Topic 3: Electrons in Atoms

1
Topic 3 Electrons in Atoms
2
Contents

1. ELECTROMAGNETIC RADIATION
2. ATOMIC SPECTRA
3. QUANTUM THEORY
4. THE BOHR ATOM
5. TWO IDEAS LEADING TO A NEW QUANTUM MECHANICS
6. WAVE MECHANICS
7. QUANTUM NUMBERS AND ELECTRON ORBITALS
8. ELECTRON SPIN THE 4. QUANTUM NUMBER
9. MULTIELECTRON ATOMS
10. ELECTRON CONFIGURATIONS

3
Electromagnetic Radiation

• Electromagnetic Radiation, is a form of energy
  transmission through a vacuum(empty space) or a
  medium(such as glass) in which electric and
  magnetic fields are propagated as waves.
• Transmits energy through an empty space
• includes visible lights, x-rays, radio waves and
  optic waves
• carries certain fundamental characteristics
• Its velocity is 3,00 x 108 m/s in all of
  vacuum environment. (Speed of light)

4
Electromagnetic Radiation

• Wave, is a disturbance that transmits energy
  through a medium .

The distance between the tops of two successive
crests ( or the bottoms of two troughs) is called
wavelength and designated by the Greek letter
lambda ? .
Frequency is the number of crests or troughs
that pass through a given unit of time and
designated by the letter ? . The unit is Hz
(s-1)
5
As the figure shows the radiation component with
the magnetic field lies in a plane perpendicular
to that of the electric field component. The
wavelength of electromagnetic radiation is
shorter for high frequencies(b) and longer for
low frequencies (a).
6
(No Transcript)
7
Wawelength and Frequency

• The relationship between the speed of light (c),
  the wavelenght (l) and the frequency (n) of
  electromagnetic radiation
• c n x l

8
Frequency, Wavelength and Velocity of
Electromagnetic Radiation The SI unit for
frequency, s-1, Hertz (Hz), and the basic SI
wavelength unit is the meter. However some of the
smaller units listed below are also used.
Unit Symbol Length (m) Type of radiation
Angstrom Å 10-10 X-ray
Nanometer nm 10-9 UV, Visible
Mikrometer ? 10-6 Infrared
Milimeter mm 10-3 Infrared
Centimeter cm 10-2 Micro wave
Meter m 1 TV, radio
9
Electromagnetic Spectrum
10
Electromagnetic Spectrum
Electromagnetic Spectrum is a concept that
describes the positions of both the forms of
radiation founded in the visible region and other
forms of electromagnetic radiation indicating
the wavelength and frequency ranges.
Visible Region Spectrum In a medium such as
glass, the speed of light is lower than vacuum.As
a consequence light is refracted or bent when it
passes from one medium to another. Colors are
made up of the beams with specific frequency
within the capability of human beings sight.
11
Atomic Spectra
Each wavelength component of the white light
yields an image of the slit in the form of a
line. There are so many of these lines that they
blend together into an unbroken band of color
from red to violet. Therefore, the spectrum of
white light is continious. On the other hand, the
spectra produced by certain gaseous substances
consist of only a limited number of colored lines
with dark spaces between them. These
discontinious spectra are called atomic spectra
or line spectra. Each element has its own
distinctive line spectrum.
12
Atomic Spectra
13
Atomic Spectra
14
Atomic Spectra
In 1885, Johann Balmer, through trial and error,
deduced a formula for the wavelengths of these
spectra lines.
15
Atomic Spectra

• The fact that atomic spectra consist of only
  limited numbers of well-defined wavelength lines
  provides a great opportunity to learn about the
  structure of atoms.
• For example, it suggests that only a limited
  number of energy values are available to excited
  gaseous atoms.

16
Quantum Theory
As with atomic spectra classical nineteenth
century physics could not provide a complete
explanation of light emission by heated solids,
As a result the quantum theory aroused.
Blackbody radiation The object that emits all
type of radiation applied on them is called
blackbody . When it is heated, it is observed
that every type of wawelength exists at their
emission.
17
Quantum Theory

• At low temperatures radiations of low energy
  (with long wavelength ), and at high
  temperatures radiations of high energy (with
  short wavelength) occur. That is the emission of
  different types of radiation by blackbodies does
  not depend on the wavelength since according to
  the wavelength theory the intensity of radiation
  is proportional to the square of the amplitude.

18
Quantum Theory

• Max Planck suggested in 1900 the quantum theory
• The energy of radiation that a system may
  possess is limited to a discrete set of values.
• The difference between two of the allowed
  energies also has a specific value, called
  quantum of energy.

19
Quantum Theory

• Planck postulated that the energy of a quantum of
  electromagnetic radiation is proportional to the
  frequency of the radiation- the higher the
  frequency the greater the energy. This is written
  as the formula below and called as Plancks
  equation
• h Plancks constant has a value of 6,626 X 10-34
  J.s.

20
Quantum Theory
The Photoelectric Effect
A beam of electrons is produced by shining light
on certain metal surfaces. This event is called
photoelectric effect, the electrons produced are
defined as photo-electrons. This feature was
discovered in 1888 by Hertz .
21
Quantum Theory

• Findings achieved by the photoelectric
  experiment

• The kinetic energy of the ejected electrons
  rises with the increase in the frequency of the
  light the kinetic energy of the ejected
  electrons does not depend on the intensity of
  light.
• If the frequency of the light is below the
  threshold value (?o ) it can not eject any
  electrons.
• As the intensity of light increases, the number
  of ejected electrons increase but the kinetic
  energy of electrons remains unchanged.

22
Quantum Theory
The Photoelectric Effect
In 1905, Einstein proposed that electromagnetic
radiation has particlelike qualities and that
particles of light, called photons have a
characteristic energy given by Plancks equation .
When the photons fall on a metal surface, they
transfer their energy to the electrons of the
metal. However, the emission of the electrons
takes place only if the photons energy is
larger than the minimum energy required by the
electrons to leave the metal surface, called Work
function.
23
Quantum Theory

• For the ejection of electrons from a plate of
  copper an ultraviolet type of radiation or
  radiation with higher frequency is adequate.
  Radiation of blue form with lower frequency is
  enough to eject electrons from potassium. If the
  supplied energy by a photon is greater than the
  the work function, the difference between them is
  transmitted as kinetic energy to the electron to
  eject it from the metal surface

kinetic energy of electrons
Work function
Supplied energy
24
The Bohr Atom
The planetary atom model of Rutherford had a
technical difficulty The electrons would lose
energy collapsing into the nucleus during the
electromagnetic radiation. This model is
disastrous because it predicts that all atoms are
unstable. To overcome this difficulty, Niels
Bohr, in 1913, proposed that electrons could
only have certain classical motions
25
The Bohr Atom

• The electrons can only travel in certain circular
  orbits At a certain discrete set of distances
  from the nucleus with specific energies.
• The electrons has only a fixed set of allowed
  orbits, called stationary states. As long as an
  electron remains in a given orbit, its energy is
  constant and no energy is emitted
• An electron can pass only from one allowed orbit
  to another. In such transitions, fixed discrete
  quantities of energy are involved, in accordance
  with Planck equation(E h?)

26
The Bohr Atom
The allowed energy states for electrons are
defined as n 1, n2,n 3 and continiued
similarly. These integers are called the
principle quantum number. The theory allows us
to determine the velocities of the electrons in
the orbits and meanwhile their kinetic energies.
27
The Bohr Atom

• When the electron is free of the nucleus,by
  convention, it is said to be zero of energy. When
  the electron is attracted to the nucleus and
  confined to the orbit n, energy is emitted. The
  electron energy is indicated with a negative sign
  to point out that its level declines.

28
The Bohr Atom
If the electron gains an energy of 2,179 x 10-18
J, it moves to the n8 orbit, that is, hydrogen
atom is ionized. If the electron falls from
higher numbered orbits to the orbit n1 is in the
form of ultraviolet light (Lyman series).
Electron transitions to the orbit n2 are called
Balmer series. Transitions to the orbit n3 yield
spectral lines in the infrared (Paschen series)
29
The Bohr Atom

• Normally the electron in a hydrogen atom is found
  in the orbit closest to the nucleus (n 1), this
  is the lowest allowed energy and called ground
  state.
• When the electron gains a quantum of energy it
  moves to a higher level (n 2 or 3, ) and the
  atom is in an excited state. When the electron
  drops from a higher to a lower numbered orbit, a
  unique quantity of energy is emitted- the
  difference between the two levels.

30
The Bohr Atom
Emission
Excitation
31
The Bohr Atom
The energy levels of hydrogen atom
32
The Bohr Atom
33
The Ideas Leading To A New Quantum Mechanics
The Lack of the Bohrs Atom Theory
The Bohr model does not do a good job of
predicting atomic spectra of many electron atoms
and the effect of magnetic field on the spectra.
After Bohrs work on hydrogen, two landmark ideas
stimulated a new approach to quantum mechanics.
We define the concept as modern quantum
mechanics composed of the ideas
34
The Ideas Leading To A New Quantum Mechanics

• 1. Wave Particle Duality

To explain the photoelectric effect Einstein
suggested that light has particle like
properties,embodied in photons. Other phenomena,
however such as the dispersion of light into a
spectrum by a prism , are best understood in
terms of the wave theory of light. In 1924 Louis
de Broglie considering the nature of the light
and matter offered a startling proposition
SMALL PARTICLES MAY AT TIMES DISPLAY WAVELIKE
PROPERTIES
35
Wave-Particle Duality
Velocity
Mass
36
The Ideas Leading To A New Quantum Mechanics
?x position ?p momentum
37
The Uncertainty Principle

• The significance of this expresssion is that we
  cannot measure position and momentum
  simultaneously. If we design an experiment to
  locate the position of a particle with great
  precision, we cannot measure its momentum
  precisely and vice versa.
• In simpler terms, if we know precisely where a
  particle is, we cannot also know where it has
  come from and where it is going. If we know
  precisely how a particle is moving we can not
  also know precisely where it is.

38
Wave Mechanics
The branch of the physics that deals with the
solutions of wave equations is called as wave
mechanics or quantum mechanics. Erwin
Schrödinger concluded an equation,that can be
applicable for the hydrogen atom , by using de
Broglies function. The acceptable solutions of
these wave equations are called wave functions,
denoted by the Greek letter ? (psi) .
39
Wave Mechanics

• For an electron the situation is more like wave
  motion in a short string with fixed ends, a type
  of wave called a standing wave. We might say that
  the permitted wavelenghts of a standing wave are
  quantized. They are related to the length of the
  string which must be equal to a whole number(n)
  times one-half the wavelength.

The total number of nodes n1
The motion of an electron in the Bohr radius
40
Wave Functions
Schrödinger, concluded the equation below that
determines the wave motion of a hydrogen atom.
From the differential equations are resulted the
wave functions and the total energy of an
electron. Each of these wave functions refers to
the energy level of an electron and is in
relation to the position of the electron where it
can be found.
41
Quantum Numbers and Orbitals

• The mathematical procedure producing acceptable
  wave functions requires the use of the integral
  parameters, so wave functions are determined
  according to these integral parameters called
  quantum numbers .

An orbital represents a region in an atom where
an electron is likely to be found.
42
Wave Functions of Hydrogen Atom
Since the Schödinger equation can not be solved
by the kartesien coordinates, it is solved by
being converted into global polar coordinates.
43
Quantum Numbers and Electron Orbitals
In the wave mechanics the electrons in an atom
composed of more than one electron are
distributed in the shells. The shells are
composed of one subshell or many subshells,the
subshells are made up of one orbital or many
orbitals. Each electron of an atom is defined
through three quantum numbers referring to the
shell, subshell and orbital.
44
Quantum Numbers and Electron Orbitals

• Principal Quantum number, n The energy levels in
  atom are divided into the shells represented by
  the principle quantum number, n. As in the Bohr
  quantum theory, it may have only positive,
  nonzero (n 1, 2, 3, ..) integral values. In
  addition to the numbers, to indicate the layers,
  some letters are also used. The shells are the
  regions where electrons are more likely to be
  found. The greater the n value, the farer the
  shell from the nucleus.
• 1 2 3 4 5...
• K L M N O

45
Quantum Numbers and Electron Orbitals
Angular momentum quantum number, l Energy levels
include sub-energy levels. Consequently, shells
are seperated into subshells each of which is
represented with angular momentum quantum number
l .This determines the geometrical shape of the
electron probability distribution. The number l
can have all values ranging from 0, 1, 2 to n-1.
For n1 the maximum and unique value of l is
0 which means that the level K contains one
sub-level. For n2 , l will have 0 and 1
values. Thus, L level is composed of two
sub-levels. The total number of sub-levels in a
level is equal to the principal quantum number.
The sub-shells are indicated as below 0
1 2 3 4 5 6 s p d f g h i
46
Quantum Numbers and Electron Orbitals

• To indicate a sub-shell in a shell, the principal
  quantum number n and the angular momentum
  quantum number are written next to each other .
  For the second shell (L), the subshells s and p
  are indicated as 2s (n 2, l 0) and 2p (n 2,
  l 1 ) .
• Magnetic quantum number, ml Each subshell is
  composed of one or more orbitals and each orbit
  in a sub-shell is defined as magnetic quantum
  number ml. This number may be a positive or
  negative integer including zero and ranging from
  l to l.

47
Principal quantum number n Orbital quantum number l Sub-shell Magnetic quantum number ml The number of orbitals in the sub-shell
3 0 3s 0 1
  1 3p -1,0,1 3
  2 3d -2,-1,0,1,2 5
48
Quantum numbers and Electron Orbitals
The shells and sub-shells of Hydrogen atom
49
s orbitals
s orbital Spherically symmetric
50
p orbitals
p orbital Electron density is in form of a
dumbbell.Two lobes are seperated by a nodal
plane in which charge density drops to zero.
51
d orbital
d orbital There are 5 different type of d
orbitals. Their orientations vary respectively.
52
Electron Spin-The fourth Quantum Number
Stern-Gerlach experiment Ag atoms vaporized in
the oven are collimated into a beam by the slit
and the beam is passed through a non-uniform
magnetic field. The beam splits in two with two
opposite directions ( A spinning unpaired
electron behaves as two magnets with opposite
pole directions.
53
Electron Spin
Spin magnetic quantum number, ms An electron
generates a magnetic field because of its spin on
its axis. As a result of this action ( spin at
one direction, and at the opposite direction) the
spin magnetic quantum number may have values
ms1/2 ve ms-1/2.
54
Multielectron Atoms

• Schrödinger developed his wave equation for the
  hydrogen atom. For multielectron atoms a new
  factor arises mutual repulsions between
  electrons. Because exact electron positions are
  not known,electron repulsions can only be
  approximated.

55
Multielectron Atoms

• In multielectron atoms the attractive force of
  nucleus for a given electron increases as the
  nuclear charge rises, which leads to a decrease
  of the energy level of an orbital. Hence,
  multielectron atoms have different orbital
  energies

The orbital energy level decreases with rising
nucleus charge
56
Electron Configurations

• The electron configuration of an atom is a
  designation of how electrons are distributed
  among various orbitals.
• Rules for Assigning Electrons in Orbitals
• Electrons occupy orbitals in a way that
  minimizes the energy of the atom.

57
Electron Configurations

• The diagram shows the order in which electrons
  occupy orbitals in these shells, first 1s then
  2s and 2p and so on. The order of the filling of
  orbitals has been established by experiment,
  principally through spectroscopy and it is the
  order that we must follow in assigning electron
  configurations to the element. Except for a few
  elements the order in which the orbitals fill in

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s,
4f, 5d, 6p, 7s, 5f, 6d, 7p
58
Electron Configuration
2. No two electrons in an atom may have all four
quantum numbers alike (Pauli exclusion
principle).
3. When orbitals of identical energy are
available, electrons initially occupy these
orbitals singly. As a result of this rule, known
as Hunds rule an atom tends to have as many
unpaired electrons as possible. The electrons do
this by seeking out empty orbitals of similar
energy in preference to pairing up with other
electrons in half-filled orbitals.
59
Notation of Electron Configuration

• Since the atomic number of Carbon element is 6,
  in all of three indications there are 6
  electrons. The electrons are those with parallel
  spins which occupy different orbitals in the same
  sub-shell singly.

60
The Aufbau Process
Aufbau means constructing or building and what
we do is assign electron configurations to the
elements in order of increasing atomic number.
61
The Electron Configuration of some elements(C, N,
Ne, Na)
62
Valence Electrons

• Electrons that are added to the electronic shell
  of highest principal quantum number(the outermost
  or valence shell) are called valence electrons.
  The electron configuration of Na is written below
  with the neon core ( 1s2s2p6 ) and for the other
  third period elements only the valence-shell
  electron configuration is shown.
• Na Mg Al Si P S Cl Ar
• Ne3s1 3s2 3s23p13s23p23s23p3 3s23p4 3s23p5
  3s23p6
• 6C He2s22p2 24Cr Ar4s13d5 53I
  Kr4d105s25p5

63
The elements of the third period end with Argon.
After argon instead of 3d the next sub-shell to
fill is 4s.
The 19. electron of potassum occupies 4s
instead of 3d orbital since 4s has lower energy
level.
64
Example Write out the electron configuration of
38Sr, 38Sr2 and 26Fe ,26Fe2 in the
condensed spdf notation ?
38Sr 1s22s22p63s23p64s23d104p65s2 (according
to the order of orbital energy levels)
65
Solution

• 38Sr 1s22s22p63s23p63d104s24p65s2 (according to
  the increasing principal quantum number n )
• 38Sr Kr5s2 (according to the order with the
  indication of noble gas core electron
  configuration )
• 38Sr2 1s22s22p63s23p63d104s24p6
• 26Fe 1s22s22p63s23p64s23d6
• 26Fe2 1s22s22p63s23p63d6