The structure of Matter
Element , Compound, and Mixture
compound
compound
Element
Mixture : MgF2 in gasoline, water-gasoline, suger in water
Element + compound 1
Compound 2
Chemical reaction
Heterogeneous mixture
Homogenous mixture
No chemical reaction
Persamaan reaksi kimia
Zn + S
C4H10 + 13 O2
ZnS
8 CO2 + 10 H2O
Struktur atom
2500 tahun yang lalu : atom = “not cut”
Dalton atomic teory:
1. Materi terdiri atas atom atom
2. Atom merupakan bagian terkecil dari materi dan tidak
dapat terbelah lagi
3. Atom dari suatu element memiliki massa dan sifat
sama
4. Atom dari element berbeda memiliki massa dan sifat
berbeda
5. Atom atom dapat bergabung membentuk senyawa
dengan rasio massa tertentu
Bagaimana cara mengetahui massa atom
saat periode teori atom Dalton?
Struktur Atom modern
Penemuan elektron
• Menurut Dalton dan ilmuwan sebelumnya, atom tak
terbagi dan merupakan komponen mikroskopik utama
materi.
Jadi, tidak ada seorangpun ilmuwan sebelum abad 19
menganggap atom memiliki struktur, atau dengan kata
lain, atom juga memiliki komponen yang lebih kecil.
• Keyakinan bahwa atom tak terbagi mulai goyah akibat
perkembangan pengetahuan hubungan materi dan
kelistrikan yang berkembang lebih lanjut.
Kemajuan pemahaman hubungan materi dan listrik.
• Faraday  jumlah zat yang dihasilkan di elektroda-elektroda saat
elektrolisis (perubahan kimia ketika arus listrik melewat larutan
elektrolit) sebanding dengan jumlah arus listrik. Jumlah listrik yang
diperlukan untuk menghasilkan 1 mol zat di elektroda adalah
tetap (96,500 C).Hubungan ini dirangkumkan sebagai Hukum
Elektrolisis Faraday.
• Irish George Johnstone Stoney (1826-1911) memiliki wawasan
sehingga mengenali pentingnya hukum Faraday pada struktur
materi; ia menyimpulkan bahwa terdapat satuan dasar dalam
elektrolisis, dengan kata lain ada analog atom untuk kelistrikan. Ia
memberi nama elektron.
• Berapa muatan 1 elektron?
Percobaan tabung vakum Plücker (1801-1868).
Bila kation mengenai anoda dan diberikan beda potensial yang tinggi pada
tekanan rendah (lebih rendah dari 10–2 - 10–4 Torr), gas dalam tabung,
walaupun merupakan insulator, menjadi penghantar dan memancarkan
cahaya. Bila vakumnya ditingkatkan, dindingnya mulai menjadi mengkilap,
memancarkan cahaya fluoresensi Beberapa partikel dipancarkan dari katoda.
Ia memberi nama sinar katoda pada partikel yang belum teridentifikasi ini
• Fisikawan Inggris Joseph John Thomson (1856-1940)
menunjukkan bahwa partikel ini bermuatan negatif.
• Fisikawan Amerika Robert Andrew Millikan (1868-1953) berhasil
membuktikan dengan percobaan yang cerdas adanya partikel
kelistrikan ini. Percobaan yang disebut dengan percobaan tetes
minyak Millikan. Tetesan minyak dalam tabung jatuh akibat
pengaruh gravitasi. Bila tetesan minyak memiliki muatan listrik,
gerakannya dapat diatur dengan melawan gravitasi dengan
diberikan medan listrik. Gerakan gabungan ini dapat dianalisis
dengan fisika klasik. Millikan menunjukkan dengan percobaan ini
bahwa muatan tetesan minyak (elektron) selalu merupaka kelipatan
1,6x10–19 C.
Muatan elektron =1,6 x 10–19 C.
Ratio muatan/massa (Thomson ) = 1,76 x108 C/g),
• Latihan 1. Perhitungan massa elektron.
Hitung massa elektron dengan menggunakan nilai yang
didapat Millikan dan Thomson.
Jawab: Anda dapat memperoleh penyelesaian dengan
mensubstitusikan nilai yang didapat Millikan pada
hubungan:
muatan/massa = 1,76 x 108 (C g–1).
Maka, m = e/(1,76 x 108 C g–1)
= 1,6 x 10–19 C/(1,76 x 108C g–1)
= 9,1 x 10–28 g.
Muatan elektron =1,6 x 10–19 C.
Ratio muatan/massa (Thomson ) = 1,76 x108 C/g),
Latihan 2. Rasio massa elektron dan atom hidrogen.
Hitung rasio massa elektron dan atom hidrogen!
Jawab:
Massa mH atom hidrogen atom adalah:
mH = 1 g/6 x 1023 = 1,67 x 10–24g.
Jadi, me : mH = 9,1 x 10–28g : 1,67 x10–24g
= 1 : 1,83 x 103.
Sangat menakjubkan bahwa massa elektron sangat
kecil. Bahkan atom yang paling ringanpun, hidrogen,
sekitar 2000 kali lebih berat dari massa elektron.
Model atom
Mengukur ukuran atom
Latihan 3. Volume satu molekul air
Dengan menganggap molekul air berbentuk kubus, hitung panjang
sisi kubusnya. Dengan menggunakan nilai yang didapat, perkirakan
ukuran kira-kira satu atom (nyatakan dengan notasi saintifik 10x).
Jawab:
Volume 1 mol air sekitra 18 cm3.
Jadi volume 1 molekul air: v = 18 cm3/6 x 1023 = 3x10–23 cm3 = 30 x
10–24 cm3.
Panjang sisi kubus adalah (30 x 10–24)1/3 cm = 3,1 x 10–8 cm. Nilai ini
mengindikasikan bahwa ukuran atom sekitar 10–8 cm.
Thomson mengasumsikan bahwa atom dengan dimensi sebesar itu
adalah bola seragam bermuatan positif dan elektron-elektron kecil
yang bermuatan negatif tersebar di bola tersebut. Dalam kaitan ini
model Thomson sering disebut dengan “model bolu kismis”,
kismisnya seolah elektron dan bolunya adalah atom.
• Apa kelemahan model atom Thomson?
- tidak dapat menerangkan susunan
muatan positif / negatif dalam sebuah
atom.
Teori atom Bohr
• The demonstration by Thompson in 1867 that all atoms
contain units of negative electric charge led to the first
science-based model of the atom which envisaged the
electrons being spread out uniformly throughout the
spherical volume of the atom. Ernest Rutherford, a New
Zealander who started out as Thompson's student at
Cambridge, distrusted this "plum pudding" model (as he
called it) and soon put it to rest; Rutherford's famous
alpha-ray bombardment experiment (carried out, in
1909, by his students Hans Geiger and Ernest Marsden)
showed that nearly all the mass of the atom is
concentrated in an extremely small (and thus
extremely dense) body called the nucleus. This led
him to suggest the planetary model of the atom, in which
the electrons revolve in orbits around the nuclear "sun".
Menurut ide Rutherford, muatan positif atom terpusat di bagian pusat (dengan jarijari terhitung sekitar 10–12 cm) sementara muatan negatifnya terdispersi di seluruh
ruang atom. Partikel kecil di pusat ini disebut dengan inti. Semua model atom
sebelumnya sebagai ruang yang seragam dengan demikian ditolak.
• Namun, model atom Rutherford yang terdiri atas inti kecil dengan
elektron terdispersi di sekitarnya tidak dapat menjelaskan semua
fenomena yang dikenal. Bila elektron tidak bergerak, elektron akan
bersatu dengan inti karena tarikan elektrostatik (gaya Coulomb). Ha
ini jeals tidak mungkin terjadi sebab atom adalah kesatuan yang
stabil. Bila elektron mengelilingi inti seperti planet dalam pengaruh
gravitasi matahari, elektron akan mengalami percepatan dan akan
kehilangan energi melalui radiasi elektromagnetik. Akibatnya,
orbitnya akan semakin dekat ke inti dan akhirnya elektron akan jatuh
ke inti. Dengan demikian, atom akan memancarkan spektrum yang
kontinyu. Tetapi faktanya, atom yang stabil dan diketahui atom
memancarkan spektrum garis bukan spektrum kontinyu.
Jelas diperlukan perubahan fundamenatal dalam pemikiran untuk
menjelaskan semua fakta-fakta percobaan ini.
Dasar-dasar teori kuantum klasik
Spektrum atom
Bila gas ada dalam tabung vakum, dan diberi beda
potensial tinggi, gas akan terlucuti dan memancarkan
cahaya. Pemisahan cahaya yang dihasilkan dengan
prisma akan menghasilkan garis spektra garis
diskontinyu. Karena panjang gelombang cahaya khas
bagi atom, spektrum ini disebut dengan spektrum atom.
Fisikawan Swedia Johannes Robert Rydberg (1854-1919)
menemukan bahwa bilangan gelombang7 σ garis spektra
dapat diungkapkan dengan persamaan berikut (1889) ni dan
nj bilangan positif bulat(ni < nj) dan R adalah tetapan khas
untuk gas yang digunakan.
Untuk hidrogen R bernilai 1,09678 x 107 m–1.
Umumnya bilangan gelombang garis spektra atom hodrogen
dapat diungkapkan sebagai perbedaan dua suku R/n2.
Spektra atom gas lain jauh lebih rumit, tetapi sekali lagi
bilangan gelombangnya juga dapat diungkapkan sebagai
perbedaan dua suku.
Model atom Bohr
• Bohr suggested that the planetary model could
be saved if one new assumption were made:
certain "special states of motion" of the electron,
corresponding to different orbital radii, would not
result in radiation, and could therefore persist
indefinitely without the electron falling into the
nucleus. Specifically, Bohr postulated that the
angular momentum of the electron, mvr (the
mass and angular velocity of the electron and in
an orbit of radius r) is restricted to values that
are integral multiples of h/2π. The radius of
one of these allowed Bohr orbits is given by
• in which h is Planck's constant, m is the mass of
the electron, v is the orbital velocity, and n can
have only the integer values 1, 2, 3, etc. The
most revolutionary aspect of this assumption was
its use of the variable integer n; this was the first
application of the concept of the quantum number
to matter. The larger the value of n, the larger the
radius of the electron orbit, and the greater the
potential energy of the electron.
• As the electron moves to orbits of increasing radius, it does so in
opposition to the restoring force due to the positive nucleus, and its
potential energy is thereby raised. This is entirely analogous to the
increase in potential energy that occurs when any mechanical
system moves against a restoring force— as, for example, when a
rubber band is stretched or a weight is lifted.
• Thus what Bohr was saying, in effect, is that the atom can exist
only in certain discrete energy states: the energy of the atom is
quantized. Bohr noted that this quantization nicely explained the
observed emission spectrum of the hydrogen atom. The electron is
normally in its smallest allowed orbit, corresponding to n = 1;
upon excitation in an electrical discharge or by ultraviolet light,
the atom absorbs energy and the electron gets promoted to
higher quantum levels. These higher excited states of the atom
are unstable, so after a very short time (around 10—9 sec) the
electron falls into lower orbits and finally into the innermost one,
which corresponds to the atom's ground state. The energy lost on
each jump is given off as a photon, and the frequency of this light
provides a direct experimental measurement of the difference in the
energies of the two states, according to the Planck-Einstein
relationship e = hν.
How the Bohr model explains the hydrogen line spectrum?
• Each spectral line represents an energy difference
between two possible states of the atom. Each of
these states corresponds to the electron in the hydrogen
atom being in an "orbit" whose radius increases with the
quantum number n. The lowest allowed value of n is 1;
because the electron is as close to the nucleus as it can
get, the energy of the system has its minimum (most
negative) value. This is the "normal" (most stable) state
of the hydrogen atom, and is called the ground state.
•If a hydrogen atom absorbs radiation
whose energy corresponds to the
difference between that of n=1 and
some higher value of n, the atom is
said to be in an excited state. Excited
states are unstable and quickly
decay to the ground state, but not
always in a single step. For example,
if the electron is initially promoted to
the n=3 state, it can decay either to the
ground state or to the n=2 state, which
then decays to n=1. Thus this single
n=1→3 excitation can result in the
three emission lines depicted in the
diagram above, corresponding to
n=3→1, n=3→2, and n=2→1.
•
If, instead, enough energy is supplied to the atom to
completely remove the electron, we end up with a
hydrogen ion and an electron. When these two particles
recombine (H+ + e– → H), the electron can initially find
itself in a state corresponding to any value of n, leading to
the emission of many lines.
• The lines of the hydrogen spectrum can be organized into different
series according to the value of n at which the emission terminates
(or at which absorption originates.) The first few series are named
after their discoverers. The most well-known (and first-observed)
of these is the Balmer series, which lies mostly in the visible
region of the spectrum. The Lyman lines are in the ultraviolet,
while the other series lie in the infrared. The lines in each series
crowd together as they converge toward the series limit which
corresponds to ionization of the atom and is observed as the
beginning of the continuum emission. Note that the ionization
energy of hydrogen (from its ground state) is 1312 kJ mol–1.
• Although an infinite number of n-values are possible, the number of
observable lines is limited by our ability to resolve them as they
converge into the continuum; this number is around a thousand.
Contoh soal:
Jari-jari r dapat diungkapan dalam persamaan
r = n2aB, n = 1, 2, 3,...
aB adalah jari-jari minimum (jari-jari Bohr= 5,2918 x 10–
11 m) bila n = 1. Tentukan jari-jari lainnya untuk n=2,3,4
Hukum Moseley
Henry Gwyn Jeffreys Moseley (1887-1915) mendapatkan, dengan
menembakkan elektron berkecepatan tinggi pada anoda logam,
bahwa frekuensi sinar-X yang dipancarkan khas bahan anodanya.
Panjang gelombang λ sinar- X berkaitan dengan muatan listrik Z inti.
Menurut Moseley, terdapat hubungan antara dua nilai ini (hukum
Moseley; 1912).
c dan s adalah tetapan yang berlaku untuk semua unsur, dan Z
adalah bilangan bulat.
Contoh: Perkiraan nomor atom dengan hukum Moseley
Didapatkan bahwa sinar-X khas unsur yang tidak diketahui adalah
0,14299 x 10–9 m. Panjang gelombang dari deret yang sama sinar-X
khas unsur Ir (Z = 77) adalah 0,13485 x 10–9 m. Dengan asumsi s =
7,4, perkirakan nomor atom unsur yang tidak diketahui tersebut.
Jawab: Pertama perkirakan √c dari persamaan :
[1/0,13485x10−9 (m)]1/2 = √ c. (77 − 7.4) = 69,6 √c; jadi √c =
1237,27, maka
[1/0,14299x10−9 (m)] = 1237 (z − 7.4) dan didapat z = 75
Keterbatasan teori Bohr
Keberhasilan teori Bohr begitu menakjubkan. Teori Bohr dengan
sangat baik menggambarkan struktur atom hidrogen, dengan
elektron berotasi mengelilingi inti dalam orbit melingkar.. Setelah
berbagai penyempurnaan, teori Bohr mampu menerangkankan
spektrum atom mirip hidrogen dengan satu elektron seperti ion
helium He+. Namun, spektra atom atom poli-elektronik tidak dapat
dijelaskan. Kemudian menjadi jelas bahwa ada keterbatasan dalam
teori ini yaitu tidak ada penjelasan persuasif tentang ikatan kimia
dapat diperoleh. Dengan kata lain,teori Bohr adalah satu langkah ke
arah teori struktur atom yang dapat berlaku bagi semua atom dan
ikatan kimia.
Pentingnya teori Bohr tidak dapat diremehkan karena teori ini
dengan jelas menunjukkan pentingnya teori kuantum untuk
memahami struktur atom, dan secara lebih umum struktur materi.
Question
1.
2.
3.
4.
5.
6.
7.
Describe the Thompson, Rutherford, and early planetary models
of the atom, and explain why the latter is not consistent with
classical physics.
State the major concepts that distinguished Bohr's model of the
atom from the earlier planetary model.
Give an example of a mechanical standing wave; state the
meaning and importance of its boundary conditions.
Sketch out a diagram showing how the concept of a standing
wave applies to the description of the electron in a hydrogen
atom.
What is an atomic line emission spectrum? What is the
significance of the continuum region of an emission spectrum?
Sketch out a drawing showing the essentials of such a spectrum,
including the ionization limit and the continuum.
Describe the way in which Bohr's quantum numbers explain the
observed spectrum of a typical atom.
Explain the relation between the absorption and emission
spectrum of an atom.
• About ten years after Bohr had developed his theory, de Broglie
showed that the electron should have wavelike properties of its
own, thus making the analogy with the mechanical theory of
standing waves somewhat less artificial. One serious difficulty with
the Bohr model still remained, however: it was unable to
explain the spectrum of any atom more complicated than
hydrogen. A refinement suggested by Sommerfeld assumed that
some of the orbits are elliptical instead of circular, and invoked a
second quantum number, l, that indicated the degree of ellipticity.
This concept proved useful, and it also began to offer some
correlation with the placement of the elements in the periodic table.
The Schrödinger equation
Of these alternative treatments, the one developed by Schrödinger is the
most easily visualized. Schrödinger started with the simple requirement
that the total energy of the electron is the sum of its kinetic and
potential energies.
•
The second term represents the potential energy of an electron (whose
charge is denoted by e) at a distance r from a proton (the nucleus of the
hydrogen atom). In quantum mechanics it is generally easier to deal with
equations that use momentum (p = mv) rather than velocity, so the next step
is to make this substitution:
This is still an entirely classical relation, as valid for the waves on a guitar string
as for those of the electron in a hydrogen atom. The third step is the big one: in
order to take into account the wavelike character of the hydrogen atom, a
mathematical expression that describes the position and momentum of the
electron at all points in space is applied to both sides of the equation. The
function, denoted by Ψ (psi), "modulates" the equation of motion of the electron
so as to reflect the fact that the electron manifests itself with greater probability
in some locations that at others. This yields the celebrated Schrödinger equation
Why doesn't the electron fall into
the nucleus?
•
We can now return to the question which Bohr was unable to answer in
1912. Even the subsequent discovery of the wavelike nature of the electron
and the analogy with standing waves in mechanical systems did not really
answer the question; the electron is still a particle having a negative
charge and is attracted to the nucleus.
•
The answer comes from the Heisenberg uncertainty principle, which says
that a quantum particle such as the electron cannot simultaneously have
sharply-defined values of location and of momentum (and thus kinetic
energy). To understand the implications of this restriction, suppose that we
place the electron in a small box. The walls of the box define the precision
δx to which the location is known; the smaller the box, the more exactly will
we know the location of the electron. But as the box gets smaller, the
uncertainty in the electron's kinetic energy will increase. As a consequence
of this uncertainty, the electron will at times possess so much kinetic energy
(the "confinement energy") that it may be able to penetrate the wall and
escape the confines of the box.
• The region near the nucleus can be
thought of as an extremely small
funnel-shaped box, the walls of
which correspond to the electrostatic
attraction that must be overcome if
an electron confined within this
region is to, the volume to which it is
confined diminishes rapidly.
Because its location is now more
precisely known escape. As an
electron is drawn toward the
nucleus by electrostatic
attraction, its kinetic energy must
become more uncertain; the
electron's kinetic energy rises
more rapidly than its potential
energy falls, so that it gets
ejected back into one of its
allowed values of n.
• We can also dispose of the question of why the orbiting
electron does not radiate its kinetic energy away as it
revolves around the nucleus?
The Schrödinger equation completely discards any
concept of a definite path or trajectory of a particle;
what was formerly known as an "orbit" is now an
"orbital", defined as the locations in space at which
the probability of finding the electrons exceeds
some arbitrary value.
It should be noted that this wavelike character of the
electron coexists with its possession of a momentum,
and thus of an effective velocity, even though its motion
does not imply the existence of a definite path or
trajectory that we associate with a more massive
particle.
Kelahiran mekanika kuantum
De Broglie (1892-1987)
P = mv
Prinsip ketidakpastian Heisenberg
Persamaan Schrödinger
Persamaan Schrödinger
BILANGAN KUANTUM
The quantum numbers
• Modern quantum theory tells us that the various allowed states of
existence of the electron in the hydrogen atom correspond to
different standing wave patterns. In the preceding lesson we showed
examples of standing waves that occur on a vibrating guitar string.
The wave patterns of electrons in an atom are different in two
important ways:
• Instead of indicating displacement of a point on a vibrating string,
the electron waves represent the probability that an electron will
manifest itself (appear to be located) at any particular point in
space. (Note carefully that this is not the same as saying that "the
electron is smeared out in space"; at any given instant in time, it is
either at a given point or it is not.)
• The electron waves occupy all three dimensions of space,
whereas guitar strings vibrate in only two dimensions.
• Aside from this, the similarities are striking. Each wave pattern is
identified by an integer number n, which in the case of the atom
is known as the principal quantum number. The value of n tells
how many peaks of amplitude (antinodes) exist in that particular
standing wave pattern; the more peaks there are, the higher the
energy of the state.
The three simplest orbitals of the hydrogen atom are depicted above in pseudo3D, in cross-section, and as plots of probability (of finding the electron) as a
function of distance from the nucleus. The average radius of the electron
probability is shown by the blue circles or plots in the two columns on the right.
These radii correspond exactly to those predicted by the Bohr model
Physical significance of n
• The potential energy of the electron is given by the formula
in which e is the charge of the electron, m is its mass, h is Planck's constant, and n is
the principal quantum number. The negative sign ensures that the potential energy is
always negative. Notice that this energy in inversely proportional to the square of n, so
that the energy rises toward zero as n becomes very large, but it can never exceed
zero.
This formula was actually part of Bohr's original theory, and is still applicable
to the hydrogen atom, although not to atoms containing two or more
electrons. In the Bohr model, each value of n corresponded to an orbit of a different
radius. The larger the orbital radius, the higher the potential energy of the electron;
the inverse square relationship between electrostatic potential energy and distance
is reflected in the inverse square relation between the energy and n in the above
formula. Although the concept of a definite trajectory or orbit of the electron is no
longer tenable, the same orbital radii that relate to the different values of n in Bohr's
theory now have a new significance: they give the average distance of the electron
from the nucleus.
The angular momentum quantum number
•
The electron wave functions that are derived from Schrödinger's
theory are characterized by several quantum numbers. The first one, n,
describes the nodal behavior of the probability distribution of the electron,
and correlates with its potential energy and average distance from the
nucleus as we have just described.
•
The theory also predicts that orbital having the same value of n can
differ in shape and in their orientation in space. The quantum number
l, known as the angular momentum quantum number, determines the
shape of the orbital. (More precisely, l determines the number of angular
nodes, that is, the number of regions of zero probability encountered in a
360° rotation around the center.)
•
When l = 0, the orbital is spherical in shape. If l = 1, the orbital is elongated
into something resembling, and higher values of l correspond to still more
complicated shapes— but note that the number of peaks in the radial
probability distributions (below) decreases with increasing l. The possible
values that l can take are strictly limited by the value of the principal
quantum number; l can be no greater than n – 1. This means that for n =
1, l can only have the single value zero which corresponds to a
spherical orbital. For historical reasons, the orbitals corresponding to
different values of l are designated by letters, starting with s for l = 0, p
for l = 1, d for l = 2, and f for l = 3.
The shapes and radial distributions of the orbitals corresponding to the three
allowed values of l for the n = 3 level of hydrogen are shown above. Notice
that the average orbital radius r decreases somewhat at higher values of l. The
function relationship is given by
in which z is the nuclear charge of the atom, which of course is unity for hydrogen.
The magnetic quantum number m
• An s-orbital, corresponding to l = 0, is spherical in shape and
therefore has no special directional properties. The probability
cloud of a p orbital is aligned principally along an axis
extending along any of the three directions of space. The
additional quantum number m is required to specify the particular
direction along which the orbital is aligned.
• The quantum number m can assume 2l + 1 values for each
value of l, from –l through 0 to +l.
When l = 0 the only possible value of m will also be zero, and
for the p orbital (l = 1), m can be –1, 0, and +1.
Higher values of l introduce more complicated orbital shapes which
give rise to more possible orientations in space, and thus to more
values of m.
Electron spin and the exclusion principle
• Certain fundamental particles have associated with them a magnetic
moment that can align itself in either of two directions with respect to
an external magnetic field. The electron is one such particle, and the
direction of its magnetic moment is called its spin.
• Electron spin is basically a relativistic effect in which the electron's
momentum distorts local space and time. It has no classical
counterpart and thus cannot be visualized other than through
mathematics.
• A basic principle of modern physics states that for particles such as
electrons that possess half-integral values of spin, no two of them
can be in identical quantum states within the same system. The
quantum state of a particle is defined by the values of its
quantum numbers, so what this means is that no two electrons
in the same atom can have the same set of quantum numbers.
This is known as the Pauli exclusion principle, named after the
German physicist Wolfgang Pauli (1900-1958, Nobel Prize 1945).
• The exclusion principle was discovered empirically and
was placed on a firm theoretical foundation by Pauli in
1925. A complete explanation requires some familiarity
with quantum mechanics, so all we will say here is that if
two electrons possess the same quantum numbers
n, l, m and s (defined below), the wave function that
describes the state of existence of the two electrons
together becomes zero, which means that this is an
"impossible" situation.
• A given orbital is characterized by a fixed set of the
quantum numbers n, l, and m. The electron spin itself
constitutes a fourth quantum number s, which can
take the two values +1 and –1. Thus a given orbital can
contain two electrons having opposite spins, which
"cancel out" to produce zero magnetic moment. Two
such electrons in a single orbital are often referred to as
an electron pair.
• Since the quantum numbers m and l are zero for n=1,
the pair of electrons in the helium orbital have the values
(n, l, m, s) = (1,0,0,+1) and (1,0,0,–1)— that is, they differ
only in spin.
These two sets of quantum numbers are the only ones
that are possible for a n=1 orbital. The additional
electrons in atoms beyond helium must go into higherenergy (n>1) orbitals. Electron wave patterns
corresponding to these greater values of n are
concentrated farther from the nucleus, with the result
that these electrons are less tightly bound to the atom
and are more accessible to interaction with the electrons
of neighboring atoms, thus influencing their chemical
behavior. If it were not for the Pauli principle, all the
electrons of every element would be in the lowest-energy
n=1 state, and the differences in the chemical behavior
the different elements would be minimal.
Summary: p orbitals and d orbitals
p orbitals look like a dumbell
with 3 orientations: px, py, pz
(“p sub z”).
Four of the d orbitals resemble two dumbells in a clover shape. The last d
orbital resembles a p orbital with a donut wrapped around the middle.
Make sure you thoroughly understand the following essential ideas
which have been presented above. It is especially imortant that you
know the precise meanings of all the highlighted terms in the
context of this topic.
1. State the fundamental distinction between Bohr's original
model of the atom and the modern orbital model.
2. Explain the role of the uncertainty principle in preventing the
electron from falling into the nucleus.
3. State the physical meaning of the principal quantum number
of an electron orbital, and make a rough sketch of the shape
of the probability-vs-distance curve for any value of n.
4. Sketch out the shapes of an s, p, or a typical d orbital.
5. Describe the significance of the magnetic quantum number
as it applies to a p orbital.
6. State the Pauli exclusion principle.
Order of sublevel
energies:
s<p<d<f
The Quantum-Mechanical Model
and The Periodic Table
• A useful way to determine the electron
configuration of the elements is to add one
electron per element to the lowest energy orbital
available. This approach called the aufbau
principle (German aufbauen, “to build up”)
• It results in ground state electron configuration.
• There are two common ways to show the orbital
occupancy:
– The electron configuration
– The orbital diagram
Building up periods 1 and 2
• The placement of electrons for carbon exemplifies
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
Sample Problems
• Write a set of quantum numbers for the
third and eighth electrons added to F
• Use the periodic table to identify the
element with the electron configuration
1s22s22p4. Write its orbital diagram and
give the quantum numbers of its sixth
electron.
Answers
• The third electron is in the 2s orbital.
n = 2. l = 0, ml = 0, ms = + ½
• The eighth electron is in the first 2p orbital
n = 2, l = 1, ml = -1, ms = - ½
• The element has eight electron so Z = 8 oxygen
    
1s 2s
2p
n = 2, l = 1, ml = 0, ms = + ½
Relation between orbital filling and
the periodic table
Categories of electrons
• Inner (core) electrons are those in the previous
noble gas and any completed transition series. They
fill all the lower energy levels of an atom
• Outer electron are those in the highest energy level
(highest n value). They spent most of their time
farthest from nucleus
• Valence electron are those involved in forming
compounds. Among the main group elements, the
valence electrons are the outer electrons. Among
the transition elements, some inner d electrons are
also often involved in bonding and are counted
among the valence electrons.
Sample Problems
•
•
Give the (1) full and condensed electron configurations, (2)
partial orbital diagrams for the valence electrons and (3)
number of inner electrons for the following element:
1. Potassium (K: Z = 19)
2. Molybdenum (Mo: Z = 42)
3. Lead (Pb: Z = 82)
Give full and condensed electron configurations, a partial
diagrams for valence electrons and the number of inner
electrons for the following element:
1. Ni (Z = 28)
2. Sr (Z = 38)
3. Po (Z = 84)
Answers
• K (Z = 19)
Full: 1s2 2s2 2p6 3s2 3p6 4s1
Condensed: [Ar] 4s1
• Mo (Z = 42)
Full: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s1 4d5
Condensed : [Kr] 5s1 4d5
• Pb (Z = 82)
Full: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10
5p6 6s2 4f14 5d10 6p2
Condensed: [Xe] 6s2 4f14 5d10 6p2
Trends in Atomic Size
• Size goes UP on going down a group.
• Because electrons are added further from
the nucleus, there is less attraction.
• Size goes DOWN on going across a
period.
Atomic Radii
Atomic Size
• Size decreases across a period owing to
increase in Z*.
• Each added electron feels a greater and greater
+ charge.
Na Mg
Al
Si
P
S
Cl
Ar
186 160
143
118 110
103 100
98
Sample Problem
•
Using only the periodic table, rank each
set of main-group elements in order of
decreasing atomic size:
1.
2.
3.
4.
Ca, Mg, Sr
K, Ga, Ca
Br, Rb, Kr
Sr, Ca, Rb
1. Sr > Ca > Mg
2. K > Ca > Ga
3. Rb > Br > Kr
4. Rb > Sr > Ca
Ion Sizes
• CATIONS are SMALLER than the atoms from
which they come.
• The electron/proton attraction has gone UP and
so size DECREASES.
• 3- > 2- > 1- > 1+ > 2+ > 3+
Ion Sizes
• ANIONS are LARGER than the atoms
from which they come.
• The electron/proton attraction has gone
DOWN and so size INCREASES.
• Trends in ion sizes are the same as atom
sizes.
Sampel problems
• Rank the ions in order of increasing
size
• Na+, Mg2+, F• Ca2+, Sr2+, Mg2+
Answers :
• Mg2+< Na+ < F• Mg2+ < Ca2+ < Sr2+
Ionization Energy
• IE = energy required to remove an
electron from an atom in the gas phase.
Mg (g) + 735 kJ ---> Mg+ (g) + eMg+ (g) + 1451 kJ ---> Mg2+ (g) + eMg2+ (g) + 7733 kJ ---> Mg3+ (g) + e-
• Energy cost is very high to dip into a shell
of lower n. This is why ox. no. = Group no.
Trends in Ionization Energy
Trend in Ionization Energy
• IE increases across a period because Z*
increases.
– Metals lose electrons more easily than nonmetals.
– Metals are good reducing agents.
– Nonmetals lose electrons with difficulty.
• IE decreases down a group because size
increases
– Reducing ability generally increases down the
periodic table.
Successive Ionization Energy
Sample Problem
•
Using the periodic table only, rank the elements
in each of the following sets in order of
decreasing IE
1.
2.
3.
4.
•
Kr, He, Ar
Sb, Te, Sn
K, Ca, Rb
I, Xe, Cs
Rank in order of increasing IE
1. Sb, Sn, I
2. Sr, Ca, Ba
Answers
•
Decreasing IE
1.
2.
3.
4.
•
He > Ar > Kr
Te > Sb > Sn
Ca > K > Rb
Xe > I > Cs
Rank in order of increasing IE
1.
2.
Sn < Sb < I
Ba < Sr < Ca
Electron Affinity
• A few elements GAIN electrons to form anions.
• Electron affinity is the energy accompanying the
addition of 1 mol electrons to 1 mol gaseous atoms
or ions.
A(g) + e-  Ion-(g)
∆E = EA1
• In most cases energy is release when the first
electron is added because it is attracted to the
atom’s nuclear charge, thus EA1 is usually negative
• Factors other than Zeff and atomic size affect
electron affinities, so trends are not as regular as
those the previous two properties
• Despite irregularities, three key points emerge
when examine ionization energy and electron
affinity values:
• Elements in groups 6A and especially 7A have high
ionization energy and highly negative (exothermic)
electron affinities. These elements lose electrons
difficulty but attract them strongly so they form
negative ions
• Elements in groups 1A and 2A have low ionization
energy and either slightly negative or positive
(endothermic) electron affinities. These elements
lose electron readily but attract them weakly,
therefore in their ionic compounds they form
positive ions
• The noble gases, group 8A have very high
ionization energy and highly positive electron
affinities, therefore these elements do not tend to
lose or gain electron.
Electronegativity
• Electronegativity is a measure of the
relative ability of an element’s atoms to
attract the shared electrons in a chemical
bond.
• Higher electronegativities mean a greater
attraction for the electrons.
• Fluorine is the highest with a value of 4.0
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