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**Quantum Model of the Atom**

Electrons in Atoms Quantum Model of the Atom

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**Schrödinger Wave Equation (1926)**

defines probability of finding an e-

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**Orbital (“electron cloud”) **

Region in space where there is 90% probability of finding an e- Orbital

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Orbital A 3-dimensional space around a nucleus in which electrons are most likely to be found Shape represents electron density (not a path the electron follows) Each orbital can hold up to 2 electrons

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**Quantum Numbers Four Quantum Numbers:**

Specify the “address” of each electron in an atom UPPER LEVEL

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**Describes the arrangement and space occupied by electrons in atoms**

Quantum Mechanics Describes the arrangement and space occupied by electrons in atoms

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Quantum Mechanics Describes the arrangement of electrons in atoms in terms of: Main or principal energy levels or shells (n) (Oklahoma City) Energy sublevels or subshells (Britton Road) Orbitals (house # 200) Electron spin (room # 4)

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**Quantum Numbers 1. Principal Quantum Number ( n )**

Energy level or shell Size of the orbital

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**Principal Quantum Number (n)**

Contain electrons that are Close in energy Similar distance from nucleus Have values of n = 1, 2, 3, 4, 5, 6…..

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**Energy Levels (Shells)**

The first shell (n = 1) is lowest in energy, 2nd level next and so on 1<2<3<4 Low energy electrons are closest to the nucleus

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**Quantum Numbers f d s p 2. Angular Momentum Quantum # ( l )**

Energy sublevel or subshell Shape of the orbital f d s p

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**Subshells Energy sublevels within energy level**

All electrons in a subshell have the same energy Designated s, p, d, f .. Sublevel energy: s<p<d<f

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**n = # of energy sublevels per energy level**

Main Energy Levels Sublevels n=4 4s, 4p, 4d, 4f n=3 3s, 3p, 3d n=2 2s, 2p n=1 1s

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Sublevels in n = 1,2, 3 n = 3 3d 3p 3s n = 2 2p 2s n = 1 1s

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**Quantum Numbers 3. Magnetic Quantum Number ( ml )**

Orientation of orbital Specifies the exact orbital within each sublevel

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**s subshell contains 1 s orbital**

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**p subshell contains 3 p orbitals**

px pz py

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**d subshell contains 5 d orbitals**

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**f subshell contains 7 f orbitals**

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**Quantum Numbers n = # of energy sublevels per energy level**

n2 = # of orbitals per energy level Sublevel sets: 1 s, 3 p, 5 d, 7 f

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**Number of Electrons Each orbital can hold up to 2 electrons**

Maximum number of electrons in any energy level = 2n2 n =1 2(1)2 = 2 n =2 2(2)2 = 8 n =3 2(3)2 = 18

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**Electrons Allowed All 2s electrons have the same energy**

All 2p electrons have the same energy which is slightly higher than the energy of the 2s electrons s sublevel 2 electrons p sublevel 6 electrons d sublevel 10 electrons f sublevel 14 electrons

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**Quantum Numbers 2s 2px 2py 2pz**

Orbitals combine to form a spherical shape. 2s 2pz 2py 2px

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**Quantum Numbers 4. Spin Quantum Number ( ms ) Electron spin +½ or -½**

An orbital can hold 2 electrons that spin in opposite directions

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**Quantum Numbers Pauli Exclusion Principle**

No two electrons in an atom can have the same 4 quantum numbers. Each e- has a unique “address” 1. Principal # 2. Ang. Mom. # 3. Magnetic # 4. Spin # energy level sublevel (s,p,d,f) orbital electron spin

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**Pauli Exclusion Principle**

Each orbital can hold TWO electrons with opposite spins.

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**A. Number of electrons in a p orbital**

1e or 2e B. Number of orbitals in a p subshell 3 C. Number of orbitals in 4d subshell 5 D. Maximum number of electrons in a 3d subshell 10e

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**ORBITAL DIAGRAM Shows the electrons in each orbital**

Circles, boxes, or lines are used to represent orbitals Arrows or half-arrows represent electrons

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l = s subshell 1 p 2 d 3 f

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s orbital ml

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p orbital Ml

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d orbital Ml

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f orbital Ml

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electron spin ms +1/ /2

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**7s 6p 5d Orbital diagram n l ml ms 7 +1/2 6 1 -1 5 2 -2 -1/2 -1 0 +1**

+1/2 6 1 -1 5 2 -2 -1/2 7s 6p 5d

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**4f 4d 5f Orbital diagram n l ml ms 4 3 -3 +1/2 2 -1 -1/2 5**

4d 5f

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Feeling overwhelmed? Read Section 4-2!

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Quantum Model of the Atom Electrons in Atoms. A. Electrons as Waves zLouis de Broglie (1924) yApplied wave-particle theory to e - ye - exhibit wave properties.

Quantum Model of the Atom Electrons in Atoms. A. Electrons as Waves zLouis de Broglie (1924) yApplied wave-particle theory to e - ye - exhibit wave properties.

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