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  1. ATOMIC STRUCTURE Presented by Naveed Nawaz

  2. Outline • Schrodinger Model of the Atom • Quantum Numbers • Periodic Table • X-Rays • Auger Electrons

  3. Schrodinger Model • Erwin Schrodinger determined that an electron can exist as a particle and a wave. With this view of an electron a new model was formulated. • This model was based on math and used Heisenberg's uncertainty principle which says that one can not determine the exact position of an electron and it's momentum at the same time.

  4. Schrodinger Model [cont’d] • Unlike Bohr's atom that had very well defined quantized orbits, Schrodinger's model shows the orbits very undefined. • The orbits represents regions of the space where electrons are likely to be found.

  5. Schrodinger Model [cont’d] • Although Bohr's model explained somehow the line spectra observed when atoms emitted energy, it couldn’t explain the behavior of the ionization energy with Z. • If the Bohr model was accurate, ionization energies of elements would increase with increasing atomic number.

  6. Schrodinger Model [cont’d] • Experimentally was found that the ionization energy drops at certain values of Z.

  7. Schrodinger Model [cont’d] • This led to the idea that there may be sub-shells within each energy level. • Further evidence for this comes from the lines in the emission spectra of atom. Some of the lines consist of two or more lines close together (i.e., at very similar energy levels).

  8. Schrodinger Model [cont’d] • These lines differ in brightness and width. This is taken to suggest that each shell has closely-related sub-shells that have slightly different properties.

  9. Quantum Numbers • Schrödinger proposed that the electrons in an atom were governed by four quantum numbers. • The first of these is called the principal quantum number, and is given the symbol n. This corresponds to the electron orbit in the Bohr model. n = 1, 2, 3, ...., denoting energy

  10. Quantum Numbers [cont’d] • The second quantum number corresponds to the sub-shell and is called the orbital angular momentum, or l. This can have one or more values, given by l = 0, 1, 2, ..., (n-1) • Therefore, if n = 1, l can be 0 or 1. This means that the shell 1 has two sub-shell.

  11. Quantum Numbers [cont’d] • Possible electrons orbits for n=3 • These sub-shells are named after the type of line they produce in the emission spectra of atom.

  12. Quantum Numbers [cont’d] • The s sub-shell gives a sharp line, the p sub-shell gives a very bright line (the principal line), the d sub-shell gives a diffuse line, and the f sub-shell gives a line described as the fundamental line. • s for l = 0, p for l = 1, d for l = 2, f for l = 3, g for l = 4 and then on alphabetically.

  13. Quantum Numbers [cont’d] • The third quantum number is called the orbital magnetic quantum number, ml. • This number tells the way an orbital aligns itself if one apply a magnetic field, hence the name. The values of ml are given by ml = -l, (-l-1), (-l-2), ..., -1, 0, 1, ..., (l-1), l

  14. Therefore, if l = 1, ml can be -1, 0, or +1. This means that the p sub-shell contains three orbitals. Possible values of ml for l=2 Quantum Numbers [cont’d]

  15. Quantum Numbers [cont’d] • The final quantum number is the spin magnetic quantum number, ms. This describes the direction the electron spins in a magnetic field and can have one of two values, -½ or +½.

  16. Quantum Numbers [cont’d] • The differences between orbitals within a shell can also be used to explain the bonding between atoms. • For this, it is useful to know about the shapes of the orbitals. •

  17. Quantum Numbers[cont’d] n=1; l=0; ml=0 n=4; l=3; ml=0 n=6; l=2; ml=1 n=2; l=1; ml=0 n=10; l=7; ml=5 n=3; l=2; ml=0

  18. Periodic Table • When discussing multielectron atoms, one speaks of "filling" the shells. • So one can assign electrons to shells by starting with the lowest quantum numbers and moving up in order until is reached the number of electrons in the atom (equal to Z for a neutral atom).

  19. Periodic Table [cont’d] • The Periodic Table is based on the observation that an element's chemical properties depend on the number of electrons in its outer (valence) shell. • The Pauli Principle states that no two electrons may be in the same quantum state. This explains the chemical properties of the elements.

  20. Periodic Table [cont’d] • Pauli's Principle means that can be only two electrons for any given values of n, l and ml; one has spin 1/2 and the other - 1/2. • Similarly, for any given values of n and l, there can only be 2l +1 pairs of electrons, corresponding to the allowable values of ml.

  21. Periodic Table [cont’d] • First shell n = 1 l = 0, ml = 0, and ms = -½ or +½. This shell therefore contains only one orbital, with one or two electrons. • Second shell n=2 l = 0 or 1;

  22. Periodic Table [cont’d] for l = 0, ml = 0, ms = -½ or +½. This gives the 2s sub-shell with 2 electrons. for l = 1, ml = -1, 0, or +1, and ms for each is -½ or +½. This gives the 2p sub-shell, containing 3 orbitals each with 2 electrons. 2nd shell contains a total of 8 electrons.

  23. Periodic Table [cont’d] • One can carry on with this process to show that the 3rd shell contains a total of 18 electrons, the 4th 32, etc. • In this way, one can deduce the electronic structure of every atom in the periodic table, just by knowing its atomic number (and so how many electrons it contains). • For Sodium it is (1s)2 (2s)2 (2p)6 (3s)1

  24. Periodic Table [cont’d] • In the filling of the fourth row, in K atom electrons start to fill the 4s state before completing 3d state. This happens because the energy level corresponding to 4s state is lower the one corresponding to 3d state. • For many other multielectron atoms electronic energy levels are not filled in order.

  25. Periodic Table [cont’d] • Elements with the same number of electrons in their outer (valence) shell go in the same column. • When the shell is full, the element goes in the (rightmost) "inert" column, since it does not easily react with a filled valence shell.

  26. Periodic Table [cont’d] • The next element goes into the leftmost column (for those elements with only one electron in their outer shell). • Atoms interact chemically by sharing or partially transferring electrons. • Atoms with filled shells only, like He and Ne, are chemically unreactive.

  27. Periodic Table [cont’d] • The valency, roughly speaking, is the number of electrons available for transfer (so Li and Na have valency 1) or available sites for reception of electrons—fluorine has an outer shell with one vacancy, so a valency of 1. • To some extent, valency can vary depending on the strength of attraction of other atoms in the chemical environment.

  28. Periodic Table [cont’d]

  29. X-rays Emission • In 1901 W. C. Roentgen discovered the X-rays. • X-rays are just like any other kind of electromagnetic radiation. • X rays are produced whenever a beam of particles (electrons), with sufficient energy collides with a target material.

  30. X-rays Emission [cont’d]

  31. X-rays Emission [cont’d] • There are two different atomic processes that can produce x-ray photons. • Bremsstrahlung, which is a German name meaning "braking radiation” • X rays are emitted in a continuous band • Characteristic X-ray

  32. X-rays Emission [cont’d] Characteristic X-rays • When the energy of the particle beam is above a certain threshold value (called the excitation potential) an electron from inner shells of atom will be ejected from the target atoms. • Then valence electrons in higher energy states of the target atoms fill the vacancies from inner shells and in the process emit X-ray photons.

  33. X-rays Emission [cont’d] • These X-ray photons have discrete energies that are equal to the difference in energy between the valence and core energy levels. • The characteristic lines are called K, L, M, ... and correspond to transitions from higher energy states to the n = 1, 2, 3, ... quantum levels, respectively.

  34. X-rays Emission [cont’d] • When the two atomic energy levels are adjacent, the transitions are described as a lines (n = 2 to n = 1, or n = 3 to n = 2) • When the two levels are separated by one or more levels, the transitions are known as b lines (n = 3 to n = 1 or n = 4 to n = 1).

  35. X-rays Emission [cont’d] • X-ray transitions in an atom with atomic number Z=36

  36. X-rays Emission [cont’d] • Because all K lines arise from a loss of electrons in the n = 1 state, the Ka and Kb lines always appear at the same. • Studing characteristic X-ray wavelengths, Mosely found that the square root of the frequencies of X-rays are linearly with Z.

  37. X-rays Emission [cont’d] • Moseley showed that the correct ordering of the periodic table is on the basis of the atomic number (the number of positive charges in the nucleus). • Before Moseley, periodic tables were created on the basis of increasing atomic weight (with two exceptions).

  38. Electron Auger • In many cases the photon emitted in an X-ray transition is absorbed by another electron within the same atom, which is therefore ejected as a result of an internal photo-electric effect. • This process of the internal conversion of X-rays into photo-electrons is called the Auger effect and the emitted photo-electrons are called auger electrons.

  39. Electron Auger [cont’d] • Auger emission is the dominant de-excitation process for low atomic number elements such as boron and carbon. • Auger electrons are emitted with specific kinetic energies T depending on the electronic levels involved in the process. • E.g.: T=EK-EL1-EL3

  40. Electron Auger [cont’d] • Schematic diagram of various two-electron de-excitation processes. • The KL1L1 Auger transition corresponds to an initial K hole which is filled with L1 electron and simultaneously the other L1 electron is ejected to the vacuum. • The LM1M1 Auger transition is the corresponding process with an initial 2s vacancy.

  41. Electron Auger [cont’d]

  42. References • Turner, J. E., Atoms, Radiation, and Radiation Protection, 2nd Ed.,John Wiley&Sons , Inc.(1995) • Hunt, S.E., Nuclear Physics for Engineers and Scientists, Ellis Horwood Ltd. (1987)

  43. Thank you. • Naveed Nawaz • B.E-electrical-HUFC