Atomic Structure

Dr. Md. Lutfor Rahman

SST, UMS
 Radioactivity
• Discovered by accident
• Becquerel
• Three types
–alpha- helium nucleus (+2 charge,
large mass)
–beta- high speed electron
–gamma- high energy light
 Rutherford’s Experiment
• Used helium to produce alpha particles.
• Aimed alpha particles at gold foil by drilling
a hole in a lead block.
• Since the mass is evenly distributed in gold
atoms, alpha particles should go straight
through.
• Used gold foil because it could be made
atoms thin.
 Florescent
Lead Uranium Screen
block

Gold Foil

Experiment set-up
What he expected
Particles would pass through

Because
Because, he thought the mass was
evenly distributed in the atom.

mass was evenly distributed

What he got
 How he explained it

• Atom is mostly empty

• Small dense, positive +
piece at center.
• Alpha particles
are deflected by it if they
get close enough.
What Rutherford Observed

+
 Models of the Atom
• Dalton
– Smallest indivisible particle

• Thomson
– Included the electron into the atom

• Rutherford
– Nuclear atom with a layer of electrons.
 Modern View

• The atom is mostly

empty space.
• Two regions
• Nucleus- protons and
neutrons.
• Electron cloud- region
where you might find
an electron.
 Max Plank added a twist
with his Quantum Theory

In 1900, Plank proposed that:

atom energy is absorbed or liberated in packets
or chunks of energy. Plank called these
packages of energy "quanta".
In order for an atom to absorb a packet of energy,
it must absorb the whole packet or none at all.
 Enter Einstein

Plank's
.
critics were legion. It wasn't until
1902 that a young man who worked at a
telegraph office near Berlin designed an
experiment that would be known as the
"Photoelectric Effect".
This young man was Albert Einstein.
 Enter Einstein
In his experiment Einstein showed that as the
frequency of radiation was directly proportional
to the energy that was absorbed by the electrons.
The math statement of this relationship is stated as
:

E = h

Where E is the energy, absorbed by the electrons,

h is Plank’s Constant and  is frequency of
 . . . FINALLY
Niels Bohr puts it all together

Bohr added Plank’s quanta idea

to the Rutherford’s atomic model.
 Bohr’s Theory

• He proposed that the electrons existed

at set levels of energy, at fixed
distances from the nucleus.
• If the atom absorbed energy, the
electron jumped to a level further from
the nucleus
 Bohr’s Theory

• If it radiated energy, it fell to a level

closer to the nucleus.
• His model was a huge leap forward in
making theory fit the experimental
evidence that other physicists had
found over the years.
 The Bohr Model of the Atom

• Nucleus • In the center, contains protons & neutrons

• Protons • positive, one atomic mass unit (amu)

• Neutrons • neutral, one amu

• energy levels around nucleus
• Shells
• negative, no effective mass
• Electrons
The Bohr Model of the Atom

e-
e - e-
e-
Protons
positive
e- e-
Neutrons
neutral

e-
e-
e- e-
 The Bohr Model of the Atom

• The atomic number is the number of protons in

an atom
• Each element has a unique atomic number
or
• Each element has a different number of protons
• When the light is passed through a prism only a
few wavelengths are present in resulting
spectra

• These appear as lines separated by dark areas,

and thus are called line spectra

• When the spectrum emitted by hydrogen gas

was
passed through a prism and separated into its
constituent wavelengths four lines appeared at
characteristic wavelengths
• Bohr began with the assumption that electrons
were orbiting the nucleus, much like the earth
orbits the sun.

• From classical physics, a charge traveling in a

circular path should lose energy by emitting
electromagnetic radiation
• If the "orbiting" electron loses energy, it should
end up spiraling into the nucleus (which it does
not).

• Therefore, classical physical laws either don't

apply
or are inadequate to explain the inner workings of
the atom
• Bohr borrowed the idea of quantize energy from
Planck

• He proposed that only orbits of certain radii,

corresponding to defined energies, are "permitted"

• An electron orbiting in one of these "allowed" orbits:

• Has a defined energy state

• Will not radiate energy

• Will not spiral into the nucleus
If the orbits of the electron are restricted,
the energies that the electron can possess
are likewise restricted and are defined by
the equation:
Bohr Model of the H atom

Z2   1 2 2 e 4
E n  R  2   R  2  R 
n  n   0
4  h
22

radius(n) = n2a0
R = 13.6 eV
a0 = Bohr radius = 0.529 Å

 = reduced mass (nucleus and electron)

Z = nuclear charge (1 for H)
e = charge of electron
0 = permittivity of a vacuum
h = Plank’s constant
Bohr
Model
H atom
  1
n = principal  Energy, Size  SHELL E n   1 3 .6  2 
n 
n = 1, 2, 3 …
E1 = -13.6 eV
n = 1 : ground state
E2 = -3.40 eV
n = 2 : first excited state
E3 = -1.51 eV
n = 3 : second excited state
E4 = -0.85 eV

E5 = -0.54 eV
•
•
•
E = 0 eV
 A. Waves

• Wavelength () - length of one complete wave

• Frequency () – Number of waves that pass a

point during a certain time period
– hertz (Hz) = 1/s

• Amplitude (A) - distance from the origin to the

trough or crest
 A. Waves
greater
 crest
amplitude
(intensity)
A
origin

 trough

greater
frequency
(color)
 B. EM Spectrum

H
L
I
O
G
W
H
E
E
N
N
E
R O Y G. B I V
E
R
R
G
G
Y
red orange yellow green blue indigo violet Y
 B. EM Spectrum

H
L
I
O
G
W
H
E
E
N
N
E
E
R
R
G
G
Y
Y
 B. EM Spectrum
• Frequency and wavelength are
inversely proportional

c = 
c: speed of light (3.00  108 m/s)
: wavelength (m, nm, etc.)
: frequency (Hz)
 B. EM Spectrum

• EX: Find the frequency of a photon with a

wavelength of 434 nm.
GIVEN: WORK:
=? =c/
 = 434 nm
= 4.34  10-7 m  = 3.00  108 m/s
4.34  10-7 m
c = 3.00  108 m/s
 = 6.91  1014 Hz
 C. Quantum Theory

• Planck (1900)
–Observed - emission of light from hot
objects
–Concluded - energy is
emitted in small, specific
amounts (quanta)
 C. Quantum Theory

• Quantum - minimum amount of energy change

• Energy can be released (or absorbed) by atoms

only in "packets" of some minimum size.

• This minimum energy packet is called a quantum

 C. Quantum Theory
• The energy (E) of a quantum is related to its
frequency () by some constant (h):
E = h

• h is known as "Planck's constant", and has a

value of 6.63 x 10-34 Joule seconds (Js)

• Electromagnetic energy is always emitted or

absorbed in whole number multiples of (h*)
 C. Quantum Theory

• Einstein (1905)
–Observed - photoelectric effect
 C. Quantum Theory

• Light shining on a metallic surface can cause

the surface to emit electrons

• For each metal there is a minimum frequency

of light below which no electrons are emitted,
regardless of the intensity of the light
 C. Quantum Theory

• The higher the light's frequency above this

minimum value, the greater the kinetic
energy of the released electron (s)

• By Planck's results Einstein (1905) was able

to established the photoelectric effect
 C. Quantum Theory

• Einstein assumed that the light was a

stream of tiny energy packets called
Photons

• Each photon has an energy proportional to

its frequency (E=h)
 C. Quantum Theory

• When a photon strikes the metal its energy

is transferred to an electron

• A certain amount of energy is needed to

overcome the attractive force between the
electron and the protons in the atom
 C. Quantum Theory

• Thus, if the quanta of light energy absorbed

by the electron are insufficient for the
electron to overcome the attractive forces
in the atom, the electron will not be ejected
- regardless of the intensity of the light.
 C. Quantum Theory

• If the quanta of light energy absorbed are

greater than the energy needed for the
electron to overcome the attractive forces of
the atom, then the excess energy becomes
kinetic energy of the released electron.
 C. Quantum Theory

• An important feature of this experiment is that

the electron is emitted from the metal with a
specific kinetic energy (i.e. a specific speed).
C. Quantum Theory
 C. Quantum Theory

• Einstein (1905)
–Concluded - light has properties of both
waves and particles

“wave-particle duality”
–Photon - particle of light that carries a
quantum of energy
 C. Quantum Theory

 The energy of a photon is proportional to its

frequency.

E = h
E: energy (J, joules)
h: Planck’s constant (6.6262  10-34 J·s)
: frequency (Hz)
 C. Quantum Theory
• EX: Find the energy of a red photon with a
frequency of 4.57  1014 Hz.

GIVEN: WORK:
E=? E = h
 = 4.57  1014 Hz E = (6.6262  10-34 J·s)
h = 6.6262  10-34 J·s (4.57  1014 Hz)
E = 3.03  10-19 J
Calculate the smallest amount of energy (i.e. one
quantum) that an object can absorb from yellow light
with a wavelength of 589 nm.
Energy quantum = h
So, we need to know the frequency 
= c
 = c/
 = (3.00 x 108 m/s)/(589 x 10-9 m)
 = 5.09 x 1014 s-1

plugging into Planck's equation:

E = (6.63 x 10-34 Js)*( 5.09 x 1014 s-1)

E (1 quanta) = 3.37 x 10-19 J
 C. Quantum Numbers

• Four Quantum Numbers:

– Specify the “address” of each electron in an atom
 C. Quantum Numbers

1. Principal Quantum Number ( n )

– Energy level

– Size of the orbital

– n2 = no. of orbitals in
the energy level
 C. Quantum Numbers

 corresponds to n from Bohr model

 describes energy level and size of orbital
 n = 1, 2, 3, ...
 as n increases,
 orbitals get larger
 orbital energy increases
 C. Quantum Numbers

2. Angular Momentum Quantum ( l )

– Energy sublevel
– Shape of the orbital

s p
d f
 C. Quantum Numbers

l = Orbital angular momentum quantum

 describes shape of orbital
 l can have integral values from 0 to n-1
 l values describe a specific shape of orbital:
if l= 0 1 2 3
s p d f
 C. Quantum Numbers

 n = no. of sublevels per level

 n2 = no. of orbitals per level
 Sublevel sets: 1s, 3p, 5d, 7f
 C. Quantum Numbers

3. Magnetic Quantum Number ( ml )

– Orientation of orbital
– Specifies the exact orbital
within each sublevel
 C. Quantum Numbers

ml = magnetic quantum
 describes orientation of orbital in space

 ml can have integral values from -l to +l

 C. Quantum Numbers

px py pz
 C. Quantum Numbers

• Orbitals combine to form a spherical shape.

2s
2px
2py 2pz
Quantum Number Relationships
 Orbital Energy Levels for Hydrogen

Orbitals with same n are degenerate (at same energy)

 C. Quantum Numbers

Multi-Electron Atoms

 Schrödinger equation can be solved only for

hydrogen atom (a one electron system)!

 For other multi-electron atoms, assume

orbitals are hydrogen-like.
 Orbital Energy Levels in Multi-Electron Atoms

For multi-electron atoms, orbitals with same n are NOT degenerate

For same n, s < p < d < f
 C. Quantum Numbers

4. Spin Quantum Number ( ms )

– Electron spin  +½ or -½
– An orbital can hold 2 electrons that spin in
opposite directions.
 C. Quantum Numbers

ms = electron spin quantum number

ms = +½ or -½
spin-up spin-
down
 
 C. Quantum Numbers

Rules for Electrons

• Aufbau Principle
• Pauli Exclusion Principle
• Hund’s Rule
 C. Quantum Numbers

Aufbau Principle
Aufbau is German for “building up”

Electrons enter orbitals of

lowest energy first.
 General Rules

• Aufbau Principle
– Electrons fill the
lowest energy
orbitals first.
– “Lazy Tenant
Rule”
 C. Quantum Numbers

Pauli Exclusion Principle

An atomic orbital may at

most describe two electrons.
 C. 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 Q. N. energy level

sublevel (s,p,d,f)

orbital
2. Ang. Mom. Q. N.
electron

 General Rules
• Pauli Exclusion Principle
– Each orbital can hold TWO electrons with opposite
spins.
 C. Quantum Numbers

Hund’s Rule
When electrons occupy orbitals
of equal energy,
– one electron enters each orbital
– until all the orbitals contain one
electron with parallel spins.
 General Rules
• Hund’s Rule
– Within a sublevel, place one e- per orbital before
pairing them.
– “Empty Bus Seat Rule”

WRONG RIGHT
Electron Configuration
 Notation for Electron Distribution

Here we see the Principle Quantum Number

electron configuration
for the element
HELIUM 
1s
2 Number of Electrons

Angular Momentum
 Principle quantum number ‘n’

The large number "1" refers to the

principle quantum number "n"

1s 2

which stands for the energy level.  It tells

us that the electrons of helium occupy
the first energy level of the atom.
 Angular momentum quantum number I

The letter "s" stands for the angular

momentum quantum number "l". 

1s 2

It tells us that the two electrons of the helium

electron occupy an "s" or spherical orbital.
 Total Number of Electrons

The exponent "2" refers to the total number

of electrons in that orbital or sub-shell. 

1s 2

In this case, we know that there are two electrons in the

spherical orbital at the first energy level.
Principle Quantum Number (n) and Sublevels

• The number of sublevels that an energy level

can contain is equal to the principle quantum
number of that level.
 Sublevels
• The second energy level would have two sublevels,
• The third energy level would have three sublevels. 
• The first sublevel is called an s sublevel. 
• The second sublevel is called a p sublevel. 
• The third sublevel is called a d sublevel and
• the fourth sublevel is called an f sublevel. 

Although energy levels that are higher than 4 would contain

additional sublevels, these sublevels have not been named because no
known atom in its ground state would have electrons that occupy
them
 Total Number of Orbital and Electrons per
Energy Level

• An easy way to calculate the number of orbitals

found in an energy level is to use the formula n2. 

• For example, the third energy level (n=3) has a total

of 32, or nine orbitals. 

• This makes sense because we know that the third

energy level would have 3 sublevels; an s sublevel
with one orbital, a p sublevel with 3 orbitals and a d
sublevel with 5 orbitals.  1 + 3 + 5 = 9, so the formula
n2 works!
Orbital Energy Levels in Multi-Electron Atoms
THE ULTIMATE TOOL
 THE TOOL

• Remember to start at the beginning of each

arrow, and then follow it all of the way to
the end, filling in the sublevels that it passes
through.  In other words, the order for filling
in the sublevels becomes;
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f,
5d, 6p, 7s, 5f, 6d,7p.
 Notation
• Orbital Diagram

O
8e- 1s 2s 2p
 Electron Configuration

1s 2s 2p
2 2 4
 Notation
• Longhand Configuration

S 16e 1s 2s 2p 3s 3p
- 2 2 6 2 4

Core Electrons Valence Electrons

 Shorthand Configuration

S 16e -
[Ne] 3s 3p2 4
 Periodic Patterns

s
1
p
2
3 d (n-1)
4
5
6
7
6
f (n-2) 7
© 1998 by Harcourt Brace & Company
III. Atomic Electron Configurations
C. Box Diagrams - Orbitals are represented by boxes and
electrons are represented by arrows.
Element Orbitals
1s 2s 2p
Li
Be
B Hund’s Rule – The
C most stable arrangement
of electrons is that with
N the maximum number of
unpaired electrons, all
O
with the same spin
F direction.
Ne
III. Atomic Electron Configurations
Element Orbitals
4s 3d
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
III. Atomic Electron Configurations
Number of electrons in orbital
D. spdf Notation - 1s1
electron shell (n) Orbital type (l)

Element Orbitals spdf notation

1s 2s 2p
Li 1s2 2s1
Be 1s2 2s2
B 1s2 2s2 2p1
C 1s2 2s2 2p2

N 1s2 2s2 2p3

O 1s2 2s2 2p4

F 1s2 2s2 2p6

Ne 1s2 2s2 2p6

III. Atomic Electron Configurations
Number of electrons in orbital
D. spdf Notation - 1s1
electron shell (n) Orbital type (l)

Element Orbitals spdf notation

3s 3p
Na [Ne] 1s2 2s1
Mg [Ne] 1s2 2s2
Al [Ne] 1s2 2s2 2p1
Si [Ne] 1s2 2s2 2p2

P [Ne] 1s2 2s2 2p3

S [Ne] 1s2 2s2 2p4

Cl [Ne] 1s2 2s2 2p6

Ar [Ne] 1s2 2s2 2p6

 Electron Configuration
Examples
Write ground state electron configurations
(using noble gas notation) for the following:
a) potassium, K
(Z=19) [Ar] 4s1
b) iodine, I
(Z=53) [Kr] 5s2 4d10 5p5
c) bismuth, Bi
(Z=83) [Xe] 6s2 4f14 5d10 6p3
Some Electron Configuration Exceptions

 Chromium, Cr (Z=24)
expected: [Ar]4s2 3d4
actual: [Ar] 4s1 3d5

 Copper, Cu (Z=29)
expected: [Ar] 4s2 3d9
actual: [Ar] 4s1 3d10
 Why Exceptions?

 Recall: energy levels get closer in energy as

n increases.

 Also, special stability of filled or half-filled

subshells.
 Stability
• Electron Configuration Exceptions
 Copper

EXPECT: [Ar] 4s2 3d9

ACTUALLY: [Ar] 4s1 3d10

 Copper gains stability with a full

d-sublevel.
 Stability
• Electron Configuration Exceptions
 Chromium

EXPECT: [Ar] 4s2 3d4

ACTUALLY: [Ar] 4s1 3d5

 Chromium gains stability with a half-full d-

sublevel.
Electrons in Subshells - a Closer Look

N (Z=7): 1s2 2s2 2p3

1s 2s 2p
 Paramagnetic vs Diamagnetic

 Paramagnetic - at least one unpaired electron.

 Diamagnetic - all electrons are paired.
 Paramagnetic species are attracted to a magnetic
field.
 Diamagnetic species are repelled by a magnetic
field.
 Electron Configurations for Ions

 Metals lose e- and nonmetals gain e-.

 Write configuration for parent atom, then
add or remove electrons in outermost shell.
 ex: Fe3+
Fe (Z=26) [Ar]4s2 3d6
Fe3+ [Ar] 3d5
 Core Electrons vs Valence Electrons

 core electrons - electrons in inner shells

 valence electrons - electrons in outer shell

Cl (Z=17): [Ne] 3s2 3p5

valence electrons
core electrons

Most chemical reactions only involve valence electrons!