Wave-Particle DualityWave-Particle Duality Louis De Broglie (1924)Louis De Broglie (1924)

– Proposed that ALL matter has wave and particle Proposed that ALL matter has wave and particle properties, not just electrons.properties, not just electrons.

– E = E E = E E = h E = hυυ or E = hc/ or E = hc/λλ & E = mc & E = mc22

– hc/hc/λλ = mc = mc22 hc = mc hc = mc22λλ h = mc h = mcλλ– λλ = h/mc OR = h/mc OR λλ = h/mv = h/mv– Example:Example:

λλ of baseball (mass = .2 kg and v = 30 m/s) of baseball (mass = .2 kg and v = 30 m/s) λλ of an electron (mass = 9.11 x 10 of an electron (mass = 9.11 x 10-31-31 kg and v = 3 x 10 kg and v = 3 x 1088 m/s) m/s)

Wave Mechanical Wave Mechanical ModelModel

Schroedinger (1887-1961)Schroedinger (1887-1961)– Developed the “wave mechanical model” of the atom Developed the “wave mechanical model” of the atom

(also known as the (also known as the quantum mechanical modelquantum mechanical model))– He used the following equation to produce scatterplots He used the following equation to produce scatterplots

that are now called “electron clouds”that are now called “electron clouds” E = 2E = 222meme22/h/h22nn22

– These electron clouds are areas in which there is a These electron clouds are areas in which there is a great probability of finding an electron (90%).great probability of finding an electron (90%).

– The cloud is more dense where the probability of The cloud is more dense where the probability of finding an electron is high.finding an electron is high.

– The cloud is less dense where the probability of finding The cloud is less dense where the probability of finding an electron is low.an electron is low.

– This is called an “orbital” – a region in space in which This is called an “orbital” – a region in space in which there is a high probability of finding an electron.there is a high probability of finding an electron.

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

Is That It? - Is That It? - UncertaintyUncertainty

Heisenberg (1927)Heisenberg (1927)– Said that because of size and speed it is Said that because of size and speed it is

impossible to know both exact position and impossible to know both exact position and momentum of and electron at the same time.momentum of and electron at the same time.

– This is referred to as the “This is referred to as the “Heisenberg Heisenberg Uncertainty PrincipleUncertainty Principle””

– To “see” an electron we strike it with something To “see” an electron we strike it with something of similar size and observe its behavior.of similar size and observe its behavior.

We cannot see an electron directly.We cannot see an electron directly.

– We use photons of energy to do this.We use photons of energy to do this.

Quantum MechanicsQuantum Mechanics The work of de Broglie, Schroedinger, Born, The work of de Broglie, Schroedinger, Born,

and Heisenberg led to the study of and Heisenberg led to the study of “quantum mechanics” and the “wave “quantum mechanics” and the “wave mechanical model”mechanical model”1. classical physics1. classical physics– describes the motion of bodies much larger describes the motion of bodies much larger

than the atoms of which they are composed.than the atoms of which they are composed.– energy can be gained or lost in any amountenergy can be gained or lost in any amount

2. quantum physics2. quantum physics– describes the motion of atoms and subatomic describes the motion of atoms and subatomic

particles as waves.particles as waves.– particles gain or lose energy in packets called particles gain or lose energy in packets called

“quanta”“quanta”

Energy Components in Energy Components in ElectronsElectrons

Each component is given a letter & a name Each component is given a letter & a name – we call them “quantum values”– we call them “quantum values”

1. n = principal1. n = principal– distance from the nucleusdistance from the nucleus

2. l = azimuthal2. l = azimuthal– angular momentumangular momentum

3. m = magnetic3. m = magnetic– interaction with electromagnetic fieldsinteraction with electromagnetic fields

4. s = spin4. s = spin– axial rotationaxial rotation

Using these we can pinpoint the location of Using these we can pinpoint the location of an ean e--..

LocationLocation n = principal energy level (shell)n = principal energy level (shell) n + l = energy sublevel (subshell); n + l = energy sublevel (subshell);

defines the type of orbital that the defines the type of orbital that the electron is inelectron is in

n + l + m = specific orbital (axis n + l + m = specific orbital (axis orientation)orientation)

n + l + m + s = spin (exact n + l + m + s = spin (exact electron), identifies the exact electron), identifies the exact electron and its locationelectron and its location

ANALOGYANALOGY

Orbital TypesOrbital Types

S-orbital = spherical shape, only 1 of themS-orbital = spherical shape, only 1 of them P-orbital = gumdrop or dumbell shape, 3 of P-orbital = gumdrop or dumbell shape, 3 of

them – one on each axis (x,y,z)them – one on each axis (x,y,z) D-orbital = donut shape, 5 of themD-orbital = donut shape, 5 of them F-orbital = cigar shape, 7 of themF-orbital = cigar shape, 7 of them Each orbital contains a max of 2 electronsEach orbital contains a max of 2 electrons Orbit – path of an electron (according to Orbit – path of an electron (according to

Bohr)Bohr) Orbital – region in space where there is a Orbital – region in space where there is a

high probability of finding an electronhigh probability of finding an electron

ENERGY ENERGY LEVELSLEVELS

ORBITAL ORBITAL TYPESTYPES

# OF # OF ORBITALSORBITALS

# OF # OF ELECTRONELECTRON

SS

n = 1n = 1 ss 11 22

n = 2n = 2 s,ps,p 44 88

n = 3n = 3 s,p,ds,p,d 99 1818

n = 4n = 4 s,p,d,fs,p,d,f 1616 3232

n = 5n = 5 s,p,d,f,”g”s,p,d,f,”g” 2525 5050

Energy level = the number of orbital typesTotal number of orbitals in an energy level = n2

Total number of electrons in any energy level = 2n2