# Wave-Particle Duality_5_

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```					Wave-Particle Duality
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Louis De Broglie (1924)
– Proposed that ALL matter has wave and particle properties, not just electrons. – E = E  E = hυ or E = hc/λ & E = mc2 – hc/λ = mc2  hc = mc2λ  h = mcλ – λ = h/mc OR λ = h/mv – Example:
λ of baseball (mass = .2 kg and v = 30 m/s)  λ of an electron (mass = 9.11 x 10-31 kg and v = 3 x 108 m/s)
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Wave-Particle Duality
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Heisenberg (1927)
– Said that because of size and speed it is impossible to know both exact position and momentum of and electron at the same time. – This is referred to as “Heisenberg Uncertainty Principle” – To “see” an electron we strike it with something of similar size and observe its behavior.
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We cannot see an electron directly.

– We use photons of energy to do this.

Quantum Mechanics
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The work of de Broglie, Schroedinger, Born, and Heisenberg led to the study of “quantum mechanics” (motion in increments) 1. classical physics
– describes the motion of bodies much larger than the atoms of which they are composed. – energy can be gained or lost in any amount

2. quantum physics
– describes the motion of atoms and subatomic particles as waves. – particles gain or lose energy in packets called “quanta”

Wave Mechanical Model
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Schroedinger (1887-1961)
– Developed the “wave mechanical model” of the atom – He used the following equation to produce scatterplots that are now called “electron clouds”
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E = 22me2/h2n2

– These electron clouds are areas in which there is a great probability of finding an electron (90%). – The cloud is more dense where the probability of finding an electron is high. – The cloud is less dense where the probability of finding an electron is low. – This is called an “orbital” – a region in space in which there is a high probability of finding an electron.

http://scienceworld.wolfram.com/physics/SchroedingerEquation.html http://www.uark.edu/misc/julio/orbitals/index.html

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Each component is given a letter & a name – we call them “quantum values” 1. n = principal
– distance from the nucleus

Energy Components in Electrons

2. l = azimuthal
– angular momentum

3. m = magnetic
– interaction with electromagnetic fields

4. s = spin
– axial rotation
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Using these we can pinpoint the exact location of an e-.

Location
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n = principal energy level (shell) n + l = energy sublevel (subshell); defines the type of orbital that the electron is in n + l + m = specific orbital (axis orientation) n + l + m + s = spin (exact electron), identifies the exact electron and its location ANALOGY

Orbital Types
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S-orbital = spherical shape, only 1 of them P-orbital = gumdrop or dumbell shape, 3 of them – one on each axis (x,y,z) D-orbital = donut shape, 5 of them F-orbital = cigar shape, 7 of them Each orbital contains a max of 2 electrons Orbit – path of an electron (according to Bohr) Orbital – region in space where there is a high probability of finding an electron

ENERGY LEVELS n=1 n=2 n=3

ORBITAL TYPES s s,p s,p,d

# OF ORBITALS 1 4 9

# OF ELECTRONS 2 8 18

n=4
n=5

s,p,d,f
s,p,d,f,”g”

16
25

32
50

Energy level = the number of orbital types Total number of orbitals in an energy level = n2 Total number of electrons in any energy level = 2n2

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 views: 4 posted: 11/11/2009 language: English pages: 10