無機(jī)化學(xué)02完整版

1、無機(jī)化學(xué)02,郝鵬，周福強(qiáng)，佘星欣，孫瑞婷，陳蘇文,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.,能級（ev）,電離能（13.6ev）,光子：電磁輻射粒子 聲子：熱輻射粒子,極光的顏色是氧原子和從+2價(jià)N離子中得到的電子的發(fā)射普線。,氧原子的發(fā)射譜線,只有一些確定值，可以參看右圖氫原子光譜的巴爾末線系,2,量子化得，固定的能量單元,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:,水分子的震動(dòng)可以概括為簡單諧波震動(dòng)，這些特殊的設(shè)置導(dǎo)致吸收約700nm（波長的光線？）,熱容,受相同輻射下沙子是熱的，水是涼的液體的熱容高是因?yàn)樗鼈兊淖杂啥雀撸?溫度是內(nèi)能對熵的偏導(dǎo)數(shù)，在定體積下,室溫下固體的熱容公式： （對聲子密度的有效測量）,但是在更低的溫度下,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.,必須對能級進(jìn)行量子化，在得拜溫度（適合實(shí)驗(yàn)曲線的一個(gè)初始值）時(shí)涉及到量子力學(xué)與經(jīng)典力學(xué)的轉(zhuǎn)變,為了計(jì)算“黑體”曲線引入普朗克常數(shù),前面提到的這些引出了德布洛伊物態(tài)方程式，建立了波長、動(dòng)量、頻率、能量之間的關(guān)系。,從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”.,薛定諤方程,描述總能量的哈密頓量,所有電子的動(dòng)能,電子與核的相互吸引,電子與電子的相互排

10、斥,核與核的相互排斥,這個(gè)偏微分方程不可能精確求解（氫除外）,仍然用上一次提出的方法：波,5,這一段描述計(jì)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?yàn)樵拥馁|(zhì)量是與原子數(shù)成比例上升的，所以門捷列夫才能做出準(zhǔn)確的預(yù)測。,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.,化學(xué)元素，原子鍵，結(jié)構(gòu),第一個(gè)元素周期表實(shí)質(zhì)上是基于原子數(shù)的。,通常用波爾模型的

13、辦法來代表一種元素。,電子都在固定的能級上-軌道,圖示的是原子核，質(zhì)子和中子，原子的質(zhì)量都在這兒了,回憶德布洛伊方程，和ED電子衍射,ED, Electric diffraction 電子衍射。 采用波長小于或接近于其點(diǎn)陣常數(shù)的電子束照射晶體樣品，由于入射電子與晶體內(nèi)周期地規(guī)則排列的原子的交互作用，晶體將作為二維或三維光柵產(chǎn)生衍射效應(yīng)，根據(jù)由此獲得的衍射花樣研究晶體結(jié)構(gòu)的技術(shù)，稱為電子衍射。,6,7,我們可以這樣認(rèn)為，粒子在繞原子核的軌道上運(yùn)動(dòng)時(shí)有一個(gè)“波”，這個(gè)“波”只能取整數(shù)值。,原理圖示，忽略了海森堡不確定關(guān)系，如下,波函數(shù)振幅(模)的平方對應(yīng)于輻射的強(qiáng)度(微觀粒子在某處出現(xiàn)的概率密度)

14、,波爾演繹的波函數(shù)表明：是模的平方可以給出粒子出現(xiàn)的概率,這個(gè)因式的與在x到x+dx區(qū)間內(nèi)出現(xiàn)粒子的概率成正比,8,波長與周長的關(guān)系,旋轉(zhuǎn)可以是順時(shí)針或者逆時(shí)針，角動(dòng)能為：,Ei與mi是相互獨(dú)立的,這樣就可以計(jì)算波函數(shù)（Y（lml），和粒子在球體軌道運(yùn)行波函數(shù)的模式。,波長與周長的關(guān)系,需要注意正負(fù),I，慣性距,原子是三維的，使用極坐標(biāo)描述。,緯度， 偏振角,能量與旋轉(zhuǎn)方向無關(guān),9,為了描述原子中電子的運(yùn)動(dòng)規(guī)律，Schrdinger提出了一種波動(dòng)方程，現(xiàn)在我們稱為Schrdinger方程。這個(gè)偏微分方程的數(shù)學(xué)解很多，但從物理意義看，這些數(shù)學(xué)解不一定都是合理的。為了得到原子中電子運(yùn)動(dòng)狀態(tài)合理的解

15、，必須引用只能取某些整數(shù)值的三個(gè)參數(shù)，稱它們?yōu)榱孔訑?shù)（下面第四個(gè)也是，但不是從Schrdinger方程求出的）。 （1）主量子數(shù)n n相同的電子為一個(gè)電子層，電子近乎在同樣的空間范圍內(nèi)運(yùn)動(dòng)，故稱主量子數(shù)。當(dāng)n=1,2,3,4,5,6,7 電子層符號分別為K,L,M,N,O,P,Q。當(dāng)主量子數(shù)增大，電子出現(xiàn)離核的平均距離也相應(yīng)增大，電子的能量增加。例如氫原子中電子的能量完全由主量子數(shù)n決定：E=-13.6(eV)/n2 （2）角量子數(shù)l 角量子數(shù)l確定原子軌道的形狀并在多電子原子中和主量子數(shù)一起決定電子的能級。電子繞核運(yùn)動(dòng)，不僅具有一定的能量，而且也有一定的角動(dòng)量M，它的大小同原子軌道的形狀有密

16、切關(guān)系。例如M=0時(shí)，即l=0時(shí)說明原子中電子運(yùn)動(dòng)情況同角度無關(guān)，即原子軌道的軌道是球形對稱的；如l=1時(shí)，其原子軌道呈啞鈴形分布；如l=2時(shí)，則呈花瓣形分布。 對于給定的n值，量子力學(xué)證明l只能取小于n的正整數(shù)：l=0,1,2,3(n-1),10,（3）磁量子數(shù)m 同一亞層（l值相同）的幾條軌道對原子核的取向不同。磁量子數(shù)m是描述原子軌道或電子云在空間的伸展方向。某種形狀的原子軌道，可以在空間取不同方向的伸展方向，從而得到幾個(gè)空間取向不同的原子軌道。這是根據(jù)線狀光譜在磁場中還能發(fā)生分裂，顯示出微小的能量差別的現(xiàn)象得出的結(jié)果。 m取值受角量子數(shù)取值限制，對于給定的l值，m= -l，.，-2，-

17、1，0，+1，+2+l，共2l+1個(gè)值。這些取值意味著在角量子數(shù)為l的亞層有2l+1個(gè)取向，而每一個(gè)取向相當(dāng)于一條“原子軌道”。如l=2的d亞層，m= -2，-1，0，+1，+2，共有5個(gè)取值，表示d亞層有5條伸展方向不同的原子軌道，即dxy、dxz、dyz、dx2y2、dz2。我們把同一亞層（l相同）伸展方向不同的原子軌道稱為等價(jià)軌道或簡并軌道。 （4）自旋量子數(shù)ms 直接從Schrdinger方程得不到第四個(gè)量子數(shù)自旋量子數(shù)ms，它是根據(jù)后來的理論和實(shí)驗(yàn)要求引入的。精密觀察強(qiáng)磁場存在下的原子光譜，發(fā)現(xiàn)大多數(shù)譜線其實(shí)由靠得很近的兩條譜線組成。這是因?yàn)殡娮釉诤送膺\(yùn)動(dòng)，還可以取數(shù)值相同，方向相反

18、的兩種運(yùn)動(dòng)狀態(tài)，通常用和表示。,11,球諧函數(shù),波函數(shù)是相似的,輻射波只在表面上,圖示的就是幾個(gè)亞層和各亞層上的軌道，S（l=1）亞層只有一條0軌道，p亞層有三條軌道，d亞層有5條?？梢园绍壍览斫鉃榍蛎嫔系膱A軌跡。,12,包含可靠半徑Rnl是有必要的，氫的三個(gè)最低能量的波函數(shù)如下,Rnl可以在下面幾個(gè)圖中得到,需要注意的是i S軌道上沒有零值 ii 出現(xiàn)輻射點(diǎn)iii r/a0增大則2 降低,13,隨I增加，角節(jié)點(diǎn)個(gè)數(shù)增加，波函數(shù)變的更彎曲了。,導(dǎo)致角動(dòng)量增加，動(dòng)能也增加,越靠近原子核，曲率變大，動(dòng)能增大,徑向節(jié)點(diǎn)增大電子能量，是因?yàn)閯?dòng)能降低而勢能增大,這個(gè)結(jié)論在動(dòng)能和勢能之間保持平衡,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為0時(shí)，角動(dòng)量l(l+1)1/2 = 0，意味著電子的運(yùn)動(dòng)是徑向的，沿著原子核進(jìn)進(jìn)出出的擺動(dòng)。,用下式規(guī)定一個(gè)單個(gè)電子的波函數(shù),前一項(xiàng)依賴于半徑，后一項(xiàng)依賴于球面諧波（兩個(gè)角度）。,旋轉(zhuǎn)的電子不只有軌道角動(dòng)量，還有自旋角動(dòng)量。,14,當(dāng)I不=0時(shí)，電子沿著原子核揮動(dòng)。,庫倫力小于離心力？,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,波爾模型認(rèn)為，單電子原子被磁性分離為兩束，重復(fù)：軌

25、道角量子數(shù)在h/2.之間。,這是按照索莫非理論（舊的量子論）得出的，與經(jīng)典理論對比，,進(jìn)行了一個(gè)著名的實(shí)驗(yàn)（SGE）看看哪個(gè)正確。,Stern和它的同事說如果波爾的狗屎理論是正確的，我們就不搞物理了,SGE實(shí)驗(yàn)：將一束銀原子通過不均勻磁場射到照相底片上。如果（I）是量子化的，就應(yīng)該得到兩個(gè)帶。 卻是觀察到了兩個(gè)帶。,Stern發(fā)了一張明信片祝賀波爾，如圖示。他不是說不搞物理了嗎？,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實(shí)驗(yàn)證實(shí)了角動(dòng)量是量子化的，徹底拋棄了傳統(tǒng)觀點(diǎn)。,但是新的量子理論-波動(dòng)力學(xué)（仍然被認(rèn)為是正確的）顯示應(yīng)該分3個(gè)帶。,實(shí)際上新量子論中銀在基態(tài)時(shí)的角量子數(shù)l應(yīng)該是0，因此磁量子數(shù)ml也一定是0，因此根據(jù)舊量子論在SGE實(shí)驗(yàn)中只

29、應(yīng)該觀察到一個(gè)帶（而不是兩個(gè)）。,泡利認(rèn)為這是由于旋轉(zhuǎn)電子不只有一個(gè)軌道角動(dòng)量，還有一個(gè)自旋角動(dòng)量。,SGE實(shí)驗(yàn)中觀察到的裂口是由于電子自旋，表明自旋角動(dòng)量的存在。,16,總的角量子數(shù)應(yīng)該等于軌道角量子數(shù)假設(shè)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論，自旋量子數(shù)有兩個(gè)可能的值,泡利：相同量子態(tài)下不可能有兩個(gè)電子，就是說不同電子的表征電子狀態(tài)的4個(gè)量子數(shù)不可能完全相同。,這些擴(kuò)充了薛定諤方程，是之包含了相反的電子自旋。,迪拉克提出了波動(dòng)方程，也包含了這些東西。,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,材料無機(jī) 化學(xué)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!”,角量子數(shù),主量子數(shù),磁量子數(shù),能級,自旋量子數(shù),總角動(dòng)量,物質(zhì)都是由波構(gòu)成的,薛定諤方程中用到的三個(gè)量子數(shù),光，無線電，電磁場，重力，能量，力場，電子及物質(zhì)本身的本質(zhì)仍然一無所知,電子自旋,方向和

35、簡并 （相同亞層不同軌道數(shù),應(yīng)用泡利不相容原理，可以精確的得到層殼狀的原子結(jié)構(gòu),E = -(Ae2Z+Z- N)r -1+ BNe-r/ - CNr-6 + 2.25Nhomax,H = E,dU/dr = 0,2,材料無機(jī) 化學(xué)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,層殼狀的原子結(jié)構(gòu),電子數(shù),銅電子躍遷,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,材料無機(jī) 化學(xué)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,上圖就是所有的能存在的能級，這些能級構(gòu)成了所有化學(xué)元素的電子分布,地球上各種元素含量,太陽系中各種元素含量,鑒別太陽系和其他地方的多種元素是通過什么方法？,光譜學(xué) 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,材料無機(jī)

40、 化學(xué)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”多用于光譜學(xué)，“orbital”（化學(xué)術(shù)語類似于波函數(shù)）用于元素周期表,以下是n=4所有可能的軌道,電子數(shù),總電子數(shù),注意角量子數(shù)l的亞層，這些用于參考化學(xué)鍵和連接,亞層,軌道,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,這四個(gè)軌道量子數(shù)用來描述原子軌道的填充，對理解元素周期表非常的重要。,AF哪個(gè)是正確的，哪個(gè)是錯(cuò)誤的？,然后將AF按能級從低到高排列。,注：n= 1 是基態(tài), l = n-1, ml= -l-2

45、,-1,0,1,2,+l, ms= +1/2, -1/2.,A: l取0到n-1的整數(shù),因此l=2不對 C：ms只能取-1/2或+1/2，因此ms=1不對 B、D正確,E：因?yàn)閘=0，所以ml只能為0 F：n必須是大于0的整數(shù),能量從低到高的順序是 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學(xué)元素中的應(yīng)用,元素周期表：它的來源及重要性,有一百多種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:,我們應(yīng)用的周期表的形式是按 電子分別填充s、p、d和f亞層 （即l值分別為0、1、2、3）,在周期表中，電子在軌道上填充 的順序并不完全按照s、p、d、f 亞層的順序 而是按照如下順序,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