Mendeleev s Periodic Law

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2 Mendeleev s Periodic Law Periodic Law When the elements are arranged in order of increasing atomic mass, certain sets of properties recur periodically. Mendeleev s Periodic Law allows us to predict what the properties of an element will be. It doesn t explain why the pattern exists. Quantum Mechanics explains why the periodic trends in the properties exist.

3 Electron Configurations Quantum-mechanical theory describes the behavior of electrons in atoms. The electrons in atoms exist in orbitals. A description of the orbitals occupied by electrons is called an electron configuration. principal energy level of orbital occupied by the electron 1s 1 number of electrons in the orbital sublevel of orbital occupied by the electron

4 How Electrons Occupy Orbitals Calculations with Schrödinger s equation show how hydrogen s one electron occupies the lowest energy orbital in the atom. Schrödinger s equation calculations for multielectron atoms cannot be exactly solved. Approximate solutions show the orbitals to be hydrogen-like. Two additional concepts affect multielectron atoms: electron spin and energy splitting of sublevels

5 Electron Spin Experiments by Stern and Gerlach showed a beam of silver atoms is split in two by a magnetic field. Electrons spin on their axis. As they spin, they generate a magnetic field. If there is an even number of electrons, about half the atoms will have a net magnetic field pointing north and the other half will have a net magnetic field pointing south.

6 Electron Spin

7 The Property of Electron Spin Spin is a fundamental property of all electrons. All electrons have the same amount of spin. The orientation of the electron spin is quantized, it can only be in one direction or its opposite. The electron s spin adds a fourth quantum number to the description of electrons in an atom, called the Spin Quantum Number, ms

8 Spin Quantum Number, ms, and Orbital Diagrams ms can have values of +½ or ½ Orbital Diagrams use a square to represent each orbital and a half-arrow to represent each electron in the orbital. By convention, a half-arrow pointing up is used to represent an electron in an orbital with spin up. Spins must cancel in an orbital or be paired

9 Orbital Diagrams We often represent an orbital as a square and the electrons in that orbital as arrows. unoccupied orbital orbital with one electron orbital with two electrons

10 Pauli Exclusion Principle No two electrons in an atom may have the same set of four quantum numbers. Therefore no orbital may have more than two electrons, and they must have opposite spins. The number orbitals in a sublevel allows us to determine the maximum number of electrons in the sublevel. s sublevel has 1 orbital, therefore it can hold 2 electrons p sublevel has 3 orbitals, therefore it can hold 6 electrons d sublevel has 5 orbitals, therefore it can hold 10 electrons f sublevel has 7 orbitals, therefore it can hold 14 electrons

11 Quantum number Values Number of values Significance Principal, n 1, 2, 3, Size and energy of orbital Azimuthal, l 0, 1, 2, n-1 n Shape of orbital Magnetic, ml Spin, ms -l, 0,+l 2l+1 -½, +½ 2 Orientation of orbital Direction of electron spin

12 Quantum Numbers of Helium s Electrons Helium has two electrons. Both electrons are in the first energy level. Both electrons are in the s orbital of the first energy level. Because they are in the same orbital, they must have opposite spins.

13 Sublevel Splitting in Multielectron Atoms The sublevels in each principal energy shell of Hydrogen all have the same energy (or other single electron systems) We call orbitals with the same energy degenerate. For multielectron atoms, the energies of the sublevels are split (caused by charge interaction, shielding and penetration). The lower the value of the l quantum number, the less energy the sublevel has. s (l = 0) < p (l = 1) < d (l = 2) < f (l = 3)

14 Coulomb s Law Coulomb s Law describes the attractions and repulsions between charged particles, where q represents charges. For like charges, the potential energy (E) is positive and decreases as the particles get farther apart. For opposite charges, the potential energy is negative and becomes more negative as the particles get closer together. The strength of the interaction increases as the size of the charges increases.(electrons are more strongly attracted to a nucleus with a 2+ charge than a nucleus with a 1+ charge)

15 Shielding & Effective Nuclear Charge Each electron in a multielectron atom experiences both the attraction to the nucleus and repulsion by other electrons in the atom. These repulsions cause the electron to have a net reduced attraction to the nucleus it is shielded from the nucleus. The total amount of attraction that an electron feels for the nucleus is called the effective nuclear charge on the electron.

16 Effective Nuclear Charge (Zeff) Outer electrons are attracted toward the nucleus by the nuclear charge but are pushed away by the repulsion of inner electrons. As a result, the nuclear charge actually felt by outer electrons is diminished, and we say that the outer electrons are shielded from the full charge of the nucleus by the inner electrons.

17 Penetration The closer an electron is to the nucleus, the more attraction it experiences. The better an outer electron is at penetrating through the electron cloud of inner electrons, the more attraction it will have for the nucleus. The degree of penetration is related to the orbital s radial distribution function.

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19 Penetration and Shielding The radial distribution function shows that the 2s orbital penetrates more deeply into the 1s orbital than does the 2p. Electrons in the 2p sublevel experience more repulsive force; they are more shielded from the attractive force of the nucleus. Electrons in the 2s sublevel experience a greater attractive force to the nucleus and are not shielded as effectively.

20 Effect of Penetration and Shielding Penetration causes the energies of sublevels in the same principal level to be non degenerate. In the fourth and fifth principal levels, the s orbital lies lower in energy than the d orbitals of the previous principal level. The energy separations between one set of orbitals and the next become smaller beyond the 4s. The ordering can therefore vary among elements.

21 6d 6s 6p 5d 5f 5p 5s 4f 4d Energy 4s 4p 3d 3p 3s 2p Degenerate Orbital Energies 2s 1s

22 Real Orbital Energies 7s 6d 6s 6p 5d 5f 5p 4f 5s 4p 4d Energy 4s 3p 3d 3s 2p 2s 1s

23 n=4 n=3 n=2 Bohr Model (shells) Modified Bohr Model (subshells) 4f 4d 4p 3d 4s 3p 3s 2p 2s ] Increasing Energy 4s lower in energy than 3d 5s lower in energy than 4d 6s lower in energy than 4f n=1 1s

24 Filling the Orbitals with Electrons Energy levels and sublevels fill from lowest energy to high. s p d f Aufbau Principle Orbitals that are in the same sublevel have the same energy No more than two electrons per orbital Pauli Exclusion Principle When filling orbitals that have the same energy, place one electron in each before completing pairs. Hund s Rule

25 Electron Configuration & the Periodic Table s d p f

26 Electron Configuration & the Periodic Table s Shell being filled = period number Shell being filled = (period number-1) d p 118 Shell being filled = (period number-2) f

27 Electron Configuration & the Periodic Table s Shell being filled = period number Shell being filled = (period number-1) d p Shell being filled = (period number-2) f What is the highest energy sublevel being filled for each of the following atoms? He K Pd Be Co Si Pt U 1s 4s 4d 2s 3d 3p 5d 5f

28 Electron Configurations of Atoms in their Ground State The electron configuration is a listing of the sublevels in order of filling with the number of electrons in that sublevel written as a superscript. Kr = 36 electrons = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 primary energy levels sublevels

29 Electron Configurations of Atoms in their Ground State The electron configuration is a listing of the sublevels in order of filling with the number of electrons in that sublevel written as a superscript. Kr = 36 electrons = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 A short-hand way of writing an electron configuration: Rb = 37 electrons = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 1 = [Kr]5s 1

30 Order of Sublevel Filling in Ground State Electron Configurations Start by drawing a diagram putting each energy shell on a row and listing the sublevels, (s, p, d, f), for that shell in order of energy (left-to-right 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f Next, draw arrows through the diagonals, looping back to the next diagonal each time 5s 5p 5d 5f 6s 6p 6d 7s

31 Notations for Electron Configurations H: 1s 1 He: 1s 2 or or 1s 1s Li: 1s 2 2s 1 or 1s 2s Be: 1s 2 2s 2 or 1s 2s

32 Notations for Electron Configurations

33 Notations for Electron Configurations

34 Practice write the full ground state orbital diagram and electron configuration of potassium. K Z = 19, therefore 19 e Based on the order of sublevel filling, we will need the first six sublevels 1s 2s 2p 3s 3p 4s s sublevel holds 2 e p sublevel holds 6 e d sublevel holds 10 e f sublevel holds 14 e Therefore the electron configuration is 1s 2 2s 2 2p 6 3s 2 3p 6 4s 1

35 Example: Write the full ground state orbital diagram and electron configuration of manganese Mn Z = 25, therefore 25 e Based on the order of sublevel filling, we will need the first seven sublevels 1s 2s 2p 3s 3p 4s s sublevel holds 2 e p sublevel holds 6 e d sublevel holds 10 e f sublevel holds 14 e 3 d Therefore the electron configuration is 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 5

36 Electron Configuration & the Periodic Table The length of each block is the maximum number of electrons the sublevel can hold. The Period number corresponds to the principal energy level of the valence electrons. The Group number corresponds to the number of valence electrons (electrons in the highest principal level).

37 Electron Sublevel Filling Order

38 Electron Sublevel Filling Order

39 Valence Electrons The electrons in all the sublevels with the highest principal energy shell are called the valence electrons. Electrons in lower energy shells are called core electrons. One of the most important factors in the way an atom behaves, both chemically and physically, is the number of valence electrons.

40 Valence Electrons of Atoms in their Ground State Kr = 36 electrons 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 there are 28 core electrons and 8 valence electrons Rb = 37 electrons 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 1 [Kr]5s 1 there are 36 core electrons and 1 valence electron

41 Elemental Properties and Electron Configuration The properties of the elements follow a periodic pattern. The quantum-mechanical model explains this because the number of valence electrons and the types of orbitals they occupy are also periodic.

42 The Noble Gas Electron Configuration ns 2 np 6 The noble gases have eight valence electrons. (except for He) We know the noble gases are especially non-reactive. The reason the noble gases are so nonreactive is that the electron configuration of the noble gases is especially stable.

43 The Alkali Metals ns 1 The alkali metals have one more electron than the previous noble gas. In their reactions, the alkali metals tend to lose one electron, resulting in the same electron configuration as a noble gas. By forming a cation with a 1+ charge.

44 The Halogens ns 2 np 5 The electron configurations of the halogens all have one fewer electron than the next noble gas. In their reactions with metals, the halogens tend to gain an electron and attain the electron configuration of the next noble gas. Forming an anion with charge 1.

45 Eight Valence Electrons Quantum mechanical calculations show that eight valence electrons should result in a very unreactive atom. The nobel gases are inert. Conversely, elements that have either one more or one less electron should be very reactive The halogen atoms are the most reactive nonmetals. The alkali metals are the most reactive metals.

46 Electron Configuration & Ion Charge Many metals and nonmetals form one ion, and that the charge on that ion is predictable based on its position on the Periodic Table. Group 1A = 1+, Group 2A = 2+, Group 7A = 1, Group 6A = 2, etc. These atoms form ions that will result in an electron configuration that is the same as the nearest noble gas.

47 Electron Configuration of Anions in Their Ground State Anions are formed when nonmetal atoms gain enough electrons to have eight valence electrons, filling the s and p sublevels of the valence shell. The sulfur atom has six valence electrons S atom = 1s 2 2s 2 2p 6 3s 2 3p 4 To have eight valence electrons, sulfur must gain two more. S 2 anion = 1s 2 2s 2 2p 6 3s 2 3p 6

48 Electron Configuration of Cations in Their Ground State Cations are formed when a metal atom loses all its valence electrons, resulting in a new lower energy level valence shell. The magnesium atom has two valence electrons Mg atom = 1s 2 2s 2 2p 6 3s 2 When magnesium forms a cation, it loses its valence electrons Mg 2+ cation = 1s 2 2s 2 2p 6

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50 Transition Elements For the d block metals, the last energy level being filled is one less than valence shell. one less than the Period number Zn Z = 30, Period 4, Group 2B [Ar]4s 2 3d 10 4s 3d For the f block metals, the last energy level being filled is two less than valence shell. two less than the Period number Eu Z = 63, Period 6 [Xe]6s 2 4f 7 6s 4f

51 Practice Use the Periodic Table to write the short electron configuration and short orbital diagram for each of the following Na (at. no. 11) Te (at. no. 52) Tc (at. no. 43) 5s [Ne]3s 1 3s [Kr]5s 2 4d 10 5p 4 4d [Kr]5s 2 4d 5 5p 5s 4d

52 Irregular Electron Configurations We know that because of sublevel splitting, the 4s sublevel is lower in energy than the 3d; and therefore the 4s fills before the 3d. But the difference in energy is not large. Some of the transition metals have irregular electron configurations in which the ns only partially fills before the (n 1)d or doesn t fill at all. Therefore, their electron configuration must be found experimentally.

53 Irregular Electron Configurations Expected Cr = [Ar]4s 2 3d 4 Cu = [Ar]4s 2 3d 9 Mo = [Kr]5s 2 4d 4 Ru = [Kr]5s 2 4d 6 Pd = [Kr]5s 2 4d 8 Found Experimentally Cr = [Ar]4s 1 3d 5 Cu = [Ar]4s 1 3d 10 Mo = [Kr]5s 1 4d 5 Ru = [Kr]5s 1 4d 7 Pd = [Kr]5s 0 4d 10