4
The Structure of
Atoms
Chapter Outline
Subatomic Particles 次原子粒子
1.
2.
3.
4.
5.
6.
7.
8.
Fundamental Particles基本粒子
The Discovery of Electrons 電子的發現
Canal Rays and Protons 陽極射線與質子
Rutherford and the Nuclear Atom 拉塞福與核型原子
Atomic Number原子序
Neutrons 中子
Mass Number and Isotopes 質量數和同位素
Mass spectrometry and Isotopic Abundance 質譜儀和
同位素豐量
9. The Atomic Weight Scale and Atomic Weights化學原子
量單位和原子量
10. The Periodic Table: Metals, Nonmetals, and Metalloids
周期表: 金屬,非金屬和類金屬
2
Chapter Outline
The Electronic Structures of Atoms 原子的電子構造
11. Electromagnetic radiation電磁輻射
12. The Photoelectric Effect 光電效應
13. Atomic Spectra and the Bohr Atom 原子光譜和波耳原子
模型
14. The Wave Nature of the Electron 電子具波的性質
15. The Quantum Mechanical Picture of the Atom 原子的量
子力學架構
16. Quantum Numbers 量子數
17. Atomic Orbitals 原子軌道
18. Electron Configurations 電子組態
19. The Periodic Table and Electron Configurations 週期表
與電子組態
20. Paramagnetism and Diamagnetism 順磁性及逆磁性
3
Fundamental Particles基本粒子
•Three fundamental particles make up atoms. The
following table lists these particles together with
their masses and their charges.
Table 4-1 Fundamental Particles of Matter
Particles
Mass (amu)
Charge
Electron 電子(e-) 0.00054858
-1
Proton 質子 (p, p+)
1.0073
+1
Neutron 中子 (n,n0)
1.0087
0
4
The Discovery of Electrons
•Humphrey Davy in the early 1800’s passed electricity
through compounds and noted:
–that the compounds decomposed into elements.
–concluded that compounds are held together by electrical
forces電力.
•Michael Faraday in 1832-1833 realized that the amount of
reaction that occurs during electrolysis電解is proportional
to the electrical current passed through the compounds.
法拉第
電學之父
戴維
無機化學之父
第一、作個人的筆記
第二、持續的上課
第三、有讀書的同伴
第四、成立讀書會
第五、學習仔細觀察和精確的用字
5
The Discovery of Electrons
•Cathode Ray Tubes 陰極射線管experiments
performed in the late 1800’s & early 1900’s.
–Consist of two electrodes 電極 sealed in a glass tube
containing a gas at very low pressure.
–When a voltage is applied to the cathodes a glow
Collimator準直儀
discharge is emitted.
燈絲加熱陰極發射電子，加速和聚焦後形成
電子束，陰性電子束會受到螢光屏的陽極吸
引而正確投射
把點光源發出的發散光或
其他輻射變成平行光束的器件
6
The Discovery of Electrons
•These “rays” are emitted from cathode (- end) and
travel to anode (+ end).
–Cathode Rays must be negatively charged!
•J.J. Thomson modified the cathode ray tube
experiments in 1897 by adding two adjustable
voltage electrodes.
–Studied the amount that the cathode ray beam was
deflected by additional electric field.
7
The Discovery of Electrons
陰極射線以直線行進
陰極射線具質量
8
The Discovery of Electrons
•Thomson used his modification to measure the charge
to mass ratio of electrons.
Charge to mass ratio 基本粒子的荷質比
e/m = -1.75881 x 108 coulomb/g of e-
•Thomson named the cathode rays electrons.
•Thomson is considered to be the “discoverer of
electrons”.
•TV sets and computer screens are cathode ray tubes.
The coulomb (C)庫侖is the standard unit of quantity of electric charge. It is defined
as the quantity of electricity transported in one second by a current of one ampere.
9
The Discovery of Electrons
•Robert A. Millikan won
the 1st American Nobel
Prize in 1923 for his
famous oil-drop
experiment 油滴實驗
•In 1909 Millikan
determined the charge
and mass of the
electron
10
The Discovery of Electrons
•Millikan determined that the charge on a single electron =
-1.60218 x 10-19 coulomb.
•Using Thomson’s charge to mass ratio we get that the mass
of one electron is 9.11 x 10-28 g.
–e/m = -1.75881 x 108 coulomb
– e = -1.60218 x 10-19 coulomb
–Thus m = 9.10940 x 10-28 g
11
Canal Rays陽極射線and Protons
質子
• Eugene Goldstein noted streams of positively charged particles in
cathode rays in 1886.
– Particles move in opposite direction of cathode rays.
– Called “Canal Rays” because they passed through holes (channels or
canals) drilled through the negative electrode.
• Canal rays must be positive.
– Goldstein postulated the existence of a positive fundamental
Atom  cation++ eparticle called the “proton”.
陽極
陰極
Canal rays particles have e/m ratios many smaller than those of electrons because of their
12
much greater masses
Rutherford拉塞福and the Nuclear
Atom 核型原子
How are these charge distributed?
•Ernest Rutherford directed Hans Geiger蓋革and Ernst
Marsden’s馬斯頓experiment in 1910.
–- particle scattering from thin Au foils
–Gave us the basic picture of the atom’s structure.
–散射粒子到金箔並且觀察到大角度的散射，提出了原
子有很小、密度大且帶正電的核
Undeflected α particles
Source of narrow beam of
fast-moving a particle
(positive charge)
Deflected particles
ZnS fluorescent screen
13
Rutherford and the Nuclear Atom
In 1912 Rutherford
decoded the -particle
scattering information
–Explanation involved a
nuclear atom with
electrons surrounding
the nucleus
14
Rutherford and the Nuclear Atom
Rutherford’s major conclusions from the -particle
scattering experiment
1. The atom is mostly empty space.
2. It contains a very small, dense center called the
nucleus.
3. Nearly all of the atom’s mass is in the nucleus.
4. The nuclear diameter is 1/10,000 to 1/100,000
times less than atom’s radius.
15
Rutherford and the Nuclear Atom
•Because the atom’s mass is contained in such a small
volume:
–The nuclear density is 1015g/mL.
–This is equivalent to 3.72 x 109 tons/in3.
–Density inside the nucleus is almost the same as a
neutron star’s density.
Rutherford Model of the atom:
Atoms consist of very small, very dense positively
charged nuclei surrounded by clouds of electrons
at relatively large distances from the nuclei
16
Atomic Number原子序
•The atomic number is equal to the number of
protons in the nucleus
–Sometimes given the symbol Z
–On the periodic chart Z is the uppermost number in
each element’s box
•In 1913 H.G.J. Moseley realized that the atomic
number determines the element
–The elements differ from each other by the number
of protons in the nucleus.
–The number of electrons in a neutral atom is also
equal to the atomic number.
17
Neutrons 中子
•James Chadwick 查兌克 in 1932 analyzed the results
of -particle scattering on thin be films.
•Chadwick recognized existence of massive neutral
particles which he called neutrons.
–Chadwick discovered the neutron.
Atoms consist of very small, very dense positively charged
nuclei surrounded by clouds of electrons at relatively large
distances from the nuclei. All nuclei contain protons; nuclei of
all atoms except the common form of hydrogen also contain
neutrons
18
Mass Number質量數 and Isotopes
同位數
•Mass number is given the symbol A.
•A is the sum of the number of protons and neutrons.
–Atomic number Z = proton number
N = neutron number
–Mass number A = Z + N
•A common symbolism used to show mass and proton
numbers is
A
12
40
197
E
for
example
C
Ca
Z
6
20
79 Au
• Can be shortened to this symbolism.
14
N 63 Cu 107 Ag
19
Mass Number and Isotopes
•Isotopes are atoms of the same element but with
different neutron numbers
–Isotopes have different masses and A values but are
the same element
•Display very similar chemical properties
•One example of an isotopic series is the hydrogen
isotopes
the most common
hydrogen
.
a radioactive hydrogen
isotope
20
Mass Number and Isotopes
•The stable oxygen isotopes provide another example.
•16O is the most abundant stable O isotope.
–How many protons and neutrons are in 16O?
8 protons and 8 neutrons
• 17O
is the least abundant stable O isotope.
 How many protons and neutrons are in 17O?
8 protons and 9 neutrons
•
18O
is the second most abundant stable O isotope.
 How many protons and neutrons in 18O?
8 protons and 10 neutrons
21
Example 4-1 Determination of Atomic Makeup
Determine the number of protons, neutrons, and electrons in each
of the following species. Are the members within each pair isotopes?
(a) 35
(b) 63 Cu and 65 Cu
37
(a)
17
35
17
37
17
(b)
Cl and
17
Cl
29
29
Cl Atomic number=17, 17protons/nucleus
mass number =35 18 neutrons
Because no charge is indicated: 17 electrons
Cl 17 protons, 20 neutrons, and 17 electrons
These are isotopes of the same element
63
29
Cu 29 protons, 34 neutrons, and 29 electrons
65
29
Cu 29 protons, 36 neutrons, and 29 electrons
These are isotopes of the same element
Exercise 18, 20
22
Mass Spectrometry質譜儀and
Isotopic Abundances
•Francis Aston devised the first mass spectrometer. 英
國物理學家，因研製質譜儀並用以準確測量原子及分子質量以及發現大
量核素，獲1922年諾貝爾化學獎
•質譜儀(mass spectrometry, MS)是以熱電子撞擊氣
體分子，使產生碎片及離子，再經磁場分離，依據
質荷比之測量，來決定分子質量的技術。
•There are four factors which determine a particle’s
path in the mass spectrometer.
1. accelerating voltage – 電場強度
2. magnetic field strength – 磁場強度
3. masses of particles – 物質質量
4. charge on particles – 物質電荷
23
Mass Spectrometry質譜儀and
Isotopic Abundances
基本原理
(1).將不同型態的樣品〈氣、液、固相〉導入質譜儀。
(2).樣品分子在離子源內游離(ionization)成氣相之離子形式。
(3).依質荷比(m/z : mass to charge ratio)不同分離各個樣品離子。
(4).各樣品離子到達偵測器被偵測出來。
(5).在資料處理系統中，離子偵測訊號被轉換成可讀或圖譜方式呈現。
24
Mass Spectrometry and
Isotopic Abundances
•Mass spectrum of Ne+ ions shown below.
–How scientists determine the masses and abundances
of the isotopes of an element.
組成比例
Isotope abundances: the relative amounts of the isotopes
同位素豐量 (isotopic abundance)：為某種同位素在此元素之各種同位素
中所占的原子百分比。
25
A modern mass spectrum
26
鈾
27
The Atomic Weight Scale原子量單位
and Atomic Weights原子量
•If we define the mass of 12C as exactly 12 atomic
mass units (amu)原子質量單位, then it is possible to
establish a relative weight scale for atoms.
–1 amu = (1/12) mass of 12C by definition
–What is the mass of an amu in grams?
28
The Atomic Weight Scale and
Atomic Weights
A
Z
E
Atomic number Z = proton number
N = neutron number
Mass number A = Z + N
•The atomic number Z =proton number in the nucleus
= electrons (in a neutral atom)
•The Mass Number A = proton number +neutron number
•The atomic weight of an element is the weighted average
of the masses of its stable isotopes
29
The Atomic Weight Scale and
Atomic Weights
•Example 4-2: Naturally occurring Cu consists of 2 isotopes. It is
69.1% 63Cu with a mass of 62.9 amu, and 30.9% 65Cu, which has
a mass of 64.9 amu. Calculate the atomic weight of Cu to one
decimal place.
63Cu isotope
65Cu isotope
Atomic weight= (0.691)x(62.9 amu) + (0.309)x(64.9amu)
=63.5 amu for copper
30
The Atomic Weight Scale and
Atomic Weights
•Example 4-3: Naturally occurring chromium consists of four
isotopes. It is 4.31% 2450Cr, mass = 49.946 amu, 83.76%
52Cr, mass = 51.941 amu, 9.55% 53Cr, mass = 52.941 amu,
24
24
54
and 2.38% 24 Cr, mass = 53.939 amu. Calculate the atomic
weight of chromium.
Atomic weight= (0.6431x49.946 amu)+(0.8376x51.941 amu)
+(0.0955x52.941 amu)+(0.0238x53.939 amu)
=51.998 amu for chromium
31
The Atomic Weight Scale and
Atomic Weights
•Example 4-4: The atomic weight of boron is 10.811 amu.
The masses of the two naturally occurring isotopes 510B
and 511B, are 10.013 and 11.009 amu, respectively.
Calculate the fraction and percentage of each isotope.
Let the 105 B fraction is x
11.811amu = (x x 10.013 amu)+((1-x ) x 11.009amu)
=(10.013 x +11.009-11.009 x)amu
(11.811-11.009) amu=(10.013-11.009) x amu
x =0.199
% abundance of 105B is 19.1%
% abundance of 115B = 100%-19.1% = 80.9%
Textbook example 4-2 and 4-3 p132-133
32
The Atomic Weight Scale and
Atomic Weights
Example 4-2 Calculation of Atomic Weight
Three isotopes of magnesium occur in nature. Their abundances an masses,
determined by mass spectrometry, are listed in the following table. Use this
information to calculate the atomic weight of magnesium.
Isotope %Abundance
Mass (amu)
24Mg
78.99
23.98504
25Mg
10.00
24.98584
26Mg
11.01
25.98259
Atomic weight = 0.7899 x (23.98504amu) + 0.1000 x (24.98584 amu) +
0.1101 x (25.98259 amu)
=18.946amu+2.4986amu+2.8607amu
= 24.30 amu
Exercise 28, 30
33
The Atomic Weight Scale and
Atomic Weights
Example 4-3 Calculation of Iostope Abundance
The atomic weight of gallium is 69.72 amu. The masses of the naturally
occurring isotopes are 69.9257 amu for 69Ga and 70.9249 amu for 71Ga.
Calculate the percent abundance of each isotope.
Let x =fraction of 69Ga Then (1-x)= fraction of 71Ga
x x (69.9257amu) + (1-x) x (70.9249amu) = 69.72amu
68.9257x + 70.9249-70.9249 x =69.72
-1.992x = -1.20
x = 0.6
x = fraction of 69Ga  60.00% 69Ga
(1-x )= 0.4=fraction of 71Ga  40.00% 71Ga
Exercise 32
34
The Periodic Table: Metals,
Nonmetals, and Metalloids
•1869 - Mendeleev & Meyer
–Discovered the periodic law
•The properties of the elements are periodic
functions of their atomic numbers.
35
The Periodic Table: Metals, Nonmetals,
and Metalloids
周期表: 金屬、非金屬、類金屬
•Groups or families (族)
–Vertical group of elements on periodic table
–Similar chemical and physical properties
鉻
鉬
鎢
36
Group (族)
鋰
鈹
鈉
鎂
鉀
鈣
銣
鍶
銫
鋇
鍅
鐳
37
The Periodic Table: Metals, Nonmetals,
and Metalloids
•Period (週期)
–Horizontal group of elements on periodic table
–Transition from metals to nonmetals
–Increasing atomic number原子序
鋰
鈹
硼
碳
氮
氧
氟
氖
38
金屬
非金屬
類金屬
鹵
素
鈍
氣
過渡元素
Most active nonmetal
Most active
Naturally occur
*
鹼 鹼
金 土
屬 金
屬
鑭系元素
錒
系
元
素
39
The Periodic Table: Metals, Nonmetals, and
Metalloids
Table 4-6 Some physical properties of metals
•
High electrical conductivity that decreases with
increasing temperature 導電性 ( 溫度升高導電性降低)
•
High Thermal conductivity導熱性
•
Metallic gray or silver luster 具金屬光澤
•
Almost all are solids
•
Malleable (can be hammered into sheets) 可塑性
•
Ductile (can be drawn into wires)具展延性
Table 4-6 Some physical properties of nonmetals
• Poor electrical conductivity (except carbon)
• Good heat insulators (except carbon)
• No metallic luster
• Solid, liquid or gases
• Brittle in solid state
• Nonductile
40
The Periodic Table: Metals, Nonmetals, and
Metalloids
Table 4-7 Some chemical properties of metals
• Outer shells contain few electrons—three or fewer
• Form cations by losing electrons (易失電子而帶正電)
• Form ionic compounds with nonmetals
與非金屬形成離子化合物
• Solid state characterized by metallic bonding 金屬鍵結
Table 4-7 Some chemical properties of nonmetals
• Outer shells contain four or more electrons
• Form anion by gating electrons (易得電子而帶負電)
• Form ionic compounds with metals and molecular (covalent)
other compounds with nonmetals
• Covalently bonded molecules 共價分子; noble gases are
monatomic
41
The Periodic Table: Metals, Nonmetals, and
Metalloids
Metallic character increases from top to bottom and decreases
from left to right with respect to position in the periodic table
Nonmetallic character decreases from top to bottom and increases
from left to right with respect to position in the periodic table
42
The Periodic Table: Metals, Nonmetals, and
Metalloids
Metalloid 類金屬
–Some properties that are characteristic of both
metals and nonmetals
–Some act as semiconductors半導體: such as silicon矽,
germanium鍺, antimony銻
•insulators at lower temperature
•Become conductors at higher temperature
–Aluminum is the least metallic of the metals and is
sometimes classified as a metalloid
•It is metallic in appearance and an excellent conductor
of electricity
43
The Periodic Table: Metals, Nonmetals,
and Metalloids
•Group IA metals (Alkali metals 鹼金屬)
–Li, Na, K, Rb, Cs, Fr
•One example of a periodic trend
–The reactions with water of Li, Na, & K
44
The Periodic Table: Metals, Nonmetals,
and
Metalloids
•Group IIA metals
–alkaline earth metals 鹼土金屬
•Be, Mg, Ca, Sr, Ba, Ra
45
The Periodic Table: Metals, Nonmetals,
and Metalloids
•Group VIIA nonmetals
–Halogens 鹵素
–F, Cl, Br, I, At
46
The Periodic Table: Metals, Nonmetals,
and Metalloids
•Group VIA nonmetals
–O, S, Se, Te
47
The Periodic Table: Metals, Nonmetals,
and Metalloids
•Group 8A nonmetals
–noble, inert or rare gases
–He, Ne, Ar, Kr, Xe, Rn
48
Electromagnetic Radiation
電磁輻射
•以電磁波方式在自由空間或實物媒質中傳播的能量，例如
無線電波、可見光和γ射線。
•The wavelength 波長of electromagnetic radiation has the
symbol .
–Wavelength is the distance from the top (crest) of one
wave to the top of the next wave.
•Measured in units of distance such as m,cm, Å.
– 1 Å = 1 x 10-10 m = 1 x 10-8 cm
•The frequency 頻率of electromagnetic radiation has the
symbol .
–Frequency is the number of crests or troughs that pass a
given point per second.
•Measured in units of 1/time - s-1
49
電磁輻射
•以具能量之光子形式，以光速 (3 x 1010
cm/sec)於空間中移動
•能量(電子伏特，eV表之)與頻率成正比
，與波長呈反比
•高能量光子具長射程、強穿透力 (遠離
發射源仍具影響力)
•依能量強弱分為游離輻射與非游離輻
射
50
Electromagnetic Radiation
For electromagnetic radiation
the velocity is 3.00 x 108 m/s= c = 
Energy increases
wavelength increases
可見光譜
頻率
7.5x1014
波長 4000
Visible spectrum
4x1014
7000
Å
51
Electromagnetic Radiation
•Example 4-5: What is the frequency of green light of
wavelength 5200 Å?
= c
= 5200 x 1x10-10 (m)=5.200x10 -7m
c = 
3.00x108m/s
=
5.200x10-7 m
= 5.77x1014 s-1
52
The Photoelectric Effect
光電效應
•Light can strike the surface of some metals causing
an electron to be ejected.
頻率夠高之光子與金屬原子中的電子碰撞，可以將電子撞離原子
53
Atomic Spectra and the Bohr
Atom原子光譜和波耳原子模型
電子只能存在某些特殊的軌道上才是穩定的，在
這些軌道上不會放射出電磁波，因此電子也不會
損失能量,在這個假設下，原子的激發光譜自然
而然也是不連續的
•Energy is quantized 能量可被量化
•Each orbit corresponds to a definite energy level
for the electron 電子軌道具有特定的能階
•When an electron is promoted form a lower
energy level to a higher one, it absorbs a definite
amount of energy 當電子從低能階移到高能階時,
必吸收能量
54
波耳倡議
•電子在特定的層殼內運動，也就是在特定分隔的能階
上運動並不會發出電磁輻射。
•當電子由較高的能階躍遷 (掉落) 至較低能階時會發出
電磁輻射
•而由較低的能階躍遷 (提昇) 至較高能階時則會吸收電
磁幅射。
•躍遷所發出或吸收的輻射能量必須等於電子在初始能
階和最後能階兩者之間的能量差。
這也可說明為何原子只吸收某些波長的輻射
nuclear
The 4 radii are in the ratio
1:22:32:42=1:4:9:16
55
Fig 4-17
The Quantum Mechanical
Picture of the Atom
Basic Postulates of Quantum Theory
1.Atoms and molecules can exist only in certain
energy states. In each energy state, the atom or
molecule has a definite energy. When an atom or
molecule changes its energy state, it must emit or
absorb just enough energy to bring it to the new
energy state (the quantum condition).原子或分子存
在特定能階
56
The Quantum Mechanical
Picture of the Atom
2.Atoms or molecules emit or absorb radiation
(light) as they change their energies. The
frequency of the light emitted or absorbed is
related to the energy change by a simple
equation. 當原子或分子改變能量時,必放出或
吸收輻射能
E  h 
hc

57
The Quantum Mechanical
Picture of the Atom
3. The allowed energy states of atoms and
molecules can be described by sets of numbers
called quantum numbers 量子數. 以數字描述原
子或分子的能量狀態稱之為量子數
– Quantum numbers are the solutions of the
Schrodinger, Heisenberg & Dirac equations.
– Four quantum numbers are necessary to describe
energy states of electrons in atoms. 有4種量子數
..
Schr o dinger equation
b2   2  2  2 
 2  2  2  2   V  E
8 m   x  y  z 
58
Quantum Numbers
•The principal quantum number 主量子數 has the
symbol – n.
n = 1, 2, 3, 4, ...... “shells” or main energy level 主能階
n = K, L, M, N, ......
The electron’s energy depends principally on n .
原子軌域分為 n = 1、2、3、4、…等正整數主殼層( 早
期科學家以K、 L 、M、N、…等符號表示主殼層)，最
大n值為∞的正整數。
原子軌域主殼層n值愈大，能量愈高，其電子
在核外空間的主要活動範圍離原子核愈遠。
59
Quantum Numbers
•The angular momentum角動量quantum number or
orbital quantum number軌道量子數 has the symbol .
 = 0, 1, 2, 3, 4, 5, .......(n-1)
 = s, p, d, f, g, h, .......(n-1)
• designates a sublevel (副殼層), tells us the shape of
the orbitals. 軌道的形狀
•These orbitals are the volume around the atom that the
electrons occupy 90-95% of the time.
This is one of the places where Heisenberg’s Uncertainty
principle comes into play.
60
原子軌域的副殼層
n主殼層又分為個副殼層，副殼層依序以s、p、d、f、
g 、 h…等符號表示。
 =(n-1)  = 0, 1, 2, 3, …
s, p, d, f
 n = 1的主殼層，只有一種副殼層，以1s表示，又
稱為1s原子軌域，簡稱1s軌域。
 n = 2的主殼層則有二種副殼層，以2s及2p表示，
又稱為2s及2p軌域。
 n = 3主殼層則有3s、3p、及3d三種副殼層軌域。
 n = 4主殼層有4s、4p、4d、4f四種副殼層軌域。
 n = 5主殼層有5s、5p、5d、5f、及5g五種副殼層
軌域，其他主殼層以此類推。
61
Quantum Numbers
•Orbital within a given subshell differ in their
orientation 方向 in space, but not in their energies.
•The symbol for the magnetic quantum number 磁量
子數is m.
m = -  , (-  + 1), (-  +2), .....0, ......., ( -2), ( -1), 
• If  = 0 (or an s orbital), then m = 0.
–Notice that there is only 1 value of m.
This implies that there is one s orbital per n value. n  1
•If  = 1 (or a p orbital), then m = -1, 0, +1.
–There are 3 values of m.
Thus there are three p orbitals per n value. n  2
62
Quantum Numbers
•If  = 2 (or a d orbital), then m = -2,-1,0,+1,+2.
–There are 5 values of m.
Thus there are five d orbitals per n value. n  3
•If  = 3 (or an f orbital), then m = -3,-2,-1,0,+1,+2, +3.
–There are 7 values of m.
Thus there are seven f orbitals per n value, n  4
•Theoretically, this series continues on to g,h,i, etc.
orbitals.
–Atoms that have been discovered or made up to
this point in time only have electrons in s, p, d, or f
orbitals in their ground state configurations.
63
Quantum Numbers
•The last quantum number is the spin quantum
number自旋磁量子數, ms.
•The spin quantum number only has two possible
values.
ms = +1/2 or -1/2
•This quantum number tells us the spin and
orientation of the magnetic field of the electrons
電子的磁場的旋轉方向.
•Wolfgang Pauli in 1925 discovered the Exclusion
Principle 包利不相容原理.
–No two electrons in an atom can have the same
set of 4 quantum numbers.
64
65
Atomic Orbitals
•Atomic orbitals are regions of space where the
probability of finding an electron about an atom
is highest.
•s orbital properties:
–There is one s orbital per n level.
– = 0
1 value of m
•s orbitals are spherically symmetric.
s副殼層只有一個軌域，稱為s軌域，其電
子在空間出現機率為球形，即與原子核等
距離的位置(球面)，電子出現的機率相同。
66
Atomic Orbitals
•p orbital properties:
–The first p orbitals appear in the n = 2 shell.
•p orbitals are peanut or dumbbell shaped volumes.
啞鈴狀
–They are directed along the axes of a Cartesian
coordinate system.
•There are 3 p orbitals per n level.
–The three orbitals are named px, py, pz.
–They have an  = 1.
–m =-1, 0, +1 3 values of m
67
Atomic Orbitals
•p orbitals are peanut or dumbbell shaped.
p副殼層有三個能量相等的軌域，其電子在空間出現機率
為啞鈴形，這三個p軌域具方位性稱為px、py及pz原子軌域。
px原子軌域的電子在空間中出現機率最大的位置在x軸座標
上，而py及pz電子最大出現機率分別在y及z軸座標上。
68
Atomic Orbitals
•d orbital properties:
–The first d orbitals appear in the n = 3 shell.
•The five d orbitals have two different shapes:
–4 are clover leaf shaped.
–1 is peanut shaped with a doughnut around it.
–The orbitals lie directly on the Cartesian axes or are
rotated 45o from the axes.
•There are 5 d orbitals per n level.
–The five orbitals are named – dxy, dyz, dxz,dx2-y2, dz2
–They have an  = 2.
–m = -2,-1,0,+1,+2
5 values of m 
69
Atomic Orbitals
•d orbital shapes
70
Atomic Orbitals
•f orbital properties:
–The first f orbitals appear in the n = 4 shell.
•The f orbitals have the most complex shapes.
•There are seven f orbitals per n level.
–The f orbitals have complicated names.
–They have an  = 3
–m = -3,-2,-1,0,+1,+2, +3
7 values of m
–The f orbitals have important effects in the
lanthanide and actinide elements.
71
Atomic Orbitals
•f orbital shapes
72
•In any atom, all orbitals
with the same principal
quantum number n are
similar in size. 具相同主量
子數n, 其原子大小相當
•In an atom, larger values
of n correspond to larger
orbital size. (n值越大, 軌域
越大)
•Each orbital with a given n
value becomes smaller as
nuclear charge increase (在
相同n值時,當核電荷增加時,
軌域越小)
73
Atomic Orbitals
•Spin quantum number自旋磁量子數effects:
–Every orbital can hold up to two electrons.
• Consequence of the Pauli Exclusion Principle.
–The two electrons are designated as having one spin
up  and one spin down 
•Spin describes the direction of the electron’s
magnetic fields.
Electron spin. The attraction due to their
opposite magnetic fields helps to overcome
the repulsion of their like charges. Two
electrons occupy the same region
74
Paramagnetism順磁性and
Diamagnetism反磁性
•Unpaired electrons have their spins aligned  or

–This increases the magnetic field of the atom.
–Atoms with unpaired electrons are called
paramagnetic .
–Paramagnetic atoms are attracted to a magnet.
•Paired electrons have their spins unaligned .
–Paired electrons have no net magnetic field.
–Atoms with paired electrons are called diamagnetic.
–Diamagnetic atoms are repelled by a magnet.
75
Paramagnetism and
Diamagnetism
• Because two electrons in the same orbital must be paired, it
is possible to calculate the number of orbitals and the
number of electrons in each n shell.
• The number of orbitals per n level is given by n2.
• The maximum number of electrons per n level is 2n2.
– The value is 2n2 because of the two paired electrons.
Shell
n
Number of subshells
Per shell
n
Number of
Atomic Orbitals
n2
Maximun Number
Of Electrons
2n2
1
1
1(1s)
2
2
2
4 (2s, 2px,2py, 2pz)
8
3
3
9 (3s, three 3p’s, five 3d’s )
18
4
4
16
32
5
5
25
50
76
電子組態
Electron Configurations
•原子內電子於原子軌域的分布情形，稱為電子
組態。
•原子最低能量的電子組態，稱為基態電子組態
(ground state electron configuration)。
•原子之基態電子組態需遵循
–構築原則 (aufbau principle)
–包立不相容原則(Pauli exclusion principle)
–洪德定則(Hund’s rule)。
77
構築原理(aufbau principle)
•Each atom is “built up” by
1. Adding the appropriate numbers of protons and
neutrons in the nucleus as specified by the atomic
number and the mass number
2. Adding the necessary number of electrons into
orbitals in the way that gives the lowest total
energy for the atom
•在不考慮原子核內中子數目，元素原子的建構方式為依序
在原子核內加入一個質子，同時在核外加入一個電子形成
•原子內質子與電子數相同，為電中性；原子核內質子數，
稱為原子序。原子序不同元素，性質不同。
•電子先填入低能量軌域，然後依序往高能量軌域填入。
78
•The largest energy gap is
between 1s and 2s orbitals
• the energies of orbitals
are generally closer
together at higher
energies.
•The gap between np and
(n+1)s is fairly high
2p 3s ; 3p 4s
•The gap between (n-1)d
and ns is quite small
3d 4s
•The gap between (n-2)f
and ns is even smaller.
4f 6s
Fig 5-29 The usual order of filling of the orbitals of an atom.
79
包立不相容原則
(Pauli Exclusion Principle)
•No two electrons in an atom may have identical sets
of four quantum number
•每一個原子軌域最多只能容納兩個電子，但這兩個
電子的自轉方向需相反，稱為包立不相容原則。
•包立不相容原則比較簡單的定義為，每一個原子軌
域最多只能容納兩個自轉方向相反的電子。
•填入兩個電子的軌域，淨電子自轉磁量為0，此為
自然法則。
80
主量子數
軌道量子數
81
82
洪德定則(Hund’s Rule)
•Electron occupy all the orbitals of a given subshell
singly before pairing begins. These unpaired electron
have parallel spins.
•電子填入能量相同的副層軌域時，電子先分別填入
不同軌域，當副層軌域各填入一個電子後 ，電子
再配對填入副層軌域至所有副層軌域各填入兩個電
子。如碳及氧原子的原子軌域電子組態：
• 6C：1s22s22px12py1 (或1s22s22px12pz1, … )
• 8O：1s22s22px22py12pz1 (或1s22s22px12py22pz1, … )
83
價電子
84
Row 2. Elements of atomic number 3 through 10 occupy the second period
in the periodic table
Atomic
number
3
4
5
6
7
8
9
10
•Hund’s rule tells us that the electrons will fill the p orbitals
by placing electrons in each orbital singly and with same
spin until half-filled. Then the electrons will pair to finish
the p orbitals.
85
Row 3. the next element beyond neon is sodium. Here we begin to add
electrons of the 3rd shell. Element 11 through 18 occupy the third
period in the periodic table
Atomic
number
10
11
12
13
14
15
16
17
18
86
•
The Periodic Table and
Electron Configurations
There are two ways to remember the correct
filling order for electrons in atoms.
1. You can use this mnemonic.
87
The Periodic Table and
Electron Configurations
2. Or you can use the periodic chart .
88
89
90
The Periodic Table and
Electron Configurations
Ar 18
19 K Ar 
3d
4s

Ca Ar 

Sc Ar  

22
Ti Ar   

23
V Ar    

Cr Ar      

20
21
24
4p
Configurat ion
Ar  4s1
Ar  4s2
Ar  4s2 3d1
Ar  4s2 3d 2
Ar  4s2 3d 3
Ar  4s1 3d5
There is an extra measure of stability associated
with half - filled and completely filled orbitals.
91
The Periodic Table and
Electron Configurations
3d
25 Mn Ar      
26
27
28
29
30
4s

Fe Ar      

Co Ar      

Ni Ar      

Cu Ar       
Zn Ar       
4p
Configurat ion
Ar  4s2 3d5
Ar  4s2 3d 6
Ar  4s2 3d 7
Ar  4s2 3d8
Ar  4s1 3d10
Ar  4s2 3d10
92
The Periodic Table and
Electron Configurations
3d
4s
4p
Configurat ion
31 Ga Ar        
Ar  4s 2 3d10 4p1
2
10
2




Ge
Ar








Ar
4s
3d
4p
32
2
10
3




As
Ar









Ar
4s
3d
4p
33
2
10
4




Se
Ar









Ar
4s
3d
4p
34
2
10
5




Br
Ar









Ar
4s
3d
4p
35
2
10
6




Kr
Ar









Ar
4s
3d
4p
36
93
Example 4-8 Electron Configurations and Quantum Numbers
Write an acceptable set of four quantum numbers for each electron in a
nitrogen atom.
Nitrogen : 7 electrons
1s 2s
Na
 
Electron
1,2
3,4
5,6,7
2p
  
e- Configuration
n
l
ml
ms
1
0
0
+1/2
1
0
0
-1/2
2
0
0
+1/2
2
0
0
-1/2
2
1
-1
+1/2 or -1/2
1p1x
2
1
0
+1/2 or -1/2
2p1y or 2p3
2
1
+1
+1/2 or -1/2
2p1z
1s2
2s2
94
Example 4-9 Electron Configurations and Quantum Numbers
Write an acceptable set of four quantum numbers for each electron in a
chlorine atom.
Chlorine : 17 electrons
1s 2s
2p
3s
3P
Na
    
Electron
n
l
ml
ms
e- Configuration
1,2
1
0
0
±1/2
1s2
3,4
2
0
0
±1/2
2s2
2
1
-1
±1/2
2
1
0
±1/2
2
1
+1
±1/2
3
0
0
±1/2
3
1
-1
±1/2
3
1
0
±1/2
3
1
+1
+1/2 or -1/2
5-10
11,12
13-17
2p6
3s2
3p5
Exercise 104,108
95
Example 4-10 Electron Configurations
Use Table 5-5 to determine the electron configurations of (a) magnesium, Mg;
(b) germanium, Ge; and (c) molybdenum, Mo.
magnesium, Mg : 12 electrons , last filled noble gas is neon
(atomic number 10)
[Ne] 3s2
germanium, Ge : 32 electrons , last filled noble gas is Argon
(atomic number 18)
[Ar] 3d10 4s2 4p2 or [Ar] 4s2 3d10 4p2
molybdenum, Mo : 42 electrons , last filled noble gas is krypton
(atomic number 36)
[Kr] 5s1 4d5 or [kr] 4d5 5s1
Exercise 106
96
Example 4-11 Unpaired electrons
Determine the number of unpaired electrons in an atom of tellurium, Te.
tellurium, Te : 52 electrons , last filled noble gas is krypton
(atomic number 36)
5s
4d
5p
Te [Kr]          5s2 4d10 5p4
two unpaired electrons
Exercise 112, 114
97