Chapter 7- Quantum Chemistry Chang 10th Ed. Quantum ... - PageOut

Chapter 7- Quantum Chemistry Chang 10 th Ed. 5/8n - Principle quantum number or main quantum numberDefines the (gross) energy level and defines how close an atom is to the nucleus. Thepossible values of n are 1 to n (simple whole integers greater than zero). If the n value islarge the electron is in a high energy orbital far away from the nuclues; if n is small theelectron is in a low energy orbital close to the nucleus.l - angular momentum quantum numberDefines the shape (in 3-D space relative to nucleus) of an orbital. Possible values of l are0 to n-1. The l values also give a fine tuning of energy for multi-electron systems (nothydrogen atoms). It turns out that the lower the value of l the lower in energy the orbitalis even if they have the same value for n. Note also the the possible values of l increaseas n increases - in other words the probability functions become more complex as thedistance from the nucleus increases.m l - magnetic quantum numberDefines the orientation in space (x,y,z axis orientation - or polar coordinate orientation)which does not effect the energy of the orbitals if they have the same n and l values. Thepossible values are -l to +l. Again the possible values for l increase and the distance fromthe nucleus increases (these probability functions become more complex)m s - spin quantum numberDefines the spin direction of an electron. Electrons have a property which is analogous toa charged particle spinning in a given direction. This is shown in the interaction of boundelectrons with magnetic fields[Figure 7.17]The ms value can be 1/2 or -1/2 only relating to clockwise and couterclockwise spinning.This value has a small but measurable impact on the energy level.The relative energies of some bound electrons can be determined by placing a sample in amagnetic field in ESR experiments.Of greater importance is the fact that nuclei also show this interaction of spin and magnetic fieldsand organic chemistry uses this greatly in what is called NMR experiments.Applications to biological systems where the spin of hydrogen nuclei in water in biologicalsamples (cells, rats, humans) is called MRI.There is a shorthand way of defining the l quantum number (which relates to shape and energy)and will be more common for us in the rest of the course. An orbital with l = 0 is called an sorbital (if n=3 and l=0 then it is a 3s orbital); l =1 is a p orbital, l=2 is a d orbital; l = 3 is an forbital; l = 4 is a g orbital. Thus we will refer to n and l often in this shorthand notation.[Table 7.2]Each electron in an atom will be defined by these four values. Let’s see what kind of values canbe found and what they mean. Remember that as n increases there are more possible values forthe others.

Chapter 7- Quantum Chemistry Chang 10 th Ed. 6/8n=0, l = 1, ml = 0 ms = 1/2 not possible because n must be greater than 0n=2, l = 1 , ml = 0, ms = 1/2 these are possible n

Chapter 7- Quantum Chemistry Chang 10 th Ed. 7/8Pauli Exclusion Principle states that each electron in an atom must have a unique set of fourquantum numbers. This means that if two electrons are present in an orbital that they must haveat least different ms values. Another way of saying this is that no two electrons can be in thesame place at the same time. It also means that each atomic orbital can contain a maximum oftwo electrons always.For hydrogen (1s 1 ) we find that the energies are ranked by n only (l has no effect) but only in this1 electron system.[Figure 7.22]In all other atoms, the l value (s, p, d, f) affects not only the shape but also a “fine tuning” of theenergy. The smaller the value of l the lower in energy the orbital [Figure 7.23] or the 3d ishigher in energy than 3p than 3s. This means that the n values which define energy also canoverlap depending upon the value of l. Thus orbitals which have different values of l are notequal in energy but the lower the value of l the lower the energy.We can talk about the population of electrons using an orbital configuration as follows: H atom1s 1 , He atom 1s 2 , Li atom 1s 2 , 2s 1 etc.Assuming that electrons will add to the lowest energy first followed by the next lowest, etc andthat two electrons can fill each orbital. We can also write this as an orbital diagram. Chang doesnot indicate energy when he writes these but I will to show that the energies of the s and p (or 1sand 2s) are not equal. Put boxes for dashes in Figure 7.23 and you have an orbital diagram for48 electrons.Hund’s rule states that if you have more than one electron in orbitals of equal energy (same n andl) then populate separate orbitals first all with the same spin before pairing up and filling orbitals.It certainly makes sense that orbitals will fill up separately before two electrons go in becausethey would be in separate regions in space. It is more subtle but true that the lower energy stateis when electrons spin are in the same direction. Show orbital diagram of C, N, O, F, Ne as wellas electron config.De-emphasize para and dimagnetic - paramagnetic means it has unpaired electrons anddiamagnetic has paired electrons. Paramagnetic materials such as LOX are attracted to a magnet.General Rules for Assigning Electrons to Atomic Orbitals (Chang pg. 305)1. Each shell or n value has n subshells.2. Each subshell of l value has 2l+1 orbitals.3. Only two electrons can be placed in any orbital.4. The maximum number of electrons in a given n level (not atom!) is 2n 2Let’s talk about how these configurations can be determined relative to the periodic table. Firstis that each orbital can have only two electrons (3 above, PEP). Second is that the number oforbitals in a subshell is 2l+1.What does that mean?

Chapter 7- Quantum Chemistry Chang 10 th Ed. 8/8l value possible ml total orbitals total electronss orbitals 0 0 1 2p orbitals 1 -1, 0 +1 3 6d orbitals 2 -2, -1, 0, 1, 2 5 10f orbitals 3 -3, -2, -1, 0, 1, 2, 3 7 14Can we find any correlation between the shape of the table and the values above? s-Block (MainBlock), p-Block (Main Block), d-Block (Transition Metals), f-Block (Actinides and Lanthanides)[Figure 2.10]The electrons in these regions are the electrons being filled from left to right. [Figure 7.23,7.27]7.9 The Aufbau (Building-up) PrincipleWe said that the s, p, d, f orbitals with the same n have different energies and that the s, p, d, fenergy distribution could expand past the n energy levels. [Figure 7.23; 7.24] We also saidthat the electrons will add to the lower energy atomic orbitals first. Thus without knowing thesetwo facts one might expect that the filling order is 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, etc. but accordingto figure 7.23 that is not true, the electrons fill as in Figure 7.24. Also note that figure 7.24 doesnot have to be memorized because we can get the same information directly from theperiodic table.[Figure 7.28, Table 7.3]Table 7.3 gives the electronic configurations for all of the elements where there is a shorthandmethod using the noble gas core rather than writing out all of the electrons. This is used becausefilling a noble gas configuration results in a high stability state called a closed subshell and theelectrons which under reactions are almost always those which have been added after the noblegas core electrons (valence electrons- the outmost or most reactive electrons). The book talksabout the several exceptions to the relationship bewteen electronic configuration as determinedfrom the table and the true configuration. For this course if you can correctly identify theconfiguration using the periodic table I will mark it as correct even though there are someexceptions. Thus the true correct answer or the one predicted from the PT will both be correct.You should be aware that again, this is in order for you to appreciate the usefulness of the tableand in “the real world” there may be exceptions to these rules. Overall the success rate will bevery high if you learn to identify electronic configurations from the table directly. Note also thatthe d subshell is one row lower and f is two rows lower than the period. For s and p n is equal tothe period.