Electronic Structure of Atoms 6.4 The Wave Behavior of Matter 6.5 Quantum Mechanics and Atomic...
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Transcript of Electronic Structure of Atoms 6.4 The Wave Behavior of Matter 6.5 Quantum Mechanics and Atomic...
![Page 1: Electronic Structure of Atoms 6.4 The Wave Behavior of Matter 6.5 Quantum Mechanics and Atomic Orbitals 6.6 Representation of Orbitals.](https://reader036.fdocuments.us/reader036/viewer/2022081421/5697c0021a28abf838cc2eb8/html5/thumbnails/1.jpg)
Electronic Structure of Atoms6.4 The Wave Behavior of Matter
6.5 Quantum Mechanics and Atomic Orbitals
6.6 Representation of Orbitals
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Bohr Model •Each energy level can contain more than 1 electron But the max # for each level is different•Electrons fill in energy levels starting from lowest energy level to the next higher energy level•REMEMBER # Protons = # Electrons in a neutral atom•Example = oxygen
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6.4 The Wave Behavior of Matter
Louis de Broglie (1892-1987) •proposed if radiant energy (under appropriate conditions) could behave as a stream of particles and exhibit properties of wave could electrons orbiting nucleus behave as a wave
λ= h / mv h = Planck’s constant 6.626 x 10-34 J/s
m = mass v = velocity mv = momentum
PRACTICE: What is the wavelength of an electron moving with a speed of 5.97 x 106 m/s? mass of e- =9.11 x 10-31 kg. 1 J =1 kg m2/s2
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Practicede Broglie’s hypo applicable to all matter any object of mass and velocity would have characteristics of a wave
•Q. Calculate the velocity of a neutron whose de Broglie wavelength is 500 pm. mass of neutron= 1.67 x 10-27 kg
λ= h / mv rearrange equationh = Planck’s constant 6.626 x 10-34 J/s m = mass v = velocity
6.626 x 10-34 kg m2/s2/s
(5x10-10m)(1.67 x 10-27 kg)
= 794 m/s or 7.92 x 102 m/s
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Wave properties of e- demonstrated
experimentally…Electron diffraction
•as electrons are passed though a crystal they are diffracted
•stream of electrons exhibits similar kind of wave behavior as EM radiation•ex: technique used in electron microscope to obtain images at atomic scale (3,000,000 x magnification)
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The Uncertainty PrincipleIf an e- exhibits wave properties, can we
calculate the position, direction of motion, and speed at any time???
Werner Heisenberg (1901- 1976) Uncertainty Principle Impossible to know both the exact momentum and exact location of an electron simultaneously
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RESULT
De Broglie’s hypo and Heisenberg’s Uncertainty Principle set stage for new approach to atomic structure model
that describes energy of e- while describing probabilities of location
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6.5 Quantum Mechanics and Atomic Orbitals
Erwin Schrodinger (1887-1961)•Austrian physicist •proposed wave equation incorporates wave and particle behavior of e- = quantum mechanics or wave mechanics Solving equation lead to Wave functions- def. mathematical description of an allowed energy state (an orbital) for an e- ex: Ψ Greek letter psiΨ2 provides info about e- location when in allowed energy state = probability density or electron density
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Orbitals• Def. wave function; space where there is a
high probability that it is occupied by a pair of electrons; each orbital has a characteristic energy and shape
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Quantum Numbers1. Principal Quantum
Number(n)• Indicates main energy levels n = 1, 2, 3, 4…
• as n increases = orbital becomes larger e spend more time farther from nucleus
• as n increases = e- has higher energy and bound less tightly to nucleus
• n determines the number of sublevels within the principle energy level
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2. Angular Momentum Quantum Number (l)
• l = n – 1
• shape of orbital Each main energy level has sub-levels= s, p, d, f
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3. Magnetic Quantum Number (ml)• describes
orientation of orbital in space
• # of orbitals• equal to –l to +l
ex: l = 3; then ml = -3,-2,-1,0,1,2,3
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• Electron shell: all orbitals that have the same value of n
• Subshell: set of orbitals that all have the same n and l values
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• Ground State: when electrons occupy lowest energy orbital
• Excited State: when electron occupies any other orbital; e- can be excited to higher-energy orbital by absorption of a photon of appropriate energy
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Sample Exercise
• Predict the number of subshells in the fourth shell?
• 4• Give the label for each of these subshells• 4s, 4p, 4d, 4f• How many orbitals are in each of theses
subshells?
• 4s=1 (l=0 ml=0) 4p=3 (l=1 ml=-1,0,1)
• 4d=5 (l=2 ml=-2,-1,0,1,2) 4f =7
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6.6 Representation of OrbitalsS orbital: spherical, 1 subshell
Radial Probability Density probability of finding an e- at specific distance from nucleusnode: intermediate point where probability goes to 0as n increases =size of orbital increases = increase in distance from nucleus
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p Orbital• dumbbell shaped, 2 lobes
• ml = 3 possible values, -1,0,1
• p size increases as move from 2p to 3p etc
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d and f Orbitalsd= four leaf clover shape orbitals
•five 3d orbitals, five 4d orbitals etc
•ml= -2,-1,0,1,2
f= complicated shape
•seven 4d orbitals, 5d
•ml = -3,-2,-1,0,1,2,3
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Electron Spin
• e- behave as tiny sphere spinning on own axis
4. Spin Magnetic Quantum Number (ms) s = spin
+1/2 (clockwise) or -1/2 (counterclockwise)
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Electron Configuration
• The arrangement of electrons in an atom around nucleus
• Ex: Hydrogen = 1s1
• Ex: Helium = 1s2
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Orbitals in SublevelsSublevel # Orbitals # electrons
s 1 2
p 3 6
d 5 10
f 7 14
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Standard Notation
of Fluorine
Main Energy
Level
Numbers
1, 2, 2Sublevels
Number of electrons in the sub level 2,2,5
1s2 2s2 2p5
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Three rules are used to build the electron configuration:– Aufbau principle
– Pauli Exclusion Principle
– Hund’s Rule
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Aufbau Principle• Electrons occupy orbitals of lower
energy first.
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Pauli Exclusion Principle• no 2 e- in an atom can have the same 4 QN
• An orbital can hold only two electrons and they must have opposite spin.
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Hund’s RuleIn a set of orbitals, the
electrons will fill the orbitals in a way that would give the maximum number of parallel spins (maximum number of unpaired electrons).
Analogy: Students could fill each seat of a school bus, one person at a time, before doubling up.
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Orbital Diagram (Box Diagram)
• Diagram in which orbitals are represented by boxes grouped by sublevels with arrows indicating electrons
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Aufbau Diagram for Hydrogen
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Aufbau Diagram
for Helium
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Aufbau Diagram
for Lithium
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Aufbau Diagram
for Beryllium
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Aufbau Diagram for Boron
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Aufbau Diagram
for Carbon
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Aufbau Diagram
for Nitrogen
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Aufbau Diagram
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Aufbau Diagram
for Fluorine
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Shorthand Notation
• Use the last noble gas that is located in the periodic table right before the element.
• Write the symbol of the noble gas in brackets.
• Write the remaining configuration after the brackets.
• Ex: Fluorine: [He] 2s2 2p5
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Blocks in the Periodic Table
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HOMEWORK • Complete WS