1. 1 The Periodic Table John F. C. Turner Department of Chemistry and Neutron Sciences Consortium The University of Tennessee Knoxville

2. 2 Structure 1.Misconceptions about the Periodic Table 2.The definition of the Periodic Table 3.Aspects of the periodicity of the elements 4.Summary 5.Questions

3. 3 Misconceptions It is hard It has no rule It is unstructured It is a barrier that can only be overcome by the brilliant or the odd

4. 4 The Definition of the Periodic Table An array of the elements in increasing atomic number or atomic mass, grouped according to chemical property

5. 5 The Beginnings of the Periodic Table In antiquity, prior to ~1800 only 15 – 20 elements were known; By 1860, ~60 were isolated – enough for trends to be apparent

6. 6 The Beginnings of the Periodic Table Most importantly, different members of the same chemical family were isolated – the groups. Li, Na, K, Be, Mg, Ca, Sr, showing similar but not identical properties

7. 7 Periodic physical properties 1.The majority of the elements are metals. A metal is defined as a material whose electrical conductivity decreases with temperature This is obscure and is determined by the manner in which the electrons are bound in the substance This leads to other properties that are more intuitively obvious

8. 8 Periodic physical properties Non-metals and metals

9. 9 Periodic physical properties Metals are ● Good conductors of heat and electricity ● Malleable and ductile ● Highly reflective ● Opaque to visible light ● Chemistry is dominated by the formation of cations – loss of electrons

10. 10 Periodic physical properties Non-metals are ● Poor conductors of heat and electricity ● Brittle ● Chemistry is dominated by the formation of anions – gain of electrons

11. 11 Periodic physical properties Solids, liquids and gases Strong correlation between Metals Solids Non-metalsGases

12. 12 Periodic physical properties These are bulk properties and do not explain the chemical periodicity and therefore the periodicity of the table

13. 13 Observed Periodicity in the physical properties Melting points Boiling points Liquid range

14. 14 Observed Periodicity in the physical properties The forces between particles are roughly the same in both the liquid and the solid Periodicity in seen in the melting point, the boiling point and the liquid range This phenomenon is independent of the phase of matter we are discussing It is more fundamental It is atomic

15. 15 Periodic physical properties However, the bulk properties and the microscopic properties must be related. What are the trends in the ionization energy?

16. 16 Periodicity of the ionization energy Across the row, it becomes increasingly difficult to remove an electron (chemical energy scale: ~0 - ~10 eV) Electrons are more tightly bound and therefore the atom is smaller across the table

17. 17 The structure of the atom and the Periodic Table Problems with the atom: It is a quantum system. What is a quantum system? One that is small on an absolute scale What is “small on an absolute scale” That is a good question.............

18. 18 The structure of the atom and the Periodic Table “Newtonian world” We live in a material, macroscopic world, where all energies are allowed and everything moves in a trajectory

19. 19 The structure of the atom and the Periodic Table “Quantum world” Objects are profoundly affected by the physics of observation. No trajectoriesNo positionsNo velocity A large object is one that is perceptibly unaffected by measurement A small object is one that is affected by measurement

20. 20 The structure of the atom and the Periodic Table The atom is a quantum system. De Broglie relationship relates the motion of a particle to wave-like properties and the electron in an atom behaves as a wave. Standing waves have fixed energies violin strings organ pipes electrons in atoms

21. 21 The atom is spherical and there are three important coordinates The distance between the electron and the nucleus The 'longitude' The 'latitude' The electron-wave is defined by all three coordinates. Each coordinate of the electron-wave has a label attached to it – the quantum number.

22. 22 The gross energy of the atom is dominated by the radial quantum number, n. The larger n, the larger the atom large n small n n n corresponds to the period number in the table

23. 23 Within each n value, there are two other labels – the longitude and the latitude These are associated with angular motion – the circulation of the electron around the nucleus. These quantum numbers apply to the number of groups – the s block, the p block, the d block and the f block. s block n p block d block f block

24. 24 The angular quantum number, l, gives Blockl value s0 p1 d2 f3 The circulation of the electron in the s block is the smallest, 1 unit, larger in the p and so on. s block n p block d block f block

25. 25 Angular momentum and the Periodic table The angular momenta associated with the latitude and the longitude are linked. For any value of l there are (2l+1) values of m l Thus: lm l s block01 p block13 d block25 f block37 and so on. The m l value can be interpreted as the orientation of the longitudinal circulation in space.

26. 26 Angular momentum and the Periodic table Given lm l s block01 p block13 d block25 f block37 We should expect 1 electron in each of the m l quantum numbers and therefore 1 s block elementper period 3 p block elementsper period 5 d block elementsper period 7 f block elementsper period Instead, there are 2, 6, 10 and 14 elements?

27. 27 The rules of angular momentum The final part of the structure of the Periodic Table is determined by the rules of angular momentum 'The rules of angular momentum' describe a whole range of different behaviors; they are difficult to present as their basis is very abstract. However, they cover the properties of any body in motion and so are extremely important.

28. 28 The rules of angular momentum The generalities of angular momentum are classically derived from the vector cross product together with the applications of the theory of symmetry. Quantum mechanical angular momentum obeys the same type of rules, but translated into the quantum world. The quantum rules are: For every value of the angular momentum l, quantum number, there are 2l+1 orientations, with m l = -l....0....l in single unit steps.

29. 29 The electron possesses an intrinsic angular momentum, s= ½ and therefore the two possible orientations are labeled as m s = + ½ or - ½ The quantum labels for any electron are PrincipleAngularElectron radius, r LongitudeLatitude spin nl m l s then four quantum numbers define the behavior of the electron in the atom.

30. 30 Each electron in an atom is unique and its behavior is defined by the four quantum numbers. All four must be different and therefore for each set of spatial quantum numbers, {n, l, m l }, we have the choice of m s = + ½ or - ½ - two choices per {n, l, m l } set. The numbers of the elements that are available are therefore: lm l m s s block01 2 p block13 6 d block2510 f block3714 as required.

31. 31 The Periodic table and the atom The structure of the periodic table is determined in a gross manner by the atomic properties of the atoms The precise details are not as quantitative as the description of the overall structure for several reasons. ● Electrons interact with the nucleus as well as with other electrons – an example of a many body problem ● These interactions are increasingly important as the atom becomes larger Several trends can be identified.

32. 32 The Periodic table and the atom As the atom becomes larger, the electrons become less strongly bound. Stronger bonds are formed between smaller atoms. Atomic size increases down the group for a given group decreases across the period with increasing atomic number

33. 33 Summary Periodicity is seen in the Periodic Table whenever a property is based on an atomic property of some description It is a powerful tool with which to introduce concepts important in the description of the atomic nature of the microscopic world It is not immensely complex, but is more easily understood through the fundamental concepts that produce the structure, rather than starting with the structure. Acknowledgments Dr. Lynn Champion Dr. Charmaine Mamantov