Download Electrons in Atoms

Topic 3:
Electrons in Atoms
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 SPİN : THE 4. QUANTUM NUMBER
9. MULTIELECTRON ATOMS
10.ELECTRON CONFIGURATIONS
2
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
• It’s velocity is
3,00 x 108 m/s in all of vacuum
environment. (Speed of light)
3
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)
4
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).
5
6
Wawelength and Frequency
• The relationship between the speed of
light (c), the wavelenght () and the
frequency () of electromagnetic
radiation:
•
c=x
7
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
10-9
UV, Visible
Mikrometer
nm

10-6
Infrared
Milimeter
mm
10-3
Infrared
Centimeter
cm
10-2
Micro wave
Meter
m
1
TV, radio
8
Electromagnetic Spectrum
9
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 being’s sight.
10
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.
11
Atomic Spectra
The spectrum of white light: When white light
is passed through a glass prism,red light is
refracted the least and violet light the most.
The other colors of the visible spectrum are
found between red and violet.
12
Atomic Spectra
Hydrogen
line
spectrum:
Only
4
lines(red,greenish blue and two violets at
diffrent wavelength) are visible in this
spectrum. In addition to these, there are
several lines in the ultraviolet region very
closed to each other .
13
Atomic Spectra
In 1885, Johann Balmer, through trial and error,
deduced a formula for the wavelengths of these
spectra lines.
 1 1 
  3,288110 s  2  2 
2 n 
15
1
n2
14
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.
15
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.
Blackbody
16
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.
17
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.
18
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 Planck’s equation :
• h: Planck’s constant has a value of
6,626 X 10-34 J.s.
E  hv
19
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 .
20
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.
21
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 Planck’s 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 photon’s energy is larger than
the minimum energy required by the electrons to
leave the metal surface, called Work function.
22
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
E foton  E0  Ek
1
h  h 0  me ve2
2
kinetic energy of electrons
Supplied energy Work function
23
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:
24
The Bohr Atom
1. The electrons can only travel in certain
circular orbits: At a certain discrete set of
distances from the nucleus with specific
energies.
2. 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
3. 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= hⱱ)
25
The Bohr Atom
The allowed energy states for
electrons are defined as n = 1,
n=2,
n = 3 and continiued similarly.
These integers are called the
principle quantum number.
The theory
determine the
electrons in
meanwhile
energies.
allows us to
velocities of the
the orbits and
their
kinetic
26
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.
The energy levels of
hydrogen atom
The orbital radius
of Hydrogen atom
Bohr radius
RH= 2,179 X 10-18 J
27
The Bohr Atom
If the electron gains an
energy of 2,179 x 10-18 J, it
moves to the n=∞ orbit, that
is,
hydrogen
atom
is
ionized. If the electron falls
from
higher
numbered
orbits to the orbit n=1 is in
the form of ultraviolet light
(Lyman series). Electron
transitions to the orbit n=2
are called Balmer series.
Transitions to the orbit n=3
yield spectral lines in the
infrared (Paschen series)
28
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.
29
The Bohr Atom
Excitation
Emission
30
The Bohr Atom
The energy levels of hydrogen atom
31
The Bohr Atom
The Bohr’s atom theory makes not only the
determination of energy levels of hydrogen
atoms but also the ones of the ions with one
electron, Example : He+, Li2+
Z: Atomic number
32
The Ideas Leading To A New Quantum
Mechanics
The Lack of the Bohr’s 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 Bohr’s 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:
33
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 TİMES DISPLAY
WAVELIKE PROPERTIES”
34
Wave-Particle Duality
De Broglie’s
wavelength
Particle’s
momentum
Mass Velocity
35
The Ideas Leading To A New Quantum
Mechanics
2. The Uncertainty Principle of Heisenberg
During the 1920’s Niels Bohr ve Werner Heisenberg
considered hypothetical experiments to establish just
how precisely the behaviour of subatomic particles can
be determined. The conclusion they reached is that
there must be always uncertainties in measurement
such that the product of the uncertainty in position(x)
and the uncertainty in momentum(p).
h
x  p 
4
x : position
p: momentum
36
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.
37
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 Broglie’s
function. The acceptable solutions of
these wave equations are called wave
functions, denoted by the Greek letter 
(psi) .
38
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.

l  n 
2
n  1,2,3,...
The total number
of nodes=
n+1
The motion of an electron in
the Bohr radius
39
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.
40
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.
41
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.
Radial part
Angular
part
Angular
part
Radial
part
42
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.
43
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…
44
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 n=1 the
maximum and unique value of “l” is 0 which means
that the level K contains one sub-level. For n=2 , “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 …
45
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.
46
Magnetic
quantum
number
ml
The
number
of
orbitals
in the
subshell
Principal
quantum
number
n
Orbital
quantum
number
l
Sub-shell
3
0
3s
0
1
1
3p
-1,0,1
3
2
3d
-2,-1,0,1,2
5
47
Quantum numbers and Electron
Orbitals
The shells and sub-shells of Hydrogen atom
48
s orbitals
s orbital: Spherically symmetric
49
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.
50
d orbital
d orbital: There are 5 different type of d
orbitals.
Their
orientations
vary
respectively.
51
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 nonuniform magnetic field. The
beam splits in two with two
opposite
directions
(
A
spinning unpaired electron
behaves as two magnets with
opposite pole directions.
52
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
: ms=+1/2 ve ms=-1/2.
53
Multielectron Atoms
Eş enerjili orbitaller
• 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.
54
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 orbitals with different energy levels
55
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
1. Electrons occupy orbitals in a way that minimizes the
energy of the atom.
56
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
57
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 Hund’s 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.
58
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.
spdf notation (condensed)
spdf notation (expanded)
orbital diagram
59
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.
60
The Electron Configuration of some
elements(C, N, Ne, Na)
61
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
• [Ne]3s1
3s2 3s23p13s23p23s23p3 3s23p4 3s23p5
3s23p6
•
[He]2s22p2
[Kr]4d105s25p5
6C:
24Cr:
[Ar]4s13d5
53I:
62
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.
63
Example: Write out the electron configuration
of 38Sr, [38Sr]+2 and 26Fe ,[26Fe]+2 in the
condensed spdf notation ?
22s22p63s23p64s23d104p65s2
Sr:
1s
38
(according to the order of orbital energy
levels)
64
Solution
•
22s22p63s23p63d104s24p65s2 (according to
Sr:
1s
38
the increasing principal quantum number “n” )
•
38Sr:
[Kr]5s2 (according to the order with the
indication of noble gas core electron
configuration )
• [38Sr]+2: 1s22s22p63s23p63d104s24p6
•
26Fe:
1s22s22p63s23p64s23d6
• [26Fe]+2: 1s22s22p63s23p63d6
65