Excited Atoms & Atomic Structure. © 2006 Brooks/Cole - Thomson The Quantum Mechanical Picture of the Atom Basic Postulates of Quantum Theory 1.Atoms and

Excited Atoms& Atomic Structure

© 2006 Brooks/Cole - Thomson

The Quantum Mechanical Picture of the Atom

Basic Postulates of Quantum Theory1. Atoms and molecules can exist only in certain energy states. In each energy

state, the atom or molecule has a definite energy. When an atom or molecule changes its energy state, it must emit or absorb just enough energy to bring it to the new energy state (the quantum condition).

2. Atoms or molecules emit or absorb radiation (light) as they change their energies. The frequency of the light emitted or absorbed is related to the energy change by a simple equation.

hc

h E


The Quantum Mechanical Picture of the Atom The allowed energy states of atoms and molecules can be described by sets of numbers called quantum

numbers.

• Quantum numbers are the solutions of the Schrodinger, Heisenberg & Dirac equations.

• Four quantum numbers are necessary to describe energy states of electrons in atoms

– n, , m, ms

2

22

mr t V r t r t i

r t

t ( , ) ( , ) ( , )

( , )

Schroedinger 3-dimensional time independent equation

Heisenberg’s uncertainty Equation

Dirac’s quantum mechanical model

E. SchrodingerE. Schrodinger1887-19611887-1961

W. HeisenbergW. Heisenberg1901-19761901-1976


1. The principal quantum number has the symbol – n.

n = 1, 2, 3, 4, ...... “shells”

n = K, L, M, N, ......

The electron’s energy depends principally on n .

n

n = 1

n = 2

n = 3

n = 4

n = 5

n = 6

n = 7


= 0 = s

= 1 = p

= 2 = d

= 3 = f

n = 1

n = 2

n = 3

n = 4

n = 5

n = 6

n = 7

2. The angular momentum quantum number has the symbol . tells us the shape of the orbitals and when linked with n defines the energy of the electron

= 0, 1, 2, 3, 4, 5, .......(n-1) = s, p, d, f, g, h, .......(n-1)


Quantum Numbers3. The symbol for the magnetic quantum number is m.

m = - , (- + 1), (- +2), .....0, ......., ( -2), ( -1),

• If = 0 (or an s orbital), then m = 0. – Notice that there is only 1 value of m.

This implies that there is one s orbital per n value. n 1

• If = 1 (or a p orbital), then m = -1,0,+1.– There are 3 values of m.

Thus there are three p orbitals per n value. n 2

• If = 2 (or a d orbital), then m = -2,-1,0,+1,+2.– There are 5 values of m.

Thus there are five d orbitals per n value. n 3

• If = 3 (or an f orbital), then m = -3,-2,-1,0,+1,+2, +3. – There are 7 values of m.

Thus there are seven f orbitals per n value, n

• Theoretically, this series continues on to g,h,i, etc. orbitals.3. Practically speaking atoms that have been discovered or made up to this point in time only

have electrons in s, p, d, or f orbitals in their ground state configurations.


Atomic Orbitals• Atomic orbitals are regions of space

where the probability of finding an electron about an atom is highest.

• s orbital properties:

• There is one s orbital per n level. = 0 1 value

of m

= 0 = s

n = 1

n = 2

n = 3

n = 4

n = 5

n = 6

n = 7


Atomic Orbitals• p orbitals are peanut or dumbbell shaped.

• They are directed along the axes of a Cartesian coordinate system.

• The first p orbitals appear in the n = 2 shell.

• There are 3 p orbitals per n level.

– The three orbitals are named px, py, pz.

– They have an = 1.

– m = -1,0,+1 3 values of m


Atomic Orbitals

• d orbital properties:– The first d orbitals appear in the n = 3 shell.

• The five d orbitals have two different shapes:– 4 are clover leaf shaped.– 1 is peanut shaped with a doughnut around it.– The orbitals lie directly on the Cartesian axes or are rotated 45o

from the axes.

222 zy-xxzyzxy d ,d ,d ,d ,d

There are 5 d orbitals per n level.–The five orbitals are named –They have an = 2.–m = -2,-1,0,+1,+2 5 values of m


Atomic Orbitals

• d orbital shapes


Atomic Orbitals

• f orbital properties:– The first f orbitals appear in the n = 4 shell.

• The f orbitals have the most complex shapes.• There are seven f orbitals per n level.

– The f orbitals have complicated names.– They have an = 3

– m = -3,-2,-1,0,+1,+2, +3 7 values of m

– The f orbitals have important effects in the lanthanide and actinide elements.


Atomic Orbitals• f orbital shapes


Quantum Numbers4. The last quantum number is the spin quantum number which has the symbol ms.

– The spin quantum number only has two possible values.• ms = +1/2 or -1/2• ms = ± 1/2

– This quantum number tells us the spin and orientation of the magnetic field of the electrons.

– Wolfgang Pauli in 1925 discovered the Exclusion Principle.• No two electrons in an atom can have the same set of 4 quantum numbers.

– Spin quantum number effects:• Every orbital can hold up to two electrons.

– Consequence of the Pauli Exclusion Principle.• The two electrons are designated as having• one spin up ↑ and one spin down↓ • Spin describes the direction of the electron’s magnetic fields.


hc

h E

(s-1)x(m) = c (ms-1)Frequency times wavelength equals the speed of light

Calculate the frequency, the energy, and determinethe color of light of an excited Li+ ion emitting radiation at 670.8nm.

(s-1) =(m)

c (ms-1)

E = h


The Periodic Table and Electron Configurations

Note that the 3d subshell is higher in energy than the 4s subshell so appears in the 4th period


The principal quantum number has the symbol ~ n which defines the energy of the shell

n = 1, 2, 3, 4, ...... “shells”

The angular momentum quantum number has the symbol ~ which defines the subshells. = 0, 1, 2, 3, 4, 5, .......(n-1) = s, p, d, f, g, h, .......(n-1)

The symbol for the magnetic quantum number is m which defines the orbital.m = - , (- + 1), (- +2), .....0, ......., ( -2), ( -1),

The last quantum number is the spin quantum number which has the symbol ms which characterizes the single electron.The spin quantum number only has two possible values.

ms = +1/2 or -1/2

one spin up ↑ and one spin down↓

Quantum Numbers

n and define the energy of the electron


The Nucleus:Build by adding the required number of protons (the atomic number) and neutrons (the mass of the atom)

Electrons:Hund’s Rule states that each orbital will be filled singlybefore pairing begins. The singly filled orbitals will have a parallel spin.

Pauli’s Exclusion Principle states that pairedelectrons in an orbital will have opposite spins.

Fill the electrons in starting with the lowest energy level adhering to Hund’s and Pauli’s rules.

Neon -



• Now we can write a complete set of quantum numbers for all of the electrons in these three elements as examples.– Na

• First for 11Na.– When completed there must be one set of 4 quantum numbers

for each of the 11 electrons in Na (remember Ne has 10 electrons)

111 s3 Ne NeNa

ionConfigurat 3p 3s

[Ne] = 1s22s22p6



electron s 31/2 0 0 3 e 11

electrons p 2

1/2 1 1 2 e 10

1/2 0 1 2 e 9

1/2 1 1 2 e 8

1/2 1 1 2 e 7

1/2 0 1 2 e 6

1/2 1- 1 2 e 5

electrons s 21/2 0 0 2 e 4

1/2 0 0 2 e 3


1/2 0 0 1 e 1

m m n

-th

-th

-th

-th

-th

-th

-th

-th

-rd

-nd

-st

s

11Na

1s22s22p63s1



• 26Fe.

– We should have one set of 4 quantum numbers for each of the 26 electrons in Fe.

• To save time and space, we use the symbol [Ar] to represent the first 18 electrons in Fe

1/2 2- 2 3 e 26

1/2 2 2 3 e 25

1/2 1 2 3 e 24

1/2 0 2 3 e 23

1/2 1- 2 3 e 22

1/2 2- 2 3 e 21


1/2 0 0 4 e 19 [Ar]

m m n

-th

-th

-th

-rd

-nd

-st

-th

-th

s

6226 3d 4s Ar Ar Fe

ionConfigurat 4p 4s 3d

3d electrons





Electron Affinities of Some Elements

-400-350-300-250-200-150-100-50

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Atomic Number

Ele

ctr

on

Aff

init

y (

kJ/m

ol)



ElectronegativityIncreases

Incr

ease

s Increases

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Excited Atoms & Atomic Structure. © 2006 Brooks/Cole - Thomson The Quantum Mechanical Picture of the Atom Basic Postulates of Quantum Theory 1.Atoms and