2Summation of last points, Lecture 15: Heisenberg:Uncertainty Principle: cannot determine simultaneouslythe exact location and energy of an electron in atomSchroedinger:Wave equation to calculate probable location of e’saround nucleus using dual matter/wave properties of e’s.Three quantum numbers from equation locate e’s ofvarious energies in probable main shells, subshells,orbitals.
3The Quantum Numbers“Locators, which describe each e- about the nucleusin terms of relative energy and probable location.”The first quantum number, n, locates each electronin a specific main shell about the nucleus.The second quantum number, l , locates the electron in asubshell within the main shell.The third quantum number, ml , locates the electron ina specific orbital within the subshell.
4Locator #1, “n”, the first quantum number “n”, the Principal quantum number:Has all integer values 1 to infinity: 1,2,3,4,...Locates the electron in an orbital in a main shellabout the nucleus, like Bohr’s orbitsdescribes maximum occupancy of shell, 2n2.The higher the n number:the larger the shellthe farther from the nucleusthe higher the energy of the orbital in the shell.
6Locator #2, “l”, the second quantum number locates electrons in a subshell region within themain shelllimits number of subshells per shell to a value equal to n:n =1, 1 subshelln = 2, 2 subshellsn= 3, 3 subshells .....only four types of subshells are found to beoccupied in unexcited, “ground state” of atom.These subshell types are known by letter:“s” “p” “d ” “f”
7Diagram of available shells and subshells On the next slide is a schematic representationof the shells and subshells available for electronplacement within the atom.Note that the 5th, 6th and 7th types are giventhe alphabetical letters following “f”.None of these types are occupied in the groundstate of the largest known atoms.
9Locator #3, “ml”, the third quantum number “ml”, the third quantum number, specifiesin which orbital within a subshell an electronmay be found.It turns out that each subshell type contains a uniquenumber of orbitals, all of the same shape and energy.Main shell subshells orbitalsml #n#l #
10This third number completes the description of where a electron is likely to be found around the nucleus:All electrons can be located in an orbital within a subshell within a main shell. To find that electron one need a locating value for each:the “n” number describes a shell(1,2,3...)the “l” number describes a subshell region(s,p,d,f...)the “ml” number describes an orbital within theregion(Each of these quantum numbers has a series of numerical values. We will only use the n number values, 1-7.)
11The Third Q#, ml continued “ml” values will describe the number of orbitals within asubshell, and give each orbital its own unique “address”:s subshell p subshell d subshell f subshell1 orbital orbitals orbitals orbitals
13It was subsequently discovered that each orbital we have described is home to not just one but twoelectrons, with opposite spins!We are now treating an electron as a spinning chargedmatter particle, rotating clockwise or counterclockwiseon its axis: (next slide)To describe this situation, a fourth quantum numberis required, the magnetic quantum number, “ms”.
14As a consequence, we now know: s subshell, one orbital, 2 e’sp subshell, three orbitals, 6 e’s,d subshell, five orbitals, 10 e’s,f subshell, seven orbitals, 14e’s,
15This 4th Q# completes the set of “descriptors” or “locators” needed to assign each electron a uniqueposition in the arrangement around the nucleus.Pauli’s Exclusion Principle sums it up: no two e’s in thesame atom, can have the same four Q#’s. .
172e’s6 e’s10 e’s14 e’ss p d fn = 4n = 3n = 2n = 1
18Now that we have found places to put our electrons, in orbitals within subshells within shells, let’s take alook at the shapes of the various types of orbitals.The “orbital shapes” are simply enclosed areas ofprobability for an electron after a three dimensionalplot is made of all solutions for that electron from thewave equation.Each orbital within a subshell is centered about thenucleus and extends out to the boundaries of itsmain shell. Its exact orientation within the subshelldepends on the value of its ml number.
20Energy Description of e’s The first two quantum numbers, n and l, giveinformation about the relative energy of electronsin their location:As the “n” number increases, the energy of the ein that shell increases: 1<2<3<4<5<6<7As the “l” number increases, the energy of the ein a subshell within the shell increases: s<p<d<f
21The “ml” number describes the number of orbitals within a subshell of the same energy.Accordingly, the relative energy of an electron inany given orbital within a subshell is given by thesum of its “n” and “l” numbers.We have described the following subshells for theelectrons:1s; 2s, 2p; 3s, 3p, 3d; 4s, 4p, 4d, 4f; 5s, 5p, 5d, 5f;6s, 6p, 6 d; 7sLet’s next discuss their relative energy...
222e’s6 e’s10 e’s14 e’ss p d fn = 4= = = 7n = 3= = 5n = 2=3n = 11
26Let’s reorder, starting off with each new shell s subshell: Is this shape familiar?1s, 1< 2s, <2p, 3< 3s , <3p, 4< 4s, <3d, <4p, 5< 5s, <4d, <5p, 6< 6s, < 4f, <5d, <6p, 7<7s, <5f, <6d, 8Let’s expand...
27THE PERIODIC TABLE, ARRANGED BY SUBSHELLS? 14e’s6 e’s2e’s10 e’s
28Subshells, relative energy (n + l) s-blockp-blockd-blockf-blockPERIODS
29Our next task is to fill electrons around the nucleus into the orbitals we have described. The electrons will fillfrom lowest energy subshell to highest.The sum of n + l gives us a ranking order of fillingsubshells which does not simply progress fromcompletion of one shell to beginning of another.However, We will use the periodic table to guide usquickly through this complex sequence order.
30Periodic Table as Guide The periodic table lists all elements sequentially in order of atomic number: this means that each element in turn has one more electron than its predecessor.We’ll call this electron, the last one to be placed aroundthe nucleus, the “distinguishing electron”...We can subdivide the PT into four blocks, showing whichelements have their “distinguishing” or “final” electronin an “s” or a “p” or a “d” or a “f” type subshell.
31Where the Final Electron Goes: s,f,d,p Blocks of Elements
32Subshells by order of filling, Lowest energy to highest
33GROUP WORK: Complete the following table: Subshells being filled in each period:1st Period:2nd Period :3rd Period :4th Period :5th Period :6th Period :7th Period :Relate subshell numbers to period numbers.
34KEY!Subshells being filled in each period:1st: 1s2nd: 2s p3rd: 3s p4th: 4s d 4p5th: 5s d 5p6th: 6s 4f 5d 6p7th: 7s 5f 6d
35Conclusions Each period begins with an element filling an e into the s subshell in a new main shell whose n# is equal tothe period number.Each period ends with an element completing a psubshell whose n# is equal to the period number.s,p: n# = period number
36ELECTRONIC CONFIGURATIONS OF THE ELEMENTSWe can now describe the arrangement of all theelectrons around the nucleus of any given atomin terms of shells and subshells.We will call these arrangements “electronicconfigurations” and they can be done in two modes:“spectroscopic notation” or “orbital box diagram”
371s1 Let’s consider Hydrogen, Z=1: “spectroscopic notation” Total e’s in subshellMain shell1s1subshell“orbital box diagram”1s
39HUND’S RULE Following the placement of the first electron into the p subshell with Boron, the question then becomes,“does the next electron into the p subshell go to thesecond p orbital or does it fill up the first p orbital?”Hund’s Rule answers that question: in fillingmulti-orbital subshells, always put one electron intoeach, same spin, then begin filling each “half full”orbital.
401st, 2nd 3rd electronin place:Filling “p” orbitals:4th electronin place