atomic orbital and electronic configurations

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ATOMIC ATOMIC ORBITAL & ORBITAL & ELECTRON ELECTRON

CONFIGURATIOCONFIGURATIONN

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s orbitalss orbitals

d orbitalsd orbitals

p orbitalsp orbitals

s orbitalss orbitals p orbitalsp orbitals d orbitalsd orbitals

No.No.orbs.orbs.

No. No. e-e-

11 33 55

22 66 1010

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Subshells & Subshells & ShellsShells

Subshells & Subshells & ShellsShells

n = 1n = 1

n = 2n = 2

n = 3n = 3

n = 4n = 4

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QUANTUM NUMBERSQUANTUM NUMBERSQUANTUM NUMBERSQUANTUM NUMBERS

The The shape, size, and energyshape, size, and energy of each orbital is a of each orbital is a function of 3 quantum numbers:function of 3 quantum numbers:

n n (major)(major) ---> shell---> shell

ll (angular) (angular) ---> subshell---> subshell

mmll (magnetic)(magnetic) ---> designates an orbital ---> designates an orbital within a subshellwithin a subshell

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SymbolSymbol ValuesValues DescriptionDescription

nn (major) (major) 1, 2, 3, ...1, 2, 3, ... Orbital Orbital sizesize, , energyenergy, and, and

# of nodes# of nodes=n-1=n-1

ll (angular) (angular) 0, 1, 2, ... n-10, 1, 2, ... n-1 Orbital Orbital shapeshape or type or type

(subshell) (subshell)

mmll (magnetic) (magnetic) -l,...0,...+l -l,...0,...+l Orbital Orbital orientationorientation

# of orbitals in subshell = 2 l + 1# of orbitals in subshell = 2 l + 1

QUANTUM NUMBERSQUANTUM NUMBERS

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Shells and SubshellsShells and SubshellsShells and SubshellsShells and Subshells

When When n = 1n = 1, then , then l = 0l = 0 and and mmll = 0 = 0

Therefore, in n = 1, there is 1 type of Therefore, in n = 1, there is 1 type of subshellsubshell

and that subshell has a single orbitaland that subshell has a single orbital

(m(mll=0 has a single value ---> 1 orbital)=0 has a single value ---> 1 orbital)

This subshell is labeled This subshell is labeled ss (“ess”) (“ess”)

Each shell has 1 orbital labeled s, Each shell has 1 orbital labeled s, and it is and it is SPHERICALSPHERICAL in shape.in shape.

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s Orbitalss Orbitalss Orbitalss Orbitals

All s orbitals are All s orbitals are spherical in spherical in shapeshape..

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1s Orbital1s Orbital

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2s Orbital2s Orbital

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3s Orbital3s Orbital

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p Orbitalsp Orbitalsp Orbitalsp OrbitalsWhen n = 2, then l = 0 and l = 1When n = 2, then l = 0 and l = 1

Therefore, when n = 2 there are Therefore, when n = 2 there are 2 types of orbitals — 2 2 types of orbitals — 2 subshellssubshells

For For l = 0l = 0mmll = 0, = 0, s subshells subshell

For For l = 1l = 1 m mll = -1, 0, +1 = -1, 0, +1

this is a this is a p subshellp subshell with with 3 orbitals3 orbitals

When n = 2, then l = 0 and l = 1When n = 2, then l = 0 and l = 1

Therefore, when n = 2 there are Therefore, when n = 2 there are 2 types of orbitals — 2 2 types of orbitals — 2 subshellssubshells

For For l = 0l = 0mmll = 0, = 0, s subshells subshell

For For l = 1l = 1 m mll = -1, 0, +1 = -1, 0, +1

this is a this is a p subshellp subshell with with 3 orbitals3 orbitals

planar node

Typical p orbital

planar node

Typical p orbital

See Screen 7.13See Screen 7.13

When l = 1, there is aWhen l = 1, there is a

NODAL PLANENODAL PLANE

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p Orbitalsp Orbitalsp Orbitalsp Orbitals

• The three p orbitals are oriented 90The three p orbitals are oriented 90oo apart apart in spacein space

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d Orbitalsd Orbitalsd Orbitalsd Orbitals

When n = 3, what are the values of l?When n = 3, what are the values of l?

l = 0, 1, 2 l = 0, 1, 2 and so there are 3 subshells in the shell.and so there are 3 subshells in the shell.

For l = 0, mFor l = 0, mll = 0 = 0

---> s subshell with single orbital---> s subshell with single orbital

For l = 1, mFor l = 1, mll = -1, 0, +1 = -1, 0, +1

---> p subshell with 3 orbitals---> p subshell with 3 orbitals

For l = 2, mFor l = 2, mll = -2, -1, 0, +1, +2 = -2, -1, 0, +1, +2

---> ---> d subshell with 5 orbitalsd subshell with 5 orbitals

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d Orbitalsd Orbitalsd Orbitalsd Orbitals

s orbitals have no planar s orbitals have no planar node (l = 0) and so are node (l = 0) and so are spherical.spherical.

p orbitals have l = 1, and p orbitals have l = 1, and have 1 planar node,have 1 planar node,

and so are “dumbbell” and so are “dumbbell” shaped.shaped.

This means d orbitals (with This means d orbitals (with l = 2) have l = 2) have

2 planar nodes2 planar nodes

typical d orbital

planar node

planar node

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3d3dxyxy Orbital Orbital

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Arrangement of Arrangement of Electrons in AtomsElectrons in Atoms

Arrangement of Arrangement of Electrons in AtomsElectrons in Atoms

Electrons in atoms are arranged asElectrons in atoms are arranged as

SHELLSSHELLS (n) (n)

SUBSHELLSSUBSHELLS (l) (l)

ORBITALSORBITALS (m (mll))

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Each orbital can be assigned no Each orbital can be assigned no

more than 2 electrons!more than 2 electrons!

This is tied to the existence of a 4th This is tied to the existence of a 4th

quantum number, the quantum number, the electron electron

spin quantum number, mspin quantum number, mss..

Arrangement of Arrangement of Electrons in AtomsElectrons in Atoms

Arrangement of Arrangement of Electrons in AtomsElectrons in Atoms

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Electron Electron Spin Spin

Quantum Quantum Number, Number,

mmss

Can be proved experimentally that electronCan be proved experimentally that electronhas a spin. Two spin directions are given byhas a spin. Two spin directions are given bymmss where m where mss = +1/2 and -1/2. = +1/2 and -1/2.

Can be proved experimentally that electronCan be proved experimentally that electronhas a spin. Two spin directions are given byhas a spin. Two spin directions are given bymmss where m where mss = +1/2 and -1/2. = +1/2 and -1/2.

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n ---> shelln ---> shell 1, 2, 3, 4, ...1, 2, 3, 4, ...

l ---> subshelll ---> subshell 0, 1, 2, ... n - 10, 1, 2, ... n - 1

mmll ---> orbital ---> orbital -l ... 0 ... +l-l ... 0 ... +l

mmss ---> electron spin ---> electron spin +1/2 and -1/2+1/2 and -1/2

n ---> shelln ---> shell 1, 2, 3, 4, ...1, 2, 3, 4, ...

l ---> subshelll ---> subshell 0, 1, 2, ... n - 10, 1, 2, ... n - 1

mmll ---> orbital ---> orbital -l ... 0 ... +l-l ... 0 ... +l

mmss ---> electron spin ---> electron spin +1/2 and -1/2+1/2 and -1/2

QUANTUMQUANTUMNUMBERSNUMBERSQUANTUMQUANTUMNUMBERSNUMBERS

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Pauli Exclusion Pauli Exclusion PrinciplePrinciple

No two electrons in the No two electrons in the same atom can have the same atom can have the same set of 4 quantum same set of 4 quantum numbers.numbers.

That is, each electron in an That is, each electron in an atom has a unique address atom has a unique address of quantum numbers.of quantum numbers.

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Electrons in AtomsElectrons in AtomsElectrons in AtomsElectrons in Atoms

When n = 1, then l = 0When n = 1, then l = 0

this shell has a single orbital (1s) to this shell has a single orbital (1s) to

which 2e- can be assigned.which 2e- can be assigned.

When n = 2, then l = 0, 1When n = 2, then l = 0, 1

2s orbital 2s orbital 2e-2e-

three 2p orbitalsthree 2p orbitals 6e-6e-

TOTAL = TOTAL = 8e-8e-

22Assigning Electrons to Assigning Electrons to

SubshellsSubshells• In H atom all subshells of In H atom all subshells of

same n have same same n have same energy.energy.

• In many-electron atom:In many-electron atom:a) subshells increase in a) subshells increase in

energy as value of (n + l) energy as value of (n + l) increases.increases.

b) for subshells of same b) for subshells of same (n + l), the subshell with (n + l), the subshell with

lower n is lower in lower n is lower in energy.energy.

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Electron Electron Filling Filling OrderOrder

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Writing Atomic Electron Writing Atomic Electron ConfigurationsConfigurations

Writing Atomic Electron Writing Atomic Electron ConfigurationsConfigurations

1111 ss

value of nvalue of nvalue of lvalue of l

no. ofno. ofelectronselectrons

spdf notationspdf notationfor H, atomic number = 1for H, atomic number = 1

Two ways of Two ways of writing configs. writing configs. One is called One is called the the spdf spdf notation.notation.

Two ways of Two ways of writing configs. writing configs. One is called One is called the the spdf spdf notation.notation.

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Writing Atomic Electron Writing Atomic Electron ConfigurationsConfigurations

Writing Atomic Electron Writing Atomic Electron ConfigurationsConfigurations

Two ways of Two ways of writing writing configs. Other configs. Other is called the is called the orbital box orbital box notation.notation.

Two ways of Two ways of writing writing configs. Other configs. Other is called the is called the orbital box orbital box notation.notation.

Arrowsdepictelectronspin

ORBITAL BOX NOTATIONfor He, atomic number = 2

1s

21 s

Arrowsdepictelectronspin

ORBITAL BOX NOTATIONfor He, atomic number = 2

1s

21 s

One electron has n = 1, l = 0, mOne electron has n = 1, l = 0, m ll = 0, m = 0, mss = + 1/2 = + 1/2

Other electron has n = 1, l = 0, mOther electron has n = 1, l = 0, m ll = 0, m = 0, mss = - 1/2 = - 1/2