quantum numbers & use those when writing structures
Realize that light has dual nature, wave or particle
Be aware how some electron structure are noted when orbitals are near half-filled
Be able to recognize various regions on periodic table that represents different orbitals
CHAPTER 6 OUTLINE
6.1 The Wave Nature of Light
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Electronic structure of an atom refers to arrangement of electrons
Visible light is form of electromagnetic radiation or radiant energy
Electromagnetic radiation is characterized by its wave nature
All waves have characteristic wavelength, lambda), and amplitude, A
Frequency, nu), is the number of cycles which pass a point in one second
• units of  are Hertz (1 Hz = 1 s–1)
• speed of a wave is frequency multiplied by wavelength, for light, speed, c = ,
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• electromagnetic radiation through a vacuum is3.00 x 10 m/s
• Electromagnetic spectrum is display of various types arranged in order increasing wavelength
• example: visible radiation has wavelengths between 400 nm (violet) and 750 nm (red)
6.2 Quantized Energy and Photons
• Photoelectric effect is emission of electrons from metal surfaces on which light shines
• Emission spectra are emissions of light from electronically excited gas atoms
Hot Objects and the Quantization of Energy
• Wavelength distribution depends on temperature ;“red hot” objects are cooler than “white hot” objects
• Planck proposed that energy only be absorbed or released in certain amounts called quanta
• Quantum is smallest amount of energy emitted or absorbed as electromagnetic radiation
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• relationship between energy and frequency is: E = h
h is Planck’s constant (6.626 x 10 J-s)
The Photoelectric Effect and Photons
• Photoelectric effect provides evidence for particle nature of light and provides evidence for quantization
• Einstein assumed light traveled in energy packets called photons & energy of one photon is E = h
• Light shining on the surface of a metal can cause electrons to be ejected from the metal
• electrons will only be ejected if the photons have sufficient energy (work function):
• Light has wave-like AND particle-like properties
6.3 Line Spectra and the Bohr Model
Line Spectra
• Radiation composed only one wavelength called monochromatic
• Radiation that spans whole array of different wavelengths called continuous
• When radiation separates into its different wavelength components producing a spectrum
• Not all radiation is continuous
• gas placed in partially evacuated tube and high voltage produces single colors of light
• spectrum we see contains radiation of only specific wavelengths; called a line spectrum
Bohr’s Model
• Rutherford assumed electrons orbited nucleus as to planets orbiting the sun
• however, a charged particle moving in circular path should lose energy
• means that atom should be unstable according to Rutherford’s theory
• Bohr noted spectra of certain elements, assumed electrons confined to specific energy states called orbits
• Bohr’s model based on three postulates:
• Energy is gained or lost as a photon
The Energy States of the Hydrogen Atom
• Colors arise because electrons move between energy states in atom
• Energy states are quantized, light emitted from excited atoms must be quantized and appear as line spectra
• Bohr showed mathematically that
 1 
 1 
E  (hcRH ) 2  (2.18 1018 J) 2 
n 
n 
• n: principal quantum number (n = 1, 2, 3, … ) and RH is Rydberg constant
• product hcRH = 2.18 x 10-18 J
• First orbit in Bohr model has n = 1 and closest to the nucleus
• Furthest orbit in Bohr model has n =  and corresponds to E = 0
• Electrons in Bohr model only move between orbits by absorbing and emitting energy in quanta (E = h
• ground state is the lowest energy state & excited state is electron in a higher energy state
• Amount of energy absorbed or emitted moving between states is
 1
1 
 E  E f  E i  h  2.18 1018 J
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n 2 n 2 

 f
i 

6.4 The Wave Behavior of Matter
• Light has a particle nature, seems reasonable to ask whether matter has a wave nature
• answered by Louis deBroglie, using Einstein’s and Planck’s equations, deBroglie derived: h/m
• Momentum, m is a particle property, whereas  is a wave property
The Uncertainty Principle
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Heisenberg’s uncertainty principle: we cannot determine the exact position, direction of motion, and
speed of subatomic particles simultaneously
For electrons: we cannot determine their momentum and position simultaneously
6.5 Quantum Mechanics and Atomic Orbitals
• Schrödinger equation containing both wave and particle terms, solving leads to wave functions, 
• Wave function describes electron’s matter wave
• Electron density is another way of expressing probability
• region of high electron density is where there is a high probability of finding an electron
Orbitals and Quantum Numbers
• Solve Schrödinger equation get wave functions and energies for the wave functions
• Schrödinger’s equation requires three quantum numbers:
• Principal quantum number, n
• n becomes larger, the atom becomes larger and electron further from nucleus
• Angular momentum quantum number, l
• depends on the value of n
• values of l begin at 0 and increase to n – 1
• use letters for l (s, p, d, and f for l = 0, 1, 2, and 3), refer to the s, p, d, and f orbitals
• defines the shape of the orbital
• Magnetic quantum number, ml
• depends on l
• has integer values between –l and +l
• are (2l+1) possible values of ml
• example, for l = 1, there are (21+1) = 3 values of ml : 0, +1, and -1
• consequently, for l = 1, there are 3 orbitals: px, py and pz.
• Collection of orbitals with same value of n called an electron shell
• n2 orbitals in a shell described by a the n value; example n = 3, are 32 = 9 orbitals
• Set of orbitals with same n and l is called a subshell
• each subshell designated by number and a letter; example, 3p orbitals have n = 3 and l = 1
• Are n types of subshells in a shell described by a the n value; example, n = 3, are 3 subshells: 3s, 3p and 3d
• Orbitals ranked in terms of energy to yield an Aufbau diagram
• as n increases the spacing between energy levels becomes smaller
6.6 Representations of Orbitals
The s Orbitals
• S orbitals are spherical, as n increases then s orbitals get larger, is given by n – 1
The p Orbitals
• 3 p orbitals: px, py, & pz along x-, y-, and z-axes; are dumbbell shaped; as n increases then p orbitals get larger
• correspond to allowed values of ml of –1, 0, and +1
The d and f Orbitals
• 5 d and 7 f orbitals
6.7 Many-Electron Atoms
Orbitals and Their Energies
• In a many-electron atom, for a given value of n, energy of orbital increases with increasing value of l
• Orbitals same energy are said degenerate
Electron Spin and the Pauli Exclusion Principle
• Electron spin (tiny sphere spinning on its own axis) is quantized
• define ms = spin magnetic quantum number = 1/2
• Pauli’s exclusion principle states: no 2 electrons can have same set of four quantum numbers
• therefore, 2 electrons in same orbital must have opposite spins
6.8 Electron Configurations
• Electron configurations tell how electrons are distributed among various orbitals of atom
• Most stable configuration (ground state) is electrons in the lowest possible energy state
• Writing ground-state electronic configurations:
• electrons fill orbitals in order of increasing energy with no more than two electrons per orbital
• no 2 electrons can fill one orbital with the same spin (Pauli)
• for degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron
• Show spin? arrow point up ms = + 1/2 (spin up) arrow point down ms = – 1/2 (spin down)
Hund's Rule
• Hund’s rule: electrons fill each orbital singly with spins parallel before any orbital gets second electron
• placing electrons in different orbitals, electron–electron repulsions are minimized
Condensed Electron Configurations
• Electron configurations written using shorthand notation (condensed electron configuration):
• write valence electrons
• write core electrons corresponding to filled noble gas in square brackets
2 2
6 2 3
2 2
6
2 3
• example: P is 1s 2s 2p 3s 3p , but Ne is 1s 2s 2p therefore, P is [Ne]3s 3p
Transition Metals
• After Ar the d orbitals begin to fill
• After the 3d orbitals are full the 4p orbitals begin to fill
• 10 elements between Ti and Zn are called the transition metals or transition elements
The Lanthanides and Actinides
• 4f orbitals begin to fill with Ce.
Note: The electron configuration of La is [Xe]6s25d1
• 4f orbitals are filled for elements Ce – Lu are called lanthanide elements (or rare earth elements)
• 5f orbitals are filled for elements Th – Lr are called actinide elements, most actinides not found in nature
6.9 Electron Configurations and the Periodic Table
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Periodic table can be used as guide for electron configurations
Period number is value of n
Groups 1A and 2A have their s orbitals being filled
Groups 3A–8A have their p orbitals being filled
The s-block and p-block of the periodic table contain the representative, or main-group, elements
Groups 3B–2B have their d orbitals being filled
The lanthanides and actinides have their f orbitals being filled
• actinides and lanthanide elements are collectively referred to as the f-block metals
• Note the 3d orbitals fill after 4s orbital. and 4f orbitals fill after 5d orbitals
Anomalous Electron Configurations
• Many elements that appear to violate electron configuration guidelines
• examples: Chromium [Ar]3d54s1 instead of [Ar]3d44s2
• copper is [Ar]3d104s1 instead of [Ar]3d94s2
• half-full (d5) and full (d10) d subshells are particularly stable