1、Chapter 9. Structure of Atoms and Periodic Table of the Elements, 9-1. Fundamentals 9-2. Structure of Hydrogen Atom 9-3. Quantum Numbers and Atomic Orbitals 9-4. Electron Configurations and Periodicity,How are the electrons distributed in this space? what are the electrons doing in the atom?,1. Fund

2、amentals, All matter is composed of indivisible atoms. An atom is an extremely small particle of matter that retains its identity during chemical reactions.,Postulates of Daltons atomic theory (1803),Fe on Cu(111),Xe on Ni (110),Single atoms can be visualized and manipulated by scanning-tunneling mi

3、croscope (STM, 掃描隧道顯微鏡).,1. Fundamentals, An element is a type of matter composed of only one kind of atom, each atom of a given kind having the same properties. Na, Cl2., A compound is a type of matter composed of atoms of two or more elements chemically combined in fixed proportions. NaCl, H2O., A

4、 chemical reaction consists of the rearrangement of the atoms present in the reactants to give new chemical combinations present in the products. Atoms are not created, destroyed, or broken into smaller particles by any chemical reaction.,John Dalton 約翰道爾頓 (1766-1844) England,atomic theory,1. Fundam

5、entals,1. Fundamentals,J. J. Thomson (18561940) English 約瑟夫湯姆遜 Nobel Prize (Physics),1906,Raisin bread model (1904),In 1897, Thomson discovered electrons, by which he proposed the raisin bread model (葡萄干面包模型) of atoms.,Discovery of electron,1. Fundamentals,William Thomson, 1st Baron Kelvin 威廉湯姆森，第一代

6、開爾文男爵 (18241907) British 熱力學(xué)之父,William Thomson, 1st Baron Kelvin 威廉湯姆森，第一代開爾文男爵 (18241907) British 熱力學(xué)之父,1. Fundamentals,1. Fundamentals,1. Fundamentals,An atom consists of two kinds of particles: a positively(+)-charged nucleus (10-15 m), which contains most (99.95%) of the atoms mass, and one or m

7、ore electrons. An electron is a negatively(-)-charged particle that exists in the region (10-10 m) around the nucleus.,1. Fundamentals,Structure of an atom?,How are the electrons distributed in this space? (What are the electrons doing in the atom?),According to Rutherfords model, an atom consists o

8、f a nucleus many times smaller than the atom itself, with electrons occupying the remaining space.,Rutherfords model posed a dilemma.,According to the nuclear model, an electron would continuously lose energy as electromagnetic radiation (photons); spiral into the nucleus (in about 10-10 s).,2. Stru

9、cture of Hydrogen Atom,continuous energy: continuous wavelength: continuous spectrum; the atom would “die”.,2. Structure of Hydrogen Atom,I. Continuous vs. line spectrum (連續(xù)光譜和線狀光譜),Dispersion of white light by a prism (棱鏡): White light, entering at the left, strikes a prism, which disperses the lig

10、ht into a continuous spectrum of wavelength.,A heated solid (such as a heated tungsten filament (鎢絲) emits light with continuous spectrum (a spectrum containing light of all wavelengths).,2. Structure of Hydrogen Atom,Emission line spectra of some elements: The lines corresponds to visible light (38

11、0780 nm) emitted by atoms.,A heated gas (atom) emits light with line spectrum (a spectrum showing only certain colors or specific wavelengths of light).,Hydrogen line spectra,Helium line spectra,2. Structure of Hydrogen Atom,2. Structure of Hydrogen Atom,In 1885 J. J. Balmer showed that the waveleng

12、ths in the visible spectrum of hydrogen could be reproduced by a simple formula:,Here n is some whole number (integer) greater than 2. The wavelengths of the four lines in the hydrogen atom visible spectrum correspond to n = 3, 4, 5, and 6, respectively.,2. Structure of Hydrogen Atom,E = n h,2. Stru

13、cture of Hydrogen Atom,2. Structure of Hydrogen Atom,Consider this analogy to help see why light of insufcient energy cannot free an electron from a metal surface. If one Ping-Pong ball does not have enough energy to knock a book off its shelf, neither does a series of Ping-Pong balls, because the b

14、ook cannot save up the energy from the individual impacts. But one base-ball traveling at the same speed does have enough energy to move the book. Whereas the energy of a ball is related to its mass and velocity, the energy of a photon is related to its frequency.,2. Structure of Hydrogen Atom,II. T

15、he Bohr Theory of the Hydrogen Atom (1913),To account for: The stability of the hydrogen atom (that the atom exists and the electron does not continuously radiate energy and spiral into the nucleus); The line spectrum of the atom.,2. Structure of Hydrogen Atom,1. Energy-level postulate: An electron

16、can have only specific energy values in an atom, which are called its energy levels (能級).,http:/www. ,ground state (基態(tài)),excited states (激發(fā)態(tài)),n: principal quantum number (主量子數(shù)),2. Structure of Hydrogen Atom,The energies have negative values because the energy of the separated nucleus and electron is

17、taken to be zero. As the nucleus and electron come together to form a stable state of the atom, energy is released and the energy becomes less than zero, or negative.,The first postulate explains the stability of hydrogen atoms.,2. Structure of Hydrogen Atom,2. Structure of Hydrogen Atom,2. Transiti

18、ons (躍遷) between energy levels: An electron in an atom can change energy only by going from one energy level to another energy level. By doing so, the electron undergoes a transition.,The second postulate explains the line spectrum emitted by hydrogen atoms.,2. Structure of Hydrogen Atom,Explaining

19、the line spectrum emission by atoms,An electron in a higher energy level (initial energy level Ei) undergoes a transition to a lower energy level (final level Ef).,2. Structure of Hydrogen Atom,Example 9-1: What is the wavelength of light emitted when the electron in a hydrogen atom undergoes a tran

20、sition from energy level n = 4 to level n = 2?,Solution:,(blue-green),2. Structure of Hydrogen Atom,Balmer series (visible):,Paschen series (infrared):,Lyman series (ultraviolet):,2. Structure of Hydrogen Atom,The nucleus is composed of two different kind of particles, protons (質(zhì)子), and neutrons (中子

21、).,Nuclear composition (1932),Subatomic Particles,2. Structure of Hydrogen Atom,2. Structure of Hydrogen Atom,Evaluation of Bohrs theory,Success: The theory firmly established the concept of atomic energy level. It can account for (1) the stability of the hydrogen atom and (2) the line spectrum of t

22、he atom.,Limitation: The theory was unsuccessful, however, in accounting for the details of atomic structure and in predicting energy levels for atoms other than hydrogen.,2. Structure of Hydrogen Atom,III. Wave-particle duality (波粒二象性) of the electron,According to Einstein, light has not only wave

23、properties, which we characterize by frequency and wavelength, but also particle properties. For example, a particle of light, photon, has momentum. This momentum, mc, is related to the wavelength of the light:,2. Structure of Hydrogen Atom,De Broglie relation:,Louis de Broglie reasoned that if ligh

24、t (considered as a wave) exhibits particle aspects, then perhaps particles of matter show characteristics of waves under the proper circumstances. He therefore postulated that a particle of matter of mass m and speed has a wavelength, by analogy with light:,2. Structure of Hydrogen Atom,De Broglie r

25、elation:,An electron (9.110-31 kg) moving at about 5.9105 ms-1 has a wavelength of about 1.210-9 m.,A basketball (0.60 kg) moving at about 10 ms-1 has a wavelength of about 10-34 m.,2. Structure of Hydrogen Atom,2. Structure of Hydrogen Atom,They showed that electrons gave a diffraction pattern (衍射圖

26、) when reflected from a crystal or pass through a very thin gold foil. Both Thomson received Nobel prizes: J. J. for showing that the electron is a particle and G. P. for showing that it is a wave.,The wave property of electrons was demonstrated by C. Davisson, L. H. Germer and G. P. Thomson (son of

27、 J. J. Thomson).,E. Ruska used this wave property to construct the first electron microscope (電子顯微鏡) in 1933. Shown is the scanning electron microscope image of a wasps head.,2. Structure of Hydrogen Atom,2. Structure of Hydrogen Atom,You cannot say that the electron will definitely be at a particul

28、ar position at a given time, we can say that the electron is likely to be at this point.,Wave property of electrons: Statistical statements about where we would find the electron (probability of finding an electron at a certain point in an atom).,2. Structure of Hydrogen Atom,De Broglie relation say

29、s that electrons can not be treated only as particles. In some circumstances, they demonstrate wave properties, which must be considered to uncover the atomic structures.,Significance of de Broglie relation,IV. Uncertainty Principle,2. Structure of Hydrogen Atom,It is impossible to know simultaneous

30、ly, with absolute precision, both the position and the momentum of a particle such as an electron.,W. Heisenberg 維爾納海森伯 (1901-1976) Germany Nobel prize (1932),Uncertainty Principle,2. Structure of Hydrogen Atom,Heisenbergs uncertainty principle (測不準(zhǔn)原理): The product of the uncertainty in position and

31、 the uncertainty in momentum of a particle can be no smaller than Planks constant divided by 4.,x: The uncertainty in the x coordinate of a particle; px: The uncertainty in the momentum in the x direction.,If you know very well where a particle is, you can not know where it is going !,2. Structure o

32、f Hydrogen Atom,For an electron with a velocity of 6.0106 ms-1 (an error of 1%):,For a basketball with a velocity of 10 ms-1 (an error of 1%),The uncertainty principle is only significant for particles of very small mass such as electrons.,2. Structure of Hydrogen Atom,Heisenbergs uncertainty princi

33、ple says that, for electrons, the uncertainties in position and momentum are normally quite large. We can not describe the electron in an atom as moving in a definite orbit.,Significance of uncertainty principle,V. Wave Function（波函數(shù)）,2. Structure of Hydrogen Atom,In 1926, E. Schrdinger devised a the

34、ory (Schrdinger equation) that could be used to find the wave properties of electrons in atoms and molecules.,E. Schrdinger 埃爾文薛定諤 (1887-1961) Austria Nobel prize (1933),De broglies relation applies quantitatively only to particles in a force-free environment. It cannot be applied directly to an ele

35、ctron in an atom, where the electron is subject to the attractive force of the nucleus.,Schrdinger equation,2. Structure of Hydrogen Atom,2. Structure of Hydrogen Atom,Information about an electron in an atom is contained in a mathematical expression called wave function, denoted by the Greek letter

36、, . The wave function is obtained by solving Schrdinger equation:,2, gives the probability of finding an electron within a region of space. The diagram shows the probability density (概率密度) (at a point) for an electron in a hydrogen atom in the ground state.,2. Structure of Hydrogen Atom,2. Structure

37、 of Hydrogen Atom,2. Structure of Hydrogen Atom,The graph shows the probability (概率) (within a spherical shell) of finding the electron within shells at various distances from the nucleus. The curve exhibits a maximum (r= 52.9 pm, Bohr radius), which means that the radial probability is greatest for

38、 a given distance from the nucleus.,Probability,2. Structure of Hydrogen Atom,Information about an electron in an atom is contained in a wave function, which can just be obtained by solving me under specific conditions. Solve me, and you get everything the states of electrons in an atom.,Significanc

39、e of Schrdinger Equation,3. Quantum Numbers and Atomic Orbitals,Information about an electron in an atom is contained in a wave function, , which gives the probability of finding the electron at various points in space.,Three different quantum numbers are needed because there are three dimensions to

40、 space.,A group of wave functions is obtained by solving Schrdinger equation. For solving Schrdinger equation, three integral conditions must be satisfied. These integers n, l, m are referred as quantum numbers.,(n, l, m) specify a wave function, n,l,m.,3. Quantum Numbers and Atomic Orbitals,A wave

41、function for an electron in an atom is called an atomic orbital (原子軌道).,Probability density for an electron in a hydrogen atom in the ground state.,An atomic orbital is pictured qualitatively by describing the region of space where there is high probability (99%) of finding the electrons. The atomic

42、 orbital so pictured has a definite shape.,I. Quantum numbers,3. Quantum Numbers and Atomic Orbitals,1. Principal quantum number (n，主量子數(shù)), The smaller n is, the lower the energy. In the case of the hydrogen atom (single electron), n is the only quantum number determining the energy. For other atoms,

43、 the energy also depends to a slight extent on the l quantum number.,General meaning:,This quantum number is the one on which the energy of an electron in an atom principally depends; it can have any positive integer value: 1, 2, 3, and so on.,3. Quantum Numbers and Atomic Orbitals, n also determine

44、s the average distance of electron to the nucleus or the size of an orbital. The larger the value of n is, the larger the orbital, or the farer the distance of an electron to the nucleus., Orbitals of the same quantum state n are said to belong to the same shell (層). Shells are sometimes designated

45、by the following letters:,LetterKLMNOPQ n1234567,3. Quantum Numbers and Atomic Orbitals,2. Angular momentum quantum number (l, 角動量量子數(shù)),This quantum number distinguish orbitals of given n having different shapes, it can have any integer value from 0 to n-1.,n = 1:,l = 0,n = 2:,l = 0, 1,n = 3:,l = 0,

46、1, 2,n = 4:,l = 0, 1, 2, 3,3. Quantum Numbers and Atomic Orbitals,Letterspdf l0123, Orbitals of the same n but different l are said to belong to different subshells (亞層) of a given shell. The different subshells are usually denoted by letters as follows:,The choice of letter symbols for quantum numb

47、ers survives from old spectroscopic terminology (describing the lines in a spectrum as sharp, principal, diffuse, and fundamental).,3. Quantum Numbers and Atomic Orbitals,To denote a subshell within a particular shell, we write the value of the n for the shell, followed by the letter designation for

48、 the subshell. For example, 2p denotes a subshell with quantum numbers n = 2 and l = 1., The energy of an orbital also depends somewhat on the l quantum number (except for the H atom). For a given n, the energy of an orbital increases with l.,3d? 4f?,energy (n,l), Within each shell of quantum number

49、 n, there are n different kinds of orbitals, each with a distinctive shape denoted by an l quantum number.,3. Quantum Numbers and Atomic Orbitals,n=1: l=0(s); 1s. n=2: l=0(s), 1(p); 2s, 2p. n=3: l=0(s), 1(p), 2(d); 3s, 3p, 3d.,3. Quantum Numbers and Atomic Orbitals,3. Magnetic quantum number (m, 磁量子

50、數(shù)),This quantum number distinguish orbitals of given n and lthat is, of given energy and shape but having a different orientation in space; the allowed values are the integers from l to l. Every value denotes an individual atomic orbital.,l = 0 (s): m = 0; There is only one orbital in the s subshell

51、.,3. Quantum Numbers and Atomic Orbitals,l = 1 (p): m = -1, 0, 1; There are three different orbitals in the p subshell.,l = 2 (d): m = -2, -1, 0, 1, 2; There are five different orbitals in the d subshell.,There is no direct relation between the values of m and the x, y, z designation of the orbitals

52、.,3. Quantum Numbers and Atomic Orbitals,Note that there are 2l+1 orbitals in each subshells of quantum number l. These orbitals have the same shape and energy, though with different orientation in space, thus called equivalent orbital (等價軌道).,3. Quantum Numbers and Atomic Orbitals,4. Spin quantum n

53、umber (ms, 自旋量子數(shù)),This quantum number refers to the two possible orientation of the spin axis of an electron; possible values are +1/2 and 1/2.,3. Quantum Numbers and Atomic Orbitals,The first three quantum numbers characterize the orbital that describe the region of space where an electron is most

54、likely to be found; we say that the electron “occupies” this orbital. The spin quantum number describes the spin orientation of the electron.,Each electron in an atom has four different quantum numbersthe principal quantum number (n), the angular momentum quantum number (l), and the magnetic quantum

55、 number (m), the spin quantum number (ms).,3. Quantum Numbers and Atomic Orbitals,3. Quantum Numbers and Atomic Orbitals,Permissible Values of Quantum Numbers for Atomic Orbitals,3. Quantum Numbers and Atomic Orbitals,Example 9-2: State whether each of the following sets of quantum numbers is permis

56、sible for an electron in an atom. If a set is not permissible, explain why.,Solution:,Not permissible. The l is equal to n; it must be less than n. Not permissible. The magnitude of the m (that is, the m value, ignoring it sign) must not be greater than l. Permissible. Not permissible. The ms can be

57、 only +1/2 or 1/2.,3. Quantum Numbers and Atomic Orbitals,The electron in a 2s orbital is likely to be found in two regions, one near the nucleus and the other in a spherical shell about the nucleus (the electron is most likely to be here).,II. Atomic orbital shapes,Cross sectional representations a

58、nd cutaway diagrams of the probability distributions of a 1s and 2s orbital.,4. Electron Configurations and Periodicity,I. Orbital energies,The energy of an orbital depends only on the quantum numbers n and l., For a given l, the smaller n is, the lower the energy., For a given n, the energy of an o

59、rbital increases with l., Interleaving (能級)交錯.,1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 7s, 5f.,4. Electron Configurations and Periodicity,The order of orbital energy (as induced from spectroscopic measurements) is shown on the right mnemonic diagram.,Diagonal rule,Write the subshell(s) in rows, each row having subshell(s) of given n. Within each row, arrange the subshell(s) by increasing l. Starting with the 1s subshell, draw a series of diagonals (對角線), as shown.,4. Electron Configurations and Periodicity,II. Electron configurations and orbital diagrams,Th