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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 Theory and the Atom. Learning Objective Describe the relationship between electron levels, sublevels and atomic orbitals.

Quantum Theory and the Atom. Learning Objective Describe the relationship between electron levels, sublevels and atomic orbitals.

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