无机化学02完整版

1、无机化学02,郝鹏，周福强，佘星欣，孙瑞婷，陈苏文,1,Last time looked at the aurora and fireworks as sources of photon (particle of e-m radiation) and phonon (particle of thermal radiation):,Aurora colors are emission lines (photons) from the oxygen atom and electron gain by N2+ion.,Spectral emission lines for oxygen atom.,

2、Noted that these are quantised (fixed units of energy).,i.e. can only have certain values, as shown by the formula for the visible line (Balmerseries) spectra of the hydrogen atom.,RH is the Rydberg constant, it can be calculated from spectroscopic data or from quantum mechanics using fundamental co

3、nstants.,能级（ev）,电离能（13.6ev）,光子：电磁辐射粒子 声子：热辐射粒子,极光的颜色是氧原子和从+2价N离子中得到的电子的发射普线。,氧原子的发射谱线,只有一些确定值，可以参看右图氢原子光谱的巴尔末线系,2,量子化得，固定的能量单元,Also saw the vibrational motions of water can be summed as simple harmonic oscillations and it is a specific set of these that result in absorption 700nm:,Looked at the heat

4、 capacity Cv:,much higher Cv for liquid due more degrees of freedom:,U=internal energy T=temperature S=entropy,sand -hot,Water-cool,both receive same amount of radiant energy (sunlight),And that at room temperature, the heat capacity Cv for a solid (effectively a measure of phonon density) can be de

5、scribed by:,However at lower temperatures saw that:,水分子的震动可以概括为简单谐波震动，这些特殊的设置导致吸收约700nm（波长的光线？）,热容,受相同辐射下沙子是热的，水是凉的液体的热容高是因为它们的自由度高，,温度是内能对熵的偏导数，在定体积下,室温下固体的热容公式： （对声子密度的有效测量）,但是在更低的温度下,3,it is necessary to quantise the energy levels and that the change from classical to quantum behavior occurs at t

6、he Debye temperature (a value initially used to fit the experimental curve) .,Saw that the Plank constant , h, was introduced to account for black body curves:,The link between all the aforementioned are the de Broglie equations:,giving rise to wave particle duality.,= wavelength, p= momentum, f = f

7、requency , E= energy, and h = Planks constant.,必须对能级进行量子化，在得拜温度（适合实验曲线的一个初始值）时涉及到量子力学与经典力学的转变,为了计算“黑体”曲线引入普朗克常数,前面提到的这些引出了德布洛伊物态方程式，建立了波长、动量、频率、能量之间的关系。,从而引出了波粒二象性,4,Finished off with a look at the Schrodinger equation:,Hamiltonian describing total energy,kinetic energy of all electrons,electron-nuc

8、lear attraction,electron-electron repulsion,nuclear-nuclear repulsion,This partial differential equation is impossible (at this time) to solve exactly (beyond the hydrogen molecule). But.,The Tianhe-1A supercomputer is about 50% faster than its closest rival!,Such high speeds need more than 7,000 Nv

9、idia graphics processors and 14,000 Intel chips.,28 October 2010 China claims supercomputer crown,100 of these,The Milky Way supercomputer.,Since we do not have help from Tianhe-1A we need to continue with the approach developed last time,namely;” waves”.,薛定谔方程,描述总能量的哈密顿量,所有电子的动能,电子与核的相互吸引,电子与电子的相互排

10、斥,核与核的相互排斥,这个偏微分方程不可能精确求解（氢除外）,仍然用上一次提出的方法：波,5,这一段描述计算器的，不用看,1. The chemical elements, atomic bonding, and structure.,Introduction. .continued:,Although the first Periodic Table of the Elements was based on atomic weights it is in fact the atomic number (Z) that is of importance.,A common way to rep

11、resent an element is by the Bohr model:,The electrons are shown orbiting at fixed energy levels.,因为原子的质量是与原子数成比例上升的，所以门捷列夫才能做出准确的预测。,Also shown is the atomic nucleus (protons and neutrons).,and this nearly accounts for the mass of an atom.,Z = 12 Magnesium (Mg),It is because the atomic weight increa

12、ses in close proportion to the atomic number that Mendeleev was able to be so accurate in his predictions!,Recall de Broglies wave particle duality:,(and ED -electron diffraction.),= wavelength, p = momentum, = frequency , E = energy, and h = Planks constant.,化学元素，原子键，结构,第一个元素周期表实质上是基于原子数的。,通常用波尔模型的

13、办法来代表一种元素。,电子都在固定的能级上-轨道,图示的是原子核，质子和中子，原子的质量都在这儿了,回忆德布洛伊方程，和ED电子衍射,ED, Electric diffraction 电子衍射。 采用波长小于或接近于其点阵常数的电子束照射晶体样品，由于入射电子与晶体内周期地规则排列的原子的交互作用，晶体将作为二维或三维光栅产生衍射效应，根据由此获得的衍射花样研究晶体结构的技术，称为电子衍射。,6,7,我们可以这样认为，粒子在绕原子核的轨道上运动时有一个“波”，这个“波”只能取整数值。,原理图示，忽略了海森堡不确定关系，如下,波函数振幅(模)的平方对应于辐射的强度(微观粒子在某处出现的概率密度)

14、,波尔演绎的波函数表明：是模的平方可以给出粒子出现的概率,这个因式的与在x到x+dx区间内出现粒子的概率成正比,8,波长与周长的关系,旋转可以是顺时针或者逆时针，角动能为：,Ei与mi是相互独立的,这样就可以计算波函数（Y（lml），和粒子在球体轨道运行波函数的模式。,波长与周长的关系,需要注意正负,I，惯性距,原子是三维的，使用极坐标描述。,纬度， 偏振角,能量与旋转方向无关,9,为了描述原子中电子的运动规律，Schrdinger提出了一种波动方程，现在我们称为Schrdinger方程。这个偏微分方程的数学解很多，但从物理意义看，这些数学解不一定都是合理的。为了得到原子中电子运动状态合理的解

15、，必须引用只能取某些整数值的三个参数，称它们为量子数（下面第四个也是，但不是从Schrdinger方程求出的）。 （1）主量子数n n相同的电子为一个电子层，电子近乎在同样的空间范围内运动，故称主量子数。当n=1,2,3,4,5,6,7 电子层符号分别为K,L,M,N,O,P,Q。当主量子数增大，电子出现离核的平均距离也相应增大，电子的能量增加。例如氢原子中电子的能量完全由主量子数n决定：E=-13.6(eV)/n2 （2）角量子数l 角量子数l确定原子轨道的形状并在多电子原子中和主量子数一起决定电子的能级。电子绕核运动，不仅具有一定的能量，而且也有一定的角动量M，它的大小同原子轨道的形状有密

16、切关系。例如M=0时，即l=0时说明原子中电子运动情况同角度无关，即原子轨道的轨道是球形对称的；如l=1时，其原子轨道呈哑铃形分布；如l=2时，则呈花瓣形分布。 对于给定的n值，量子力学证明l只能取小于n的正整数：l=0,1,2,3(n-1),10,（3）磁量子数m 同一亚层（l值相同）的几条轨道对原子核的取向不同。磁量子数m是描述原子轨道或电子云在空间的伸展方向。某种形状的原子轨道，可以在空间取不同方向的伸展方向，从而得到几个空间取向不同的原子轨道。这是根据线状光谱在磁场中还能发生分裂，显示出微小的能量差别的现象得出的结果。 m取值受角量子数取值限制，对于给定的l值，m= -l，.，-2，-

17、1，0，+1，+2+l，共2l+1个值。这些取值意味着在角量子数为l的亚层有2l+1个取向，而每一个取向相当于一条“原子轨道”。如l=2的d亚层，m= -2，-1，0，+1，+2，共有5个取值，表示d亚层有5条伸展方向不同的原子轨道，即dxy、dxz、dyz、dx2y2、dz2。我们把同一亚层（l相同）伸展方向不同的原子轨道称为等价轨道或简并轨道。 （4）自旋量子数ms 直接从Schrdinger方程得不到第四个量子数自旋量子数ms，它是根据后来的理论和实验要求引入的。精密观察强磁场存在下的原子光谱，发现大多数谱线其实由靠得很近的两条谱线组成。这是因为电子在核外运动，还可以取数值相同，方向相反

18、的两种运动状态，通常用和表示。,11,球谐函数,波函数是相似的,辐射波只在表面上,图示的就是几个亚层和各亚层上的轨道，S（l=1）亚层只有一条0轨道，p亚层有三条轨道，d亚层有5条。可以吧轨道理解为球面上的圆轨迹。,12,包含可靠半径Rnl是有必要的，氢的三个最低能量的波函数如下,Rnl可以在下面几个图中得到,需要注意的是i S轨道上没有零值 ii 出现辐射点iii r/a0增大则2 降低,13,随I增加，角节点个数增加，波函数变的更弯曲了。,导致角动量增加，动能也增加,越靠近原子核，曲率变大，动能增大,径向节点增大电子能量，是因为动能降低而势能增大,这个结论在动能和势能之间保持平衡,For

19、l = 0 (so ml = 0), the magnitude of the angular momentum, l(l+1)1/2 = 0, this means the motion of the electron is radial; swinging in and out from the nucleus!,When l 0 (i.e. there is angular momentum ) the electron is flung away from the nucleus.,re: columbic force 1/r2 and so is less than centrifu

20、gal force J2/r3 ,Hence l 0 has a zero value at the nucleus.,Finally we can state the single electron atom (e.g. hydrogen) wave functions are of the form:,It had been suggested (by Wolfgang Pauli and others) that a spinning electron not only had orbital angular momentum but also had spin angular mome

21、ntum.,I为0时，角动量l(l+1)1/2 = 0，意味着电子的运动是径向的，沿着原子核进进出出的摆动。,用下式规定一个单个电子的波函数,前一项依赖于半径，后一项依赖于球面谐波（两个角度）。,旋转的电子不只有轨道角动量，还有自旋角动量。,14,当I不=0时，电子沿着原子核挥动。,库伦力小于离心力？,The Bohr model suggests that “hydrogenic atoms” (single electron atoms) would be magnetically split into two beams, re: orbital angular momentum is

22、limited to h/2.,This followed with Sommerfeld theory (old quantum theory), in contrast to the classical theory which stated there would be a spread of magnetic values.,A famous (for a number of reasons) experiment; the Stern Gerlach experiment or SGE, was done to see which was correct.,Stern (who wo

23、rked with Einstein) and a colleague are quoted as saying: “ If this nonsense of Bohr is proved correct we will quit physics!”.,The SGE passes a beam of silver (Ag) atoms through an inhomogenous(uneven) magnetic field and onto a photographic plate.,.and if (l) is quantised, re: the Bohr model and Som

24、merfeldtheory (old quantum theory). then 2 bands should result.,Two bands were observed:,Stern sent a congratulatory postcard to Bohr and later went on to show the existence of sub-atomic particles! (So he was not a man of his word?).,Copy of the postcard sent to Niels Bohr,波尔模型认为，单电子原子被磁性分离为两束，重复：轨

25、道角量子数在h/2.之间。,这是按照索莫非理论（旧的量子论）得出的，与经典理论对比，,进行了一个著名的实验（SGE）看看哪个正确。,Stern和它的同事说如果波尔的狗屎理论是正确的，我们就不搞物理了,SGE实验：将一束银原子通过不均匀磁场射到照相底片上。如果（I）是量子化的，就应该得到两个带。 却是观察到了两个带。,Stern发了一张明信片祝贺波尔，如图示。他不是说不搞物理了吗？,15,The SGE seemed to confirm quantitation of angular momentum (l) AND definitely discarded the classical vie

26、wpoint,But new quantum theory wave mechanics (still considered correct) shows that 3 bands should observed for l=1 (i.e. ml= +1, 0, -1) !,In fact in new quantum theory l for silver Ag in its ground state is 0 (hydrogen atom, i.e. s = 1) therefore ml must be 0!,So for old quantum mechanics a single b

27、and should have been observed in the SGE!,The suggestion of Wolfgang Pauli and others that a spinning electron not only had orbital angular momentum but also had spin angular momentum was the solution!,Stud. Hist. Phil. Mod. Phys., Vol. 26, No. 1, pp. 7546, 1995,Total angular momentum; J = L + S.,L=

28、 orbital angular momentum,S= spin angular momentum,The splitting observed in the SGE was due to electron spin (1/2), showing an electron posses both orbital and spin angular momentum.,SGE实验证实了角动量是量子化的，彻底抛弃了传统观点。,但是新的量子理论-波动力学（仍然被认为是正确的）显示应该分3个带。,实际上新量子论中银在基态时的角量子数l应该是0，因此磁量子数ml也一定是0，因此根据旧量子论在SGE实验中只

29、应该观察到一个带（而不是两个）。,泡利认为这是由于旋转电子不只有一个轨道角动量，还有一个自旋角动量。,SGE实验中观察到的裂口是由于电子自旋，表明自旋角动量的存在。,16,总的角量子数应该等于轨道角量子数假设自旋。,The new quantum number (spin quantum number), with two possible values, lead to the famous:,“Pauli exclusion principle”,Namely: “no two electrons can exist in the same quantum state” (i.e. hav

30、e the same 4 quantum numbers),All that remained was to expand the Schrodinger equation to include opposing electron spins.,A student, then postdoctoral researcher, at Cambridge University; Paul Dirac, supplied the wave equation, which also includes relativity.,Wolfgang Pauli,Paul Dirac,Schrodinger a

31、nd Dirac shared Physics Nobel Prize in 1933.,= wave functions, i ，Dirac matrices, c = speed light, m = mass of the particle,基于著名的泡利不相容理论，自旋量子数有两个可能的值,泡利：相同量子态下不可能有两个电子，就是说不同电子的表征电子状态的4个量子数不可能完全相同。,这些扩充了薛定谔方程，是之包含了相反的电子自旋。,迪拉克提出了波动方程，也包含了这些东西。,17,休息，休息一下.,18,E = -(Ae2Z+Z- N)r -1+ BNe-r/ - CNr-6 + 2.2

32、5Nhomax,H = E,dU/dr = 0,2,材料无机 化学APB 2010 MATERIALS INORGANIC,CHEMISTRY S65010020,“Matter is made of waves. . the true nature of light, radio waves, electric and magnetic fields, gravity, energy, fields of force, electrons and matter itself,is still totally unknown.”,“and my mojo. ?”,Using the three

33、 quantum numbers obtained from Schrodinger equation, namely :,1. Principle Quantum number n,= Energy level, n = 1,2,3 etc.,2. Angular Quantum number l,= Total angular momentum, l = n 1.,4. Spin Quantum number m s,= Electron spin, ms = -1/2, +1/2,and applying the Pauli exclusion principle the shell s

34、tructure of the atom is obtained exactly:,3. Magnetic Quantum number m l = orientation and degeneracy, ml = -l.-1,-1,0,1,2,.l (number of orbitals of the same type),Austin Powers “.its all waves, baby!”,角量子数,主量子数,磁量子数,能级,自旋量子数,总角动量,物质都是由波构成的,薛定谔方程中用到的三个量子数,光，无线电，电磁场，重力，能量，力场，电子及物质本身的本质仍然一无所知,电子自旋,方向和

35、简并 （相同亚层不同轨道数,应用泡利不相容原理，可以精确的得到层壳状的原子结构,E = -(Ae2Z+Z- N)r -1+ BNe-r/ - CNr-6 + 2.25Nhomax,H = E,dU/dr = 0,2,材料无机 化学APB 2010 MATERIALS INORGANIC,CHEMISTRY S65010020,m=0,m = -1,n=1,l = 0 ml = 0,ms = +1/2 ms = -1/2,n=2,l=1,l=0,m=0 m=1,ms = +1/2 ms = -1/2 ms = +1/2,ms = -1/2,ms = +1/2 ms = -1/2,ms = +1/

36、2 ms = -1/2,2,8,?,32,K shell,L shell,n=3,M shell,N shell,Electronic transitions for Cu.,J. Scanning Electron Microscopy and X-Ray,Microanalysis, 3rd ed., Kluwer: New York. 2003,See page 381 of hand-out,l = 0, 1, and 2,n = 4 l = 0, 1, 2, and 3,?,18,The shell structure of the atom:,Number of electrons

37、,+6,+10,+14,+2,层壳状的原子结构,电子数,铜电子跃迁,Mass Fraction,Atoms per 1012 H,differ.,Atomic number,10,20,30,40,50,60,70,80,90,108 106 104 102 101,1012 1010,Elements in the Solar System,E = -(Ae2Z+Z- N)r -1+ BNe-r/ - CNr-6 + 2.25Nhomax,H = E,dU/dr = 0,2,材料无机 化学APB 2010 MATERIALS INORGANIC,CHEMISTRY S65010020,The

38、 identification of many elements in the solar system and elsewhere is by? 祝郡璋,Zhun Junzhang “spectroscopy”. Note that the different scale AND the quantities,10,20 30,40,50,60,70,80,90,10-2 10-4 10-6 10-8 10-10,Atomic number Abundance of the,Abundance of the Elements on Earth.,These are the only avai

39、lable energy levels for any two electrons to occupy and these levels make up the electron distribution in all the chemical elements: 1,上图就是所有的能存在的能级，这些能级构成了所有化学元素的电子分布,地球上各种元素含量,太阳系中各种元素含量,鉴别太阳系和其他地方的多种元素是通过什么方法？,光谱学 不同的比例不同的含量,E = -(Ae2Z+Z- N)r -1+ BNe-r/ - CNr-6 + 2.25Nhomax,H = E,dU/dr = 0,2,材料无机

40、 化学APB 2010 MATERIALS INORGANIC,CHEMISTRY S65010020,Note the labels used for l, these are used in reference to chemical bonds and bonding.,I,0 0 1 0 1 2 0 1 2,3,ml,0 0 1, 0, -1 0 1, 0, -1 2, 1, 0, -1, -2 0 1, 0, -1 2, 1, 0, -1, -2,3, 2, 1, 0, 1, -2, -3,label,1s 2s 2p 3s 3p 3d 4s 4p 4d,4f,No,orbitals

41、,1 1 3 1 3 5 1 3 5,7,Number of,electrons,2 2 6 2 6 10 2 6 10,14,Total,electrons,2 8 18 32,n,1 2 2 3 3 3 4 4 4,4,ms,1 2 1 2 1 2 1 2,+/- +/- +/- +/-,K shell L shell M shell N shell,The K, L, M, N etc. shells are more relevant to spectroscopy and orbitals (a chemists term that is comparable to wave fun

42、ctions) are more relevant to the Periodic Table of the Elements”. Below are shown all the available orbitals up to n = 4:,K，L，M，N等，“shells”多用于光谱学，“orbital”（化学术语类似于波函数）用于元素周期表,以下是n=4所有可能的轨道,电子数,总电子数,注意角量子数l的亚层，这些用于参考化学键和连接,亚层,轨道,The 4 orbital numbers (n, l, mland ms) used to describe the filling of a

43、tomic orbitals, are central to understanding the Periodic Table of the Elements,Look at the sets of the 4 shown in A to F, which of theses are allowed and which are not ?,Recall:,n= 1 is the ground state, l = n-1, ml= -l-2,-1,0,1,2,+l, ms= +1/2, -1/2.,Write done what is wrong, if anything with the q

44、uantum numbers (n, l, ml, ms) in the examples A to F?,You have 5 -10 minutes to do complete this.,Anyone finishing early can list, the allowable sets in A to F, in order of energy (lowest to highest),23,这四个轨道量子数用来描述原子轨道的填充，对理解元素周期表非常的重要。,AF哪个是正确的，哪个是错误的？,然后将AF按能级从低到高排列。,注：n= 1 是基态, l = n-1, ml= -l-2

45、,-1,0,1,2,+l, ms= +1/2, -1/2.,A: l取0到n-1的整数,因此l=2不对 C：ms只能取-1/2或+1/2，因此ms=1不对 B、D正确,E：因为l=0，所以ml只能为0 F：n必须是大于0的整数,能量从低到高的顺序是 FAB、CED,1. The chemical elements, atomic bonding, and structure.,Includes :,Introduction,Periodic Table and availability of the chemical elements.,Electronegativity.,Crystal c

46、hemistry and space groups.,Nonstoichiometryand solid solutions.,Phase transitions.,The Periodic Table: Its Story and Its Significance,There are over a hundred different ways to represent the Periodic Table of the Elements.,Eric R. Scerri, Oxford University Press, 2007, 368 pages. $35 hardback (ISBN

47、13 978-0-19-530573-9).,Chemical Galaxy IIby P.J.Stewart 2007.,元素周期表及其在化学元素中的应用,元素周期表：它的来源及重要性,有一百多种不同的表示元素周期表方法,But the format used here will be: Where s, p, d, and f refer to the electrons filling l = 0, 1, 2, and 3 respectively.,It is noticeable that the order of filling of atomic orbitalsis not f

48、ollowed in the Periodic Table:,Instead the order is:,我们应用的周期表的形式是按 电子分别填充s、p、d和f亚层 （即l值分别为0、1、2、3）,在周期表中，电子在轨道上填充 的顺序并不完全按照s、p、d、f 亚层的顺序 而是按照如下顺序,Why does the 4s orbital fill before the 3d?,The radial probability (rdf) shows that the 3d orbital penetrates closer to the nucleus. This lowers the energy of the 3d orbital.,So scandium (Sc) Z=21 does not have electrons filling in the order:,. but pairing of electrons (2 in a s orbital) re