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Introduction Measurement Matter Atoms & ions Compounds Chemical change The mole Gases Energy & change The quantum theory The periodic table
 
Learning objectives
 Explain the difference between a continuous spectrum and a line spectrum.
 Explain the difference between an emission and an absorption spectrum.
 Use the concept of quantized energy states to explain atomic line spectra.
 Given an energy level diagram, predict wavelengths in the line spectrum, and vice versa.
 Define and distinguish between shells, subshells, and orbitals.
 Explain the relationships between the quantum numbers.
 Use quantum numbers to label electrons in atoms.
 Describe and compare atomic orbitals given the n and quantum numbers.
 List a set of subshells in order of increasing energy.
 Write electron configurations for atoms in either the subshell or orbital box notations.
 Write electron configurations of ions.
 Use electron configurations to predict the magnetic properties of atoms.
Lecture outlineThe quantum theory was used to show how the wavelike behavior of electrons leads to quantized energy states when the electrons are bound or trapped. In this section, we'll use the quantum theory to explain the origin of spectral lines and to describe
the electronic structure of atoms.
Emission Spectra
 experimental key to atomic structure: analyze light emitted by high temperature gaseous elements
 experimental setup: spectroscopy
 atoms emit a characteristic set of discrete wavelengths not a continuous spectrum!
 atomic spectrum can be used as a "fingerprint" for an element
 hypothesis: if atoms emit only discrete wavelengths, maybe atoms can have only discrete energies
 an analogy

A turtle sitting on a ramp can have any height above the ground and so, any potential energy


A turtle sitting on a staircase can take on only certain discrete energies 
 energy is required to move the turtle up the steps (absorption)
 energy is released when the turtle moves down the steps (emission)
 only discrete amounts of energy are absorbed or released (energy is said to be quantized)
 energy staircase diagram for atomic hydrogen
  bottom step is called the ground state
 higher steps are called excited states

 computing line wavelengths using the energy staircase diagram
 computing energy steps from wavelengths in the line spectrum
 summary: line spectra arise from transitions between discrete (quantized) energy states
The quantum mechanical atom
 Electrons in atoms have quantized energies
 Electrons in atoms are bound to the nucleus by electrostatic attraction
 Electron waves are standing matter waves
 standing matter waves have quantized energies, as with the "electron on a wire" model
 Electron standing matter waves are 3 dimensional
 The electron on a wire model was one dimensional; one quantum number was required to describe the state of the electron
 A 3D model requires three quantum numbers
 A threedimensional standing matter wave that describes the state of an electron in an atom is called an atomic orbital
 The energies and mathematical forms of the orbitals can be computed using the Schrödinger equation
 quantization isn't assumed; it arises naturally in solution of the equation
 every electron adds 3 variables (x, y, z) to the equation; it's very hard to solve equations with lots of variables.
 energylevel separations computed with the Schrödinger equation agree very closely with those computed from atomic spectral lines
Quantum numbers
 Think of the quantum numbers as addresses for electrons
 the principal quantum number, n
 determines the size of an orbital (bigger n = bigger orbitals)
 largely determines the energy of the orbital (bigger n = higher energy)
 can take on integer values n = 1, 2, 3, ...,
 all electrons in an atom with the same value of n are said to belong to the same shell
 spectroscopists use the following names for shells
Spectroscopist's notation for shells.
n  shell name 
 n  shell name 
1  K  
5  O 
2  L  
6  P 
3  M  
7  Q 
4  N  

 the azimuthal quantum number,
 designates the overall shape of the orbital within a shell
 affects orbital energies (bigger = higher energy)
 all electrons in an atom with the same value of are said to belong to the same subshell
 only integer values between 0 and n1 are allowed
 sometimes called the orbital angular momentum quantum number
 spectroscopists use the following notation for subshells
Spectroscopist's notation for subshells.
 subshell name 
0  s 
1  p 
2  d 
3  f 

 the magnetic quantum number, m_{}
 determines the orientation of orbitals within a subshell
 does not affect orbital energy (except in magnetic fields!)
 only integer values between  and + are allowed
 the number of m_{} values within a subshell is the number of orbitals within a subshell
The number of possible m_{} values determines the number of orbitals in a subshell.

possible values of m_{} 
number of orbitals in this subshell 
0 
0 
1 
1 
1, 0, +1 
3 
2 
2, 1, 0, +1, +2 
5 
3 
3, 2, 1, 0, +1, +2, +3 
7 

 the spin quantum number, m_{s}
 several experimental observations can be explained by treating the electron as though it were spinning
 spin makes the electron behave like a tiny magnet
 spin can be clockwise or counterclockwise
 spin quantum number can have values of +1/2 or 1/2
Electron configurations of atoms
 a list showing how many electrons are in each orbital or subshell in an atom or ion
 subshell notation: list subshells of increasing energy, with number of electrons in each subshell as a superscript
 examples
 1s^{2} 2s^{2} 2p^{5} means "2 electrons in the 1s subshell, 2 electrons in the 2s subshell, and 5 electrons in the 2p subshell"
 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{3} is an electron configuration with 15 electrons total; 2 electrons have n=1 (in the 1s subshell); 8 electrons have n=2 (2 in the 2s subshell, and 6 in the 2p subshell); and 5 electrons have n=3 (2 in the 3s subshell, and 3 in the 3p subshell).
 ground state configurations fill the lowest energy orbitals first
Electron configurations of the first 11 elements, in subshell notation. Notice how configurations can be built by adding one electron at a time.
atom  Z  ground state electronic configuration 
H 
1 
1s^{1} 
He 
2 
1s^{2} 
Li 
3 
1s^{2} 2s^{1} 
Be 
4 
1s^{2} 2s^{2} 
B 
5 
1s^{2} 2s^{2} 2p^{1} 
C 
6 
1s^{2} 2s^{2} 2p^{2} 
N 
7 
1s^{2} 2s^{2} 2p^{3} 
O 
8 
1s^{2} 2s^{2} 2p^{4} 
F 
9 
1s^{2} 2s^{2} 2p^{5} 
Ne 
10 
1s^{2} 2s^{2} 2p^{6} 
Na 
11 
1s^{2} 2s^{2} 2p^{6 }3s^{1} 

Writing electron configurations
 strategy: start with hydrogen, and build the configuration one electron at a time (the Aufbau principle)
 fill subshells in order by counting across periods, from hydrogen up to the element of interest:
 rearrange subshells (if necessary) in order of increasing n & l
 examples: Give the ground state electronic configurations for:
 watch out for d & f block elements; orbital interactions cause exceptions to the Aufbau principle
 halffilled and completely filled d and f subshells have extra stability
Know these exceptions to the Aufbau principle in the 4th period. (There are many others at the bottom of the table, but don't worry about them now.)
exception 
configuration predicted by the Aufbau principle 
true ground state configuration 
Cr 
1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 3d^{4} 4s^{2} 
1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 3d^{5} 4s^{1} 
Cu 
1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 3d^{9} 4s^{2} 
1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 3d^{10} 4s^{1} 
Electron configurations including spin
 unpaired electrons give atoms (and molecules) special magnetic and chemical properties
 when spin is of interest, count unpaired electrons using orbital box diagrams
 drawing orbital box diagrams
 write the electron configuration in subshell notation
 draw a box for each orbital.
 Remember that s, p, d, and f subshells contain 1, 3, 5, and 7 degenerate orbitals, respectively.
 Remember that an orbital can hold 0, 1, or 2 electrons only, and if there are two electrons in the orbital, they must have opposite (paired) spins (Pauli principle)
 within a subshell (depicted as a group of boxes), spread the electrons out and line up their spins as much as possible (Hund's rule)
 the number of unpaired electrons can be counted experimentally
 configurations with unpaired electrons are attracted to magnetic fields (paramagnetism)
 configurations with only paired electrons are weakly repelled by magnetic fields (diamagnetism)
Core and valence electrons
 chemistry involves mostly the shell with the highest value of principal quantum number, n, called the valence shell
 the noble gas core under the valence shell is chemically inert
 simplify the notation for electron configurations by replacing the core with a noble gas symbol in square brackets:
Examples of electron configurations written with the core/valence notation
atom 
full configuration 
core 
valence configuration 
full configuration using core/valence notation 
O 
1s^{2} 2s^{2} 2p^{4} 
He 
2s^{2} 2p^{4} 
[He] 2s^{2} 2p^{4} 
Cl 
1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{5} 
Ne 
3s^{2} 3p^{5} 
[Ne] 3s^{2} 3p^{5} 
Al 
1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{1} 
Ne 
3s^{2} 3p^{1} 
[Ne] 3s^{2} 3p^{1} 

 electrons in d and f subshells outside the noble gas core are called pseudocore electrons
Examples of electron configurations containing pseudocore electrons
atom 
core 
pseudocore 
valence 
full configuration 
Fe 
Ar 
3d^{6} 
4s^{2} 
[Ar] 3d^{6 }4s^{2} 
Sn 
Kr 
4d^{10} 
5s^{2} 5p^{2} 
[Kr] 4d^{10} 5s^{2} 5p^{2} 
Hg 
Xe 
4f^{14} 5d^{10} 
6s^{2} 
[Xe] 4f^{14} 5d^{10} 6s^{2} 
Pu 
Rn 
5f^{6} 
7s^{2} 
[Rn] 5f^{6} 7s^{2} 

