Heisenberg: Uncertainty Principle: cannot determine simultaneously the exact location and energy of an electron in atom Schroedinger: Wave equation to calculate probable location of e’s around nucleus using dual matter/wave properties of e’s. Three quantum numbers from equation locate e’s of various energies in probable main shells, subshells, orbitals. Summation of last points, Lecture 15 :
The Quantum Numbers “Locators, which describe each e - about the nucleus in terms of relative energy and probable location.” The first quantum number, n, locates each electron in a specific main shell about the nucleus. The second quantum number, l, locates the electron in a subshell within the main shell. The third quantum number, m l, locates the electron in a specific orbital within the subshell.
“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 shell about the nucleus, like Bohr’s orbits describes maximum occupancy of shell, 2n 2. The higher the n number: the larger the shell the farther from the nucleus the higher the energy of the orbital in the shell. Locator #1, “n”, the first quantum number
Locator #2, “l”, the second quantum number limits number of subshells per shell to a value equal to n: n =1, 1 subshell n = 2, 2 subshells n= 3, 3 subshells..... only four types of subshells are found to be occupied in unexcited, “ground state” of atom. These subshell types are known by letter: “s” “p” “d ” “f” locates electrons in a subshell region within the main shell
Diagram of available shells and subshells On the next slide is a schematic representation of the shells and subshells available for electron placement within the atom. Note that the 5th, 6th and 7th types are given the alphabetical letters following “f”. None of these types are occupied in the ground state of the largest known atoms.
n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f (5g) 6s 6p 6d (6f 6g 6h) 7s (7p 7d 7f 7g 7h 7i) Lowest energy, smallest shell Highest, biggest
Locator #3, “m l ”, the third quantum number “m l ”, the third quantum number, specifies in which orbital within a subshell an electron may be found. It turns out that each subshell type contains a unique number of orbitals, all of the same shape and energy. Main shell subshells orbitals n# l # m l #
This 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 “m l ” number describes an orbital within the region (Each of these quantum numbers has a series of numerical values. We will only use the n number values, 1-7.)
The Third Q #, m l continued “m l ” values will describe the number of orbitals within a subshell, and give each orbital its own unique “address”: s subshell p subshell d subshell f subshell 1 orbital 3 orbitals 5 orbitals 7 orbitals
d ppp s dd dd f f ffff f f d p s “m l ” “l”“l”
It was subsequently discovered that each orbital we have described is home to not just one but two electrons, with opposite spins! We are now treating an electron as a spinning charged matter particle, rotating clockwise or counterclockwise on its axis: (next slide) To describe this situation, a fourth quantum number is required, the magnetic quantum number, “m s ”.
As a consequence, we now know: s subshell, one orbital, 2 e’s p subshell, three orbitals, 6 e’s, d subshell, five orbitals, 10 e’s, f subshell, seven orbitals, 14e’s,
This 4th Q# completes the set of “descriptors” or “locators” needed to assign each electron a unique position in the arrangement around the nucleus. Pauli’s Exclusion Principle sums it up: no two e’s in the same atom, can have the same four Q#’s..
f d p s “m l ” “l”“l” “m s ”
n = 1 n = 2 n = 3 n = 4 s p d f 2e’s6 e’s10 e’s 14 e’s
Now that we have found places to put our electrons, in orbitals within subshells within shells, let’s take a look at the shapes of the various types of orbitals. The “orbital shapes” are simply enclosed areas of probability for an electron after a three dimensional plot is made of all solutions for that electron from the wave equation. Each orbital within a subshell is centered about the nucleus and extends out to the boundaries of its main shell. Its exact orientation within the subshell depends on the value of its m l number.
Energy Description of e’s The first two quantum numbers, n and l, give information about the relative energy of electrons in their location: As the “n” number increases, the energy of the e in that shell increases: 1<2<3<4<5<6<7 As the “l” number increases, the energy of the e in a subshell within the shell increases: s
The “m l ” number describes the number of orbitals within a subshell of the same energy. Accordingly, the relative energy of an electron in any given orbital within a subshell is given by the sum of its “n” and “l” numbers. We have described the following subshells for the electrons: 1s; 2s, 2p; 3s, 3p, 3d; 4s, 4p, 4d, 4f; 5s, 5p, 5d, 5f; 6s, 6p, 6 d; 7s Let’s next discuss their relative energy...
n = 1 n = 2 n = 3 n = 4 s p d f 2e’s6 e’s10 e’s 14 e’s = = = = = =3 1
Relative energy of subshells s p d f
Order of Filling, Lowest energy to Highest s p d f START HERE
High energy Low energy
Let’s reorder, starting off with each new shell s subshell: 1s, 1 < 2s, 2 <2p, 3 < 3s,3 <3p, 4 < 4s, 4 <3d, 5 <4p, 5 < 5s, 5 <4d, 6 <5p, 6 < 6s, 6 < 4f, 7 <5d, 7 <6p, 7 <7s, 7 <5f, 8 <6d, 8 Is this shape familiar? Let’s expand...
THE PERIODIC TABLE, ARRANGED BY SUBSHELLS? 2e’s 14e’s 10 e’s 6 e’s
s-block p-block d-block f-block PERIODS Subshells, relative energy (n + l)
Our next task is to fill electrons around the nucleus into the orbitals we have described. The electrons will fill from lowest energy subshell to highest. The sum of n + l gives us a ranking order of filling subshells which does not simply progress from completion of one shell to beginning of another. However, We will use the periodic table to guide us quickly through this complex sequence order.
Periodic 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 around the nucleus, the “distinguishing electron”... We can subdivide the PT into four blocks, showing which elements have their “distinguishing” or “final” electron in an “s” or a “p” or a “d” or a “f” type subshell.
Where the Final Electron Goes: s,f,d,p Blocks of Elements s f d p
Subshells by order of filling, Lowest energy to highest
GROUP 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.
Subshells being filled in each period: 1st: 1s 2nd: 2s 2p 3rd: 3s 3p 4th: 4s 3d 4p 5th: 5s 4d 5p 6th: 6s 4f 5d 6p 7th: 7s 5f 6d KEY!
Conclusions Each period begins with an element filling an e into the s subshell in a new main shell whose n# is equal to the period number. Each period ends with an element completing a p subshell whose n# is equal to the period number. s,p: n# = period number
ELECTRONIC CONFIGURATIONS OF THE ELEMENTS We can now describe the arrangement of all the electrons around the nucleus of any given atom in terms of shells and subshells. We will call these arrangements “electronic configurations” and they can be done in two modes: “spectroscopic notation” or “orbital box diagram”
Let’s consider Hydrogen, Z=1: “spectroscopic notation” 1s 1 Main shell subshell Total e’s in subshell “orbital box diagram” 1s
1s 2s 2p THE NEXT 4 ELEMENTS
HUND’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 the second p orbital or does it fill up the first p orbital?” Hund’s Rule answers that question: in filling multi-orbital subshells, always put one electron into each, same spin, then begin filling each “half full” orbital.
1st, 2nd 3rd electron in place: 4th electron in place Filling “p” orbitals: