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1. Chapter 5
Electronic Structure and Periodic Properties of
Elements

2. 5.1. Electromagnetic energy
 Visible light, x-rays, 𝛾 − 𝑟𝑎𝑦 and microwaves are some of the types of
electromagnetic radiation (also called electromagnetic energy or radiant
energy).
 All electromagnetic radiation consists of energy propagated by electric and
magnetic fields that increase and decrease in intensity as they move through
space.
 This classical wave model explains why rainbows form, how magnifying
glasses work, and many other familiar observations.

3. 5.1.1. Characteristics of Light
The Wave Nature of Light
 The wave properties of electromagnetic radiation are described by three
variables and one constant.
 Frequency (v, Greek nu): The frequency of a wave is the
number of cycles it undergoes per second, expressed by the unit
1/second [s-1; also called a hertz (Hz)].
 Wavelength (λ, Greek lambda) The wavelength is the distance
between any point on a wave and the corresponding point on the
next crest (or trough) of the wave, that is, the distance the wave
travels during one cycle.
Wavelength has units of meters or, for very short wavelengths,
nanometers (nm, 10-9 m), picometers (pm= 10-12 m), or the non-SI
unit angstroms (Å= 10-10 m).

4.  Speed: The speed of a wave is the distance it moves per unit time (meters
per second), the product of its frequency (cycles per second) and
wavelength (meters per cycle):
 In a vacuum, electromagnetic radiation moves at 2.997924583X108 m/s
(3.00 X 108 m/s to three significant figures), a physical constant called the
speed of light (c):
C = v x λ……………………..5.1
 Since the product of v and λ is a constant, they have a reciprocal
relationship radiation with a high frequency has a short wavelength, and
vice versa.
Cont…

5. Cont…

6.  Amplitude: The amplitude of a wave is the height of the crest (or depth of
the trough).
 For an electromagnetic wave, the amplitude is related to the intensity of the
radiation, or its brightness in the case of visible light.
 Light of a particular color has a specific frequency (and thus, wavelength)
(lower amplitude, less intense) or brighter (higher amplitude, more intense).
Cont…

7. The Electromagnetic Spectrum
 Visible light represents a small region of the electromagnetic spectrum.
 All waves in the spectrum travel at the same speed through a vacuum but differ
in frequency and, therefore, wavelength.
 The spectrum is a continuum of radiant energy, so each region meets the next.
 For instance, the infrared (IR) region meets the microwave region on one end
and the visible region on the other.
 We perceive different wavelengths (or frequencies) of visible light as colors,
from red (λ< 750 nm) to violet (λ < 400 nm).
 Light of a single wavelength is called monochromatic (Greek, “one color”),
whereas light of many wavelengths is polychromatic. White light is
polychromatic.

8.  The region adjacent to visible light on the short-wavelength end consists of
ultraviolet (UV) radiation (also called ultraviolet light).
 Still shorter wavelengths (higher frequencies) make up the x-ray and
gamma (g) ray regions.
 Some types of electromagnetic radiation are utilized by familiar devices;
for example, long-wavelength, low-frequency radiation is used by
microwave ovens, radios and cell phones.
Cont…

9. Regions of the electromagnetic spectrum.
Cont…

10. For example: A dental hygienist uses x-rays (λ = 1.00 Å) to take a series of
dental radiographs while the patient listens to a radio station (λ = 325 cm) and
looks out the window at the blue sky (λ = 473 nm). What is the frequency (in
s-1) of the electromagnetic radiation from each source? (Assume that the
radiation travels at the speed of light, 3.00 X 108 m/s.)
Solution
Cont…

11. The Particle Nature of Light
 Three observations involving matter and light confounded physicists at the
turn of the 20th century: blackbody radiation, the photoelectric effect and
atomic spectra.
 Explaining these phenomena required a radically new picture of energy.
Blackbody Radiation and the Quantum Theory of Energy
 The light given off by an object being heated
 The quantum theory. In 1900, the German physicist Max Planck
 He proposed that a hot, glowing object could emit (or absorb) only certain
quantities of energy:
E = nhv
• where E is the energy of the radiation, v is its frequency, n is a positive integer (1, 2, 3, and
so on) called a quantum number, and h is Planck’s constant. (h = 6.626 X 10-34J.s).

12.  The energy of an atom is quantized energy packet is called a quantum
(“fixed quantity”; plural, quanta).
 A quantum of energy is equal to hv.
 An atom changes its energy state by emitting or absorbing one or more
quanta, and the energy of the emitted (or absorbed) radiation is equal to
the difference in the atom’s energy states:
∆𝑛 = 1
Cont…

13. The Photoelectric Effect and the Photon Theory of Light
 When monochromatic light of sufficient frequency shines on a metal plate,
a current flows
 For current to flow, the light shining on the metal must have a minimum, or
threshold, frequency,

14.  The photon theory. Building on Planck’s ideas, Albert Einstein proposed in
1905 that light itself is particulate, quantized into tiny “bundles” of energy,
later called photons.
 One “particle” of light, whose energy is related to its frequency, not its
amplitude:
Example: A student uses a microwave oven to heat a meal. The wavelength of
the radiation is 1.20 cm. What is the energy of one photon of this microwave
radiation?
Cont…

15. Atomic Spectra
Line Spectra and the Rydberg Equation
 Instead, it creates a line spectrum, a series of fine lines at specific
frequencies separated by black spaces.
 The Rydberg equation, that predicted the position and wavelength of any
line in a given series:

16.  Two years after the nuclear model was proposed, Niels Bohr (1885–
1962), a young Danish physicist working in Rutherford’s laboratory,
suggested a model for the H atom that did predict the existence of line
spectra.
5.2. The Bohr Model of the Hydrogen Atom

17. Cont…

18. Features of the Mode
 Quantum numbers and electron orbit.
 The quantum number n is a positive integer (1, 2, 3, . . .) associated with the
radius of an electron orbit, which is directly related to the electron’s energy:
the lower the n value, the smaller the radius of the orbit, and the lower the
energy level.
 Ground state: When the electron is in the first orbit (n = 1), it is closest to
the nucleus, and the H atom is in its lowest (first) energy level, called the
ground state.
 Excited states: If the electron is in any orbit farther from the nucleus, the
atom is in an excited state.
 Absorption: If an H atom absorbs a photon whose energy equals the
difference between lower and higher energy levels, the electron moves to the
outer (higher energy) orbit.

19.  Emission: If an H atom in a higher energy level (electron in farther orbit)
returns to a lower energy level (electron in closer orbit), the atom emits a
photon whose energy equals the difference between the two levels.
Limitations of the Model
 Despite its great success in predicting the spectral lines of H, the Bohr
model failed with every other atom. The reason is that it is a one electron
model.
 Electrons do not move in fixed, defined orbits.
 the energy of an atom occurs in discrete levels, and an atom changes
energy by absorbing or emitting a photon of specific energy.
Cont…

20. The Energy Levels of the Hydrogen Atom

21. • Finding the wavelength of a spectral line. with Planck’s expression for the
change in energy of an atom
Example: A hydrogen atom absorbs a photon of UV light and its electron
enters the n = 4 energy level. Calculate (a) the change in energy of the atom
and (b) the wavelength (in nm) of the photon.
solution
Cont…

22. Spectral Analysis in the Laboratory
• Analysis of the spectrum of the H atom led to the Bohr model, the first step
toward our current model of the atom.
• The terms spectroscopy, spectrophotometry, and spectrometry refer to a large
group of instrumental techniques that obtain spectra that correspond to a
substance’s atomic or molecular energy levels.
• The two types of spectra most often obtained are emission and absorption
spectra:
• An emission spectrum is produced when atoms in an excited state emit
photons characteristic of the element as they return to lower energy states.
• An absorption spectrum is produced when atoms absorb photons of certain
wavelengths and become excited from lower to higher energy states.

23. The Wave-Particle Duality of Matter and Energy
 The early proponents of quantum theory demonstrated that energy is
particle-like and matter is wave like properties.
The Wave Nature of Electrons
 Attempting to explain why an atom has fixed energy levels, a French
physics student, Louis de Broglie, considered other systems such as the
vibrations of a plucked guitar string.
 de Broglie proposed that if energy is particle-like, perhaps matter is
wavelike.
 He reasoned that if electrons have wavelike motion in orbits of fixed radii,
they would have only certain allowable frequencies and energies.
5.3. Development of Quantum theory

24. de Broglie Equation
 famous equation for mass-energy equivalence
E = mc2
 Equation for the energy of a photon
E = hv =
ℎ𝑐
λ
 de Broglie derived an equation for the wavelength of any particle of
mass m—whether planet, baseball, or electron—moving at speed u:

25. The Particle Nature of Photons
 If electrons have properties of energy, do photons have properties of matter?
The de Broglie equation suggests that we can calculate the momentum (p), the
product of mass and speed, for a photon.
 Wave-Particle Duality Classical experiments had shown matter to be particle-
like and energy to be wavelike.
 But results on the atomic scale show electrons moving in waves and photons
having momentum.
 Thus, every property of matter was also a property of energy.
 The truth is that both matter and energy show both behaviors:
 This dual character of matter and energy is known as the wave-particle
duality

26. Heisenberg’s Uncertainty Principle
 1927, the German physicist Werner Heisenberg postulated the uncertainty
principle, which states that it is impossible to know simultaneously the
position and momentum (mass times speed) of a particle.
 For a particle with constant mass m, the principle is expressed mathematically
as
 where ∆x is the uncertainty in position, ∆u is the uncertainty in speed, and h
is Planck’s constant.
 The more accurately we know the position of the particle (smaller ∆x), the
less accurately we know its speed (larger ∆u) and vice versa.

27. The Quantum-Mechanical Model of the Atom
 Acceptance of the dual nature of matter and energy and of the uncertainty
principle culminated in the field of quantum mechanics, which examines
the wave nature of objects on the atomic scale.
 In 1926, Erwin Schrödinger derived an equation that is the basis for the
quantum-mechanical model of the H atom.
 The model describes an atom with specific quantities of energy that result
from allowed frequencies of its electron’s wavelike motion.
 The electron’s position can only be known within a certain probability.
 The electron’s matter wave occupies the space near the nucleus and is
continuously influenced by it.

28.  “orbital” in the quantum-mechanical model bears no resemblance to an
“orbit” in the Bohr model: an orbit is an electron’s actual path around the
nucleus, whereas an orbital is a mathematical function that describes the
electron’s matter-wave but has no physical meaning.
Quantum Numbers of an Atomic Orbital
 An atomic orbital is specified by four quantum numbers that are part of the
solution of the Schrödinger equation and indicate the size, shape,
orientation and direction in space of the orbital.
1. The principal quantum number (n)
is a positive integer (1, 2, 3, and so forth). It indicates the relative size of the
orbital.
Cont…

29.  The principal quantum number specifies the energy level of the H atom:
 the higher the n value, the higher the energy level. When the electron
occupies an orbital with n = 1, the H atom is in its ground state and has its
lowest energy. When the electron occupies an orbital with n = 2 (first
excited state), the atom has more energy.
2. The angular momentum quantum number (l)
 is an integer from 0 to n - 1. It is related to the shape of the orbital. Note
that the principal quantum number sets a limit on the angular momentum
quantum number:
 n limits l. For an orbital with n = 1, l can have only one value, 0. For
orbitals with n = 2, l can have two values, 0 or 1. For orbitals with n = 3, l
can have three values, 0, 1, or 2; and so forth. Thus, the number of possible
l values equals the value of n.
Cont…

30. The magnetic quantum number (ml)
 is an integer from -l through 0 to +l. It prescribes the three- dimensional
orientation of the orbital in the space around the nucleus.
 The angular momentum quantum number sets a limit on the magnetic
quantum number:
 l limits ml An orbital with l = 0 can have only ml = 0.
 However, an orbital with l = 1 can have one of three ml values, -1, 0, or
+1; that is, there are three possible orbitals with l = 1, each with its own
orientation.
 Note that the number of ml values equals 2l+1, which is the number of
orbitals for a given l.
 The total number of ml values, that is, the total number of orbitals, for a
given n value is n2

31. Example: What values of the angular momentum (l) and magnetic (ml)
quantum numbers are allowed for a principal quantum number (n) of 3? How
many orbitals are allowed?
Solution
n Determining l values: for n = 3, l = 0, 1, 2.
Determining ml for each l value:
For l = 0, ml = 0, For l = 1, ml = -1, 0, +1, For l = 2, ml = -2, -1, 0, +1, +2
There are nine ml values, so there are nine orbitals with n = 3.
 As we saw, the total number of orbitals for a given n value is n2, and for n
= 3, n2 = 9.
 Exercise: What are the possible l and ml values for n = 4?

32. The Hierarchy of Quantum Numbers for Atomic Orbitals

33. Summary of quantum numbers of electrons in atoms

34. Quantum Numbers and Energy Levels
 The energy states and orbitals of the atom are described with specific terms
and are associated with one or more quantum numbers:
 1. Level. The atom’s energy levels, or shells, are given by the n value: the
smaller the n value, the lower the energy level and the greater the probability
that the electron is closer to the nucleus.
 2. Sublevel. The atom’s levels are divided into sublevels, or subshells, that are
given by the l value. Each designates the orbital shape with a letter:
 l = 0 is an s sublevel.
 l = 1 is a p sublevel.
 l = 2 is a d sublevel.
 l = 3 is an f sublevel.

35.  (The letters derive from names of spectroscopic lines: sharp, principal,
diffuse and fundamental.) Sublevels with l values greater than 3 are
designated by consecutive letters after f: g sublevel, h sublevel, and so on.
 A sublevel is named with its n value and letter designation; for example, the
sublevel (subshell) with n = 2 and l = 0 is called 2s.
 3. Orbital. Each combination of n, l, and ml specifies the size (energy),
shape, and spatial orientation of one of the atom’s orbitals. We know the
quantum numbers of the orbitals in a sublevel from the sublevel name and
the quantum-number hierarchy.
Cont…

36.  For example, any orbital in the 2s sublevel has n = 2 and l =0, and given
that l value, it can have only ml = 0; thus, the 2s sublevel has only one
orbital.
 Any orbital in the 3p sublevel has n = 3 and l = 1, and given that l value,
one orbital has ml = -1, another has ml = 0, and a third has ml = +1; thus,
the 3p sublevel has three orbitals.
Cont…

37. Shapes of Atomic Orbitals
The s Orbital: An orbital with l = 0 has a spherical shape with the nucleus at
its center and is called an s orbital. Because a sphere has only one orientation,
an s orbital has only one ml value: for any s orbital, ml = 0
 node, where the probability of finding the electron drops to zero
 The p Orbital An orbital with l = 1 is called a p orbital and has two
regions (lobes) of high probability, one on either side of the nucleus. The
nucleus lies at the nodal plane of this dumbbell-shaped orbital.
 The d Orbital An orbital with l = 2 is called a d orbital. There are five
possible ml values for l = 2: -2, -1, 0, +1, and +2. Thus, a d orbital has any
one of five orientations.

38. Orbitals with Higher l Values Orbitals with l = 3 are f orbitals and have a principal
quantum number of at least n=4. Figure shows one of the seven f orbitals (2l + 1 = 7);
each f orbital has a complex, multi lobed shape with several nodal planes.

39. The Exclusion Principle and Orbital Occupancy
 no two electrons in the same atom can have the same four quantum
numbers. Therefore, the second He electron occupies the same orbital as
the first but has an opposite spin:
 An atomic orbital can hold a maximum of two electrons and they must
have opposing spins.
5.4.2. The Aufbau principle
(German aufbauen, “to build up”) We start at the beginning of the periodic
table and add one proton to the nucleus and one electron to the lowest energy
sublevel available.
5.4. Electronic structure of atoms

40. 5.4.3. Electronic configuration and the periodic table
 There are two common ways to indicate the distribution of electrons:
 The electron configuration: This shorthand notation consists of the
principal energy level (n value), the letter designation of the sublevel (l
value), and the number of electrons (#) in the sublevel, written as a
superscript: nl#.
 The orbital diagram: An orbital diagram consists of a box (or circle, or
just a line) for each orbital in a given energy level, grouped by sublevel
(with nl designation shown beneath), with an arrow representing an
electron and its spin: ↑ is +1/2 and ↓ is -1/2.

41. Building Up Period 1
Building Up Period 2
Lithium, Beryllium, Boron, Carbon, Nitrogen, Oxygen, Fluorine, Neon
Cont…

43. Hund’s rule
 When orbitals of equal energy are available, the electron configuration of
lowest energy has the maximum number of unpaired electrons with parallel
spins.
Building Up Period 3
Partial orbital diagrams show only the sublevels being filled, here the 3s and
3p.
• Condensed electron configurations (rightmost column) have the element
symbol of the previous noble gas in brackets, to stand for its configuration,
followed by the electron configuration of filled inner sublevels and the energy
level being filled.

44. Partial orbital diagrams and electronic configuration for the
elements in period 3

45. General Principles of Electron Configurations
 The partial (highest energy sublevels being filled) ground-state electron
configurations of the known elements.
 Similar Outer Electron Configurations Within a Group Among the
main-group elements (A groups)—the s-block and p-block elements—
outer electron configurations within a group are identical.
 Some variations in the transition elements (B groups, d block) and inner
transition elements ( f block) occur
 Orbital Filling Order: When the elements are “built up” by filling levels
and sublevels in order of increasing energy, we obtain the sequence in the
periodic table

48. Categories of Electrons We can describe three categories of electrons:
1) Inner (core) electrons: are those an atom has in common with the previous
noble gas and any completed transition series. They fill all the lower energy
levels of an atom.
2) Outer electrons are those in the highest energy level (highest n value). They
spend most of their time farthest from the nucleus.
3) Valence electrons are those involved in forming compounds:
• For main-group elements, the valence electrons are the outer electrons.
• For transition elements, in addition to the outer ns electrons, the (n - 1)d
electrons are also valence electrons, though the metals Fe (Z = 26) through Zn
(Z = 30) may use only a few, if any, of their d electrons in bonding.
Cont…

49. Group and Period Numbers
• Among the main-group elements (A groups), the A number equals the
number of outer electrons (those with the highest n); thus, chlorine (Cl; Group
7A) has 7 outer electrons, and so forth.
• The period number is the n value of the highest energy level.
• For an energy level, the n value squared (n2) is the number of orbitals, and
2n2 is the maximum number of electrons (or elements).
 For example, consider the n = 3 level. The number of orbitals is n2 = 9:
one 3s, three 3p, and five 3d.
 The number of electrons is 2n2 = 18: two 3s and six 3p electrons for the
eight elements of Period 3, and ten 3d electrons for the ten transition
elements of Period 4

50. Transition and Inner Transition Elements
The d block and f block occur between the main-group s and p blocks
1) Transition series: Periods 4, 5, 6, and 7 incorporate the 3d, 4d, 5d, and 6d
sublevels, respectively
2) Inner Transition: Period 6 holds the first of two series of inner transition
elements, those in which f orbitals are being filled. The two inner transition
series
 The Period 6 inner transition series, called the lanthanides (or rare
earths), occurs after lanthanum (La; Z = 57), and the 4f orbitals are
filled.
 The Period 7 inner transition series, called the actinides, occurs after
actinium (Ac; Z = 89), and the 5f orbitals are filled.
3) Irregular filling patterns: Irregularities in the filling pattern, such as those for
Cr and Cu in Period 4, occur in the d and f blocks because the sublevel energies in
these larger atoms differ very little.

51. Exercise
Using the periodic table and assuming a regular filling pattern, give the full and condensed
electron configurations, partial orbital diagrams showing valence electrons only, and number of
inner electrons for the following elements:
(a) Potassium (K; Z = 19) (b) Technetium (Tc; Z = 43) (c) Lead (Pb; Z = 82), d) Ni (Z = 28) e) Sr
(Z = 38) f) Po (Z = 84)
Cont…
24Cr = and 29Cu =

52. 5.5. Periodic variation in element properties
 In this section, we focus on three atomic properties that reflect the central
importance of electron configuration and effective nuclear charge: atomic
size, ionization energy, and electron affinity.
 Most notably, these properties are periodic, which means they generally
exhibit consistent changes, or trends, within a group or period.
Trends in Atomic Size
 Atomic size (the extent of the contour) in terms of how closely one atom
lies next to another.
 We measure the distance between atomic nuclei in a sample of an element
and divide that distance in half. The size of an atom in a compound
depends somewhat on the atoms near it.
 In other words, an element’s atomic size varies slightly from substance to
substance.

53. 1) Metallic radius: Used mostly for metals, it is one-half the shortest distance
between nuclei of adjacent, individual atoms in a crystal of the element.
2) Covalent radius: Used for elements occurring as molecules, mostly non
metals, it is one-half the shortest distance between nuclei of bonded atoms.
 Radii measured for some elements are used to determine the radii of other
elements from distances between atoms in compounds.
 For instance, in a carbon-chlorine compound, the distance between nuclei
in a C—Cl bond is 177 pm.
 Using the known covalent radius of Cl (100 pm), we find the covalent
radius of C (177 pm - 100 pm = 77 pm)
Cont…

54.  As the principal quantum number (n) increases, the probability that outer
electrons spend most of their time farther from the nucleus increases as
well; thus, atomic size increases.
 As the effective nuclear charge (Zeff) increases, outer electrons are pulled
closer to the nucleus ; thus, atomic size decreases.
 The net effect of these influences depends on how effectively the inner
electrons shield the increasing nuclear charge:
– Atomic radius generally increases down a group. Because As we move down a
main group, each member has one more level of inner electrons that shield the
outer electrons very effectively.
– Atomic radius generally decreases across a period. Because greater electron
repulsions, outer electrons shield each other only slightly, so Zeff rises
significantly, and the outer electrons are pulled closer to the nucleus:
Cont…

55. Transition Elements
1. Down a transition group, n increases, but shielding by an additional level
of inner electrons results in only a small size increase from Period 4 to 5 and
none from 5 to 6.
2. Across a transition series, atomic size shrinks through the first two or
three elements because of the increasing nuclear charge.
3. A transition series affects atomic size in neighbouring main groups.
Shielding by d electrons causes a major size decrease from Group 2A(2) to
Group 3A(13) in Periods 4 through 6.

56. Example: Using only the periodic table rank each set of main-group
elements in order of decreasing atomic size:
(a) Ca, Mg, Sr (b) K, Ga, Ca (c) Br, Rb, Kr (d) Sr, Ca, Rb
Solution
(a) Sr > Ca > Mg. These three elements are in Group 2A(2), and size
decreases up the group.
(b) K > Ca > Ga. These three elements are in Period 4, and size decreases
across a period.
(c) Rb > Br > Kr > Rb is largest because it has one more energy level (Period
5) and is farthest to the left. Kr is smaller than Br because Kr is farther to the
right in Period 4.
(d) Rb > Sr > Ca> Ca is smallest because it has one fewer energy level. Sr is
smaller than Rb because it is farther to the right.

57. Trends in Ionization Energy
 The ionization energy (IE) is the energy required for the complete removal
of 1 mol of electrons from 1 mol of gaseous atoms or ions.
 Pulling an electron away from a nucleus requires energy to overcome their
electrostatic attraction. Because energy flows into the system, the
ionization energy is always positive (like ∆H of an endothermic reaction).
• Atoms with a low IE tend to form cations during reactions.
• Atoms with a high IE (except the noble gases) tend to form anions.
 Ionization energy generally decreases down a group.
 Ionization energy generally increases across a period.

58. Example: Using the periodic table only, rank the elements in each set in order of
decreasing IE1: (a) Kr, He, Ar; (b) Sb, Te, Sn; (c) K, Ca, Rb; (d) I, Xe, Cs.
Solution
(a) He > Ar> Kr. These are in Group 8A(18), and IE1 decreases down a group.
(b) Te > Sb > Sn. These are in Period 5, and IE1 increases across a period.
(c) Ca > K > Rb. IE1 of K is larger than IE1 of Rb because K is higher in Group
1A(1). IE1 of Ca is larger than IE1 of K because Ca is farther to the right in
Period 4.
(d) Xe > I > Cs. IE1 of I is smaller than IE1 of Xe because I is farther to the left.
IE1 of I is larger than IE1 of Cs because I is farther to the right and in the previous
period.

59. Trends in Electron Affinity
 The electron affinity (EA) is the energy change (kJ/mol) accompanying
the addition of 1 mol of electrons to 1 mol of gaseous atoms or ions.
 The first electron affinity (EA1) refers to the formation of 1 mol of
monovalent (1-) gaseous anions:

60.  We might expect a smooth decrease (smaller negative number) down a
group because size increases, and the nucleus is farther away from an
electron being added.
 We might expect a regular increase (larger negative number) across a
period because size decreases, and higher Zeff should attract the electron
being added more strongly. There is an overall left-to-right increase, but it
is not at all regular.
Cont…