Chapter 6 Electronic Structure of Atoms

1. Chapter 6Electronic Structureof Atoms

2. The electronic structure of an atom refers to its number of electrons, how these electrons are distributed around the nucleus, and to their energies. • Much of our understanding of the electronic structure of atoms has come from the analysis of light either absorbed or emitted by substances.

3. 6.1 The Wave Nature of Light • To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation (EMR). • Because EMR carries energy through space, it is also known as radiant energy. • There are many forms of EMR, to include visible light, radio waves, infrared waves, X-rays, etc. (See fig 6.4). • All EMR consists of photons, the smallest increments of radiant energy.

4. Different forms of EMR share characteristics: • All have wavelike characteristics (much like waves of water). • The distance between corresponding points on adjacent waves is the wavelength(). • The amplitude – or, maximum extent of oscillation of the wave -- is related to the intensity of the radiation • The number of waves passing a given point per unit of time is the frequency (). • For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

5. Electromagnetic Radiation Spectrum • All EMR moves through travels at the same velocity: the speed of light (c), 3.00  108 m/s. • Therefore, c = 

6. As you can see from the electromagnetic spectrum, there are many forms of EMR. • The difference in the forms is due to their different wavelengths, which are expressed in units of length. • Wavelengths vary from10-11 m to 103 m. • Frequency is expressed in cycles per second, also called a hertz. • Units of frequency are usually given simply as “per second,” denoted as s-1 or /s. As in 820 kilohertz (kHz), written as 820,000 s-1 or 820,000/s • See Table 6.1 for types of radiation and associated wavelength.

7. Wavelength and frequency problems

8. 6.2 Quantized Energy and Photons • The wave nature of light does not explain how an object can glow when its temperature increases. • Max Planck explained it by assuming that energy comes in packets (discrete “chunks”) called quanta. • He proposed that the energy of a single quantum, E, equals a constant times the frequency of the radiation: • The constant h is called the Planck constant and has a value of 6.626 x 10-34 J·s

9. Einstein used this assumption to explain the photoelectric effect. • When photons of sufficiently high energy strike a metal surface, electrons are emitted from the metal. • Electrons are not emitted unless photons exceed a certain minimal energy. • E.g., light with a frequency of 4.60 x 1014 s-1 or greater will cause cesium atoms to emit electrons, but light of lower frequency has no effect. • He concluded that the radiant energy striking the surface of the metal behaved like a stream of tiny energy packets. • Each packet, like a “particle” of energy, is called a photon. • Einstein applied Planck’s equation of quantum energy to the photon, thereby quantizing radiant energy.

10. Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c =  E = h

11. 6.3 Line Spectra and the Bohr Model • Another mystery involved the emission spectra observed from energy emitted by atoms and molecules when they are heated. • For example, H2 gas, when heated in an enclosed tube by an electrical current, produced light that when passed through a prism showed that it contained only four distinct wavelengths of visible light, as shown below. Sodium atoms, when excited, gave off light in the yellow portion of the spectrum. • Why does this happen? No one knew.

12. White light, as from the sun or a light bulb, shows a continuous spectrum when analyzed. This shows that its light is composed of all wavelengths, not just some. • In 1885 a Swiss schoolteacher, Johann Balmer, showed that the visible lines for hydrogen gas followed a formula called the Rydberg equation, where RH is the Rydberg constant and n1 and n2 are whole number integers with n2 being the larger. • This equation did not explain why there should be emission lines in the first place, it only showed the wavelengths for light emitted by hydrogen gas could be precisely calculated. • The Rydberg equation worked only for hydrogen gas. It could not accurately calculate the wavelengths of light emitted by any other element or molecules.

13. Bohr’s Model • Niels Bohr adopted Planck’s assumption that energies are quantized and explained these phenomena in this way: • Electrons in an atom can only occupy certain orbits (corresponding to certain energies). • Electrons in permitted orbits have specific, “allowed” energies; these energies are not radiated from the atom. • Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by E = h h = Planck’s constant,  = frequency

14. 1 nf2 J)() - E = (−2.18 x 10-18 )() 1 n2 E = (−2.18 x 10-18J 1 ni2 The Energy States of the Hydrogen Atom • Bohr calculated the energies corresponding to each orbit for the electron in the hydrogen atom: • The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:

15. Hydrogen emission spectra

16. Energy states of hydrogen atom problems

17. Limitations of the Bohr Model • The Bohr model explains the line spectrum of the hydrogen atom, but not (accurately) the spectra of other atoms. • Also, the Bohr model assumes the electron behaves as a particle. However, Bohr model is important because: • It shows electrons as existing in only certain discrete energy levels, which are described by quantum numbers. • Energy is involved in moving an electron from one level to another.

18. h mv  = 6.4 The Wave Nature of Matter • In the years after development of the Bohr model, the dual nature of light became known: EMR (i.e., light) can exhibit both particle-like (photon) character as well as wave-like character. • Louis de Broglie (in 1924) extended this idea to electrons, proposing a relationship between the wavelength of an electron (or any other particle), its mass, and velocity:

19. h 4 (x)(mv)  The Uncertainty Principle • Werner Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known: • In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself! • In sum, you cannot accurately know both an electron’s position and momentum at the same time.

20. 6.5 Quantum Mechanics • Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. • It is known as quantum mechanics.

21. Quantum Numbers • Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. • Each orbital describes a spatial distribution of electron density. • An orbital is described by a set of three quantum numbers. • Quantum numbers are important because they can be used to determine the electron configuration of an atom and the probable location of the atom's electrons.  • Quantum numbers are also used to determine other characteristics of atoms, such as ionization energy and the atomic radius.

22. Principal Quantum Number, n • The principal quantum number, n, describes the energy level on which the orbital resides. • The values of n are integers > 0. Azimuthal Quantum Number, l • This quantum number defines the shape of the orbital. • Allowed values of l are integers ranging from 0 to n − 1. • We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.

23. Magnetic Quantum Number, ml • Describes the three-dimensional orientation of the orbital. • Values are integers ranging from -l to l: −l ≤ ml ≤ l • Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc. • Orbitals with the same value of n form a shell. • Different orbital types within a shell are subshells.

25. 6.6 Representations of Orbitals s Orbitals • Value of l = 0. • Spherical in shape. • Radius of sphere increases with increasing value of n.

26. s Orbitals • Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.

27. p Orbitals • Value of l = 1. • Have two lobes with a node between them.

28. d Orbitals • Value of l is 2. • Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.

29. f orbitals • When n = 4 or greater, there are seven equivalent f orbitals for which l= 3. • F orbital shapes are very complicated:

30. Interesting Links • A depiction of the orbitals for scandium: • https://www.youtube.com/watch?v=sMt5Dcex0kg • What does an atom really look like? • https://www.youtube.com/watch?v=EOHYT5q5lhQ • Electrons in orbitals: • https://www.youtube.com/watch?v=4WR8Qvsv70s • Orbitals, the basics: • https://www.youtube.com/watch?v=Ewf7RlVNBSA • Quantum Theory – documentary (1 hour): • https://www.youtube.com/watch?v=CBrsWPCp_rs • Quantum mechanics • https://www.youtube.com/watch?v=BMIvWz-7GmU

31. 6.7 Many-Electron AtomsOrbitals and Their Energies • For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. • That is, they are degenerate.

32. As the number of electrons increases, though, so does the repulsion between them. • Orbitals within a subshell are degenerate. • All orbitals at the same energy level are not degenerate.

33. Spin Quantum Number, ms • In the 1920s it was discovered that the spectral lines of many-electron atoms could be observed as two very closely spaced pairs. This meant there were twice as many energy levels as thought. • To account for this observation, scientists postulated that an electron has an intrinsic property called “spin” that causes it to behave as though it were a tiny sphere spinning on its axis. • This led to a fourth quantum number that has only 2 allowed values: +1/2 and −1/2. • The two opposite directions of spin creates oppositely directed magnetic fields which can split the spectral lines of many-electron atoms into closely spaced pairs

34. Pauli Exclusion Principle • In 1925 Wolfgang Pauli discovered the principle that governs the arrangement of electrons in many-electron atoms • No two electrons in the same atom can have the same set of four quantum numbers. • For a given orbital, the values of n, l, and mlare fixed. • Within an orbital the two electrons differ by their spin: +1/2 or -1/2. • Therefore, an orbital can only hold two electrons of opposite spin.

35. 6.8 Electron Configurations • Show the distribution of all electrons in an atom. • Electrons are in lowest possible energy states. • Per the Pauli exclusion principle, there can be no more than two electrons per orbital. • Per the aufbau principle, orbitals are filled in order of increasing energy • Some exceptions after element 18.

36. Electron Configuration examples: Condensed (Abbreviated) Electron Configuration:

37. Transition Metals • Begin to fill d-sublevel orbitals according to Hund’s Rule • 4s, though, is filled first because it is slightly lower in energy than 3d. • Examples: The Lanthanides and Actinides • Lanthanides are also known as the rare earth elements. The 4f sublevel is filled though some involve a 5d electron. • Actinides are all radioactive and most are not found in nature. The 5f sublevel is filled though some involve 6d electrons.

38. Orbital Diagrams • Each box represents one orbital. • Half-arrows represent the electrons. • The direction of the arrow represents the spin of the electron. • Hund’s Rule: For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized. (I.e., orbitals are filled with an electron of one spin before being filled with an electron of th opposite spin.)

39. 6.9 Electron Configurations and the Periodic Table • Orbitals are filled in increasing order of energy.

40. Different blocks on the periodic table, then, correspond to different types of orbitals. • Electron configuration of any element can be determined merely by its position on the periodic table.

41. Outer-shell electron configurations of the elements

42. For representative elements (Grps 1, 2 13-18), d and f subshells are not considered valence electrons. • For transition elements, completely filled f subshells are not among the valence electrons. Some d subshell electrons can be valence electrons. • Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row. • For instance, the electron configuration for chromium is: [Ar] 4s1 3d5 rather than the expected [Ar] 4s2 3d4. • Another example is copper: [Ar] 4s1 3d10 rather than the expected [Ar] 4s2 3d9 This occurs because the 4s and 3d orbitals are very close in energy. • These anomalies also occur in some f-block atoms.