Electronic Structure of Atoms

1. Electronic Structure of Atoms Justin Green

2. What we will discuss • The Wave Nature of Light • Quantized Energy and Photons • Bohr’s Model of the Hydrogen Atom • The Wave Behavior of Matter • Quantum Mechanics and Atomic Orbitals • Representations of Orbitals • Orbitals in Many-Electron Atoms • Electron Configurations • Electron Configurations and the Periodic Table

3. The Wave Nature of Light • Electromagnetic Radiation • We can see it with our eyes • 3 different forms • Radio waves • Infrared Radiation (heat) • X-rays • Have the same fundamental characteristics • All types move through a vacuum at light speed (3.00 x 108 m/s) • Cross section of waves show a periodic pattern (pattern of peaks and troughs and repeats itself • Distance between the peaks is called Wavelength • Number of complete wavelengths that pass a point in 1 second is the Frequency • Wavelength and frequency are related, and the product of the two equals the speed of light  c = λ ν • Wavelength = λ, frequency = ν, speed of light = C

4. The Wave Nature of Light Continued • Different forms of electromagnetic radiation have different properties due to length of their Wavelengths, as seen on the electromagnetic spectrum www.dnr.sc.gov

5. The Wave Nature of Light ContinuedPractice Problem • Electromagnetism • Frequency is measured in Hertz (Hz) and expresses cycles per second • Example problem: The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589nm. What is the frequency of this radiation? How to do this: We already know that c = λ νand that the speed of light is 3.00 x 108, and we are given that the wavelength is 589nm, so we can divide C/λ = V (3.00 x 108 (m/s) / 589nm)(1nm/10-9 m) = 5.09 x 1014 s-1

6. Quantized Energy and Photons • Max Planck • Assumed that energy can be released by atoms only in chunks of some minimum size • Gave the name quantum to the smallest quantity that can be emitted as electromagnetic radiation • Proposed that the energy of a quantum equals a constant times it’s frequency (E=hv) • Planck’s constant has a value of 6.63 x 10-34 Joule-seconds (J-s)

7. Quantized Energy and PhotonsExample Problem • Calculate the smallest increment of energy, that is, the quantum of energy, that an object can absorb from yellow light whose wavelength is 589nm We have already determined that the frequency of 589nm wavelength is 5.09 x 1014 s-1 and we already have Planck’s constant of 6.63 x 10-34 We can use the equation E = hv to solve this equation E = (6.63 x 10-34 J-s) (5.09 x 1014 s-1 ) E = 3.37 x 10-19 J What this is telling us is that an atom emitting radiation whose wavelength is that of 589nm cannot gain or lose energy by radiation except in multiples of 3.37 x 10-19 J.

8. Quantized Energy and Photons Continued • The Photoelectric Effect • Experiments had shown that light shining on a clean metal surface causes the surface to emit electrons • For each metal, there is a minimum frequency of light below which no electrons are emitted • Einstein concluded that this can be explained that the radiant energy that was hitting the metal surface is a stream of tiny energy packets. Each energy packet behaves like a tiny particle of light and is called a photon and it has an energy proportional to that of the speed of light, thus radiant energy is quantized • In English, what is happening is that when a photon hits the metal, the energy is transferred to an electron in the metal and there is a certain amount of energy that can overcome the attractive forces that hold it to the metal, and we have the Photoelectric Effect • However this has caused controversy to a mystery that is still pondered upon, is light a wave or does it consist of particles? Who knows? It has properties of both, and that’s good enough for us.

9. Bohr’s Model of the Hydrogen Atom • Line Spectra • Radiation composed of a single wavelength is said to be monochromatic • When radiation from such sources is separated into its different wavelength components, a spectrum is produced • In the visible spectrum the colors blend into one another • The rainbow of colors is called a continuous spectrum • However not all radiation sources produce a continuous spectrum, they only emit certain colors • V = C (1/22 – 1/n2 ) n = 3,4,5,6 • C is the constant equal to 3.29 x 1015 s-1

10. Bohr’s Model of the Hydrogen Atom • Bohr’s Model • Electrons travel in a circular motion around the nucleus and when they lose energy they spiral into the nucleus • He proposed that only orbits of certain radii are permitted • Using these assumptions, Bohr showed that the electron could circle the nucleus only in orbits of certain specific radii, and the allowed orbits have specific energies… En = (-RH)(1/n2) • n can have a value from 1 to infinity, and it is the principle quantum number • RH is the Rydberg constant and has the value of 2.18 x 10-18 J • v = ΔE/h = (RH/h)(l/ni2– l/ni2) Combined formula • Bohr introduced the idea of quantized energy states for electrons in atoms

11. The Wave Behavior of Matter • De Broglie • Suggested that the electron in its movement about the nucleus has associated with it a particular wavelength • λ = h/mv (wavelength = Planck’s constant/mass x velocity) • Sample problem: What is the characteristic wavelength of an electron with a velocity of 5.97 x 106 m/s? (The mass of an electron is 9.11 x 10-28 g) We know that λ = h/mv , and we also know Planck’s constant is 6.63 x 10-34 J-s, and the other information given to us can help us determine that… λ = 6.63 x 10-34 J-s / ((9.11 x 10-28g)(5.97 x 106 m/s)) We also know that to cancel out Joules you need to multiply this by (1 kg-m2/ s2)/ 1 J and we multiply this by 1000g to cancel out Kg. The end result will be 1.22 x 10-10m or 0.122 nm

12. The Wave Behavior of Matter • The Uncertainty Principle • Developed by Werner Heisenberg (1901-1976) • Claimed that the dual nature of matter places a fundamental limitation on how precisely we can know both the location and the momentum of any object • The limitation becomes important only when we deal with matter at the subatomic level, that is, with masses as small as that of an electron • Called the Uncertainty Principle because its IMPOSSIBLE to determine the exact location and momentum of an electron (sneaky eh?) • Plus they don’t have set orbits, which doesn’t help us either

13. Quantum Mechanics and Atomic Orbitals • Schrodinger’s equation • Requires advanced calculus and leads to a series of mathematical functions called wave functions • The square of this function provides information about an electron’s location when it is in an allowed energy state • For the Hydrogen atom, the allowed energies are the same as those predicted by the Bohr model • However the Bohr model has the electron in a circular orbit around the nucleus, but in the quantum-mechanical model, the electron’s location cannot be described so simply • Wave function2 gives us the Probability density, uncertain about the actual location but gives us an area in which the electron may be • Another way to express probability location is Electron Density

14. Quantum Mechanics and Atomic Orbitals • Electron density distribution of Hydrogen wiki.chemeddl.org

15. Quantum Mechanics and Atomic Orbitals • Orbitals and Quantum Numbers • Orbitals describe a specific distribution of electron density in space as given by its probability density • Quantum Mechanical Model • Uses three quantum numbers • n, l, and ml • Quantum number n (Principle quantum number) • Can have integral values of 1,2,3…etc. • As n increases, so does the orbital and the electron spends more time far from the nucleus • An increase in n could also mean that the electron has a higher energy and therefore is less tightly bound to the nucleus • Quantum number l (azimuthal quantum number) • Can have integral values from 0 to n-1 • Defines the shape of the orbital • Designated by the letters s, p, d, and f corresponding the values to 0, 1, 2, 3 (correspondingly)

16. Quantum Mechanics and Atomic Orbitals • Orbitals and Quantum Numbers (continued) • Quantum Number ml (magnetic quantum number) • Can have integral values between l and –l including 0 • Describes the orientation of the orbital in space

17. Quantum Mechanics and Atomic Orbitals Here’s a chart to help you visualize the relationship among these quantum numbers www.chem.ufl.edu

18. Quantum Mechanics and Atomic Orbitals An attempt at explaining the relationship values of n, l, and ml The shell with principal quantum number n will consist of exactly n subshells. Each subshell corresponds to a different allowed value of l from 0 to n-1. Thus, the first shell (n=1) consists of only one subshell, and the ls (l = 0); the second shell (n=2) consists of two subshells, the 2s (l=0) and 2p (l = 1) and the third shell consisting of three subshells, 3s, 3p, and 3d and so on Each subshell consists of a specific number of orbitals. Each orbital corresponds to a different allowed value of ml. For a given value of l, there are 2l + 1 allowed values of ml, ranging from –l to l. Thus, each s (l=0) subshell consists of one orbital; each p (l=1) subshell consists of three orbitals; each d (l=2) subshell consists of five orbitals, and so forth. The total number of orbitals in a shell is n2, where n is the principle quantum number of the shell. The resulting number of orbitals for the shells – 1, 4, 9, 16 – has a special significance with regard to the periodic table: We see that the number of elements in the rows of the periodic table – 2, 8, 18, and 32 – are equal to twice these numbers.

19. Quantum Mechanics and Atomic Orbitals Orbital Energy Levels Chart http://www.sparknotes.com/chemistry/fundamentals/atomicstructure/section1.html

20. Representation of Orbitals • The “s” Orbitals • Lowest energy orbital is 1s orbital • Shows that the farther we move away from the nucleus the less chance we will find electrons • The electron which is drawn by electrostatic attractions is unlikely to be found far from the nucleus • The 2s and 3s orbitals • Spherically symmetrical • In 2s, the chances of finding electrons when moving away from the nucleus go down then up then down again due to a second sublevel • In 3s, the chances of finding electrons when moving away from the nucleus go down then up then down then up then down again, with the central focus then two more sublevels outside creating rings around the nucleus

21. Representation of Orbitals • 1s, 2s, and 3s orbital diagram • If you’ll notice in 1s, there is only one area where the electrons are densely located. In 2s, there another sublevel where the electrons are focused in, and in 3s there are three sublevels where the electrons are densely located • (Pardon the bad drawing) I drew this one

22. Representation of Orbitals • The p Orbitals • In (a) it shows the electron density • In (b) it shows the three p orbitals on a 3-D plane (x axis, y axis, and z axis) chemistry.umeche.maine.edu

23. Representation of Orbitals • The p Orbitals • Electron density is concentrated on two sides of the nucleus, separated by a node (two lobes in the orbital) • Each shell beginning with n = 2 has three p orbitals: three 2p orbitals, three 3p orbitals and so on • When increasing size we move up from 2p to 3p to 4p and so on

24. Representation of Orbitals • The d and f Orbitals • When n is 3 or greater we get the d orbitals (l = 2) • Five of each d orbital each having a specific shape in space cnx.org

25. Representation of Orbitals • The d and f orbitals continued • When n is 4 or greater, there are seven equivalent f orbitals (l = 3) • The shapes of f orbitals are more complicated than d orbitals are

26. Orbitals in Many-Electron Atoms • Effective Nuclear Charge • In a many-electron atom, each electron is simultaneously attracted to the nucleus and repelled by the other electrons • Effective nuclear charge, Zeff, equals the number of protons in the nucleus, Z, minus the average number of electrons, S • Zeff = Z – S • Screening effect • The inner electrons shield the outer electron from the full charge of the nucleus • Energies of Orbitals • The extent to which an electron will be screened by the other electrons depends on its electron distribution as we move outward • For a given value of n, the distribution differs in each subshell • For example, n = 3, a 3s orbital is more likely to be closer to the nucleus than a 3p orbital, and 3p closer than 3d. So 3s experiences less shielding than 3p orbitals, 3p experiences less shielding than 3d and so on • Hence, 3s have a greater Zeff than 3p, 3p greater than 3d… ET CETERA! • THE EXCITEMENT CONTINUES ONTO THE NEXT SLIDE

27. Orbitals in Many-Electron Atoms • Energies of Orbitals continued • Energies of electrons depend on the effective nuclear charge (Zeff) • Because Zeff is greater in 3s, 3s has less energy than 3p and etc. • In a many-electron atom, for a given value of n, the energy of an orbital increases with increasing value of l • Electron Spin and the Pauli Exclusion Principle • Electron spin is the electron spinning around its own axis one way or another • Another quantum number for this, the Electron Spin Quantum Number (ms) where the only possible values are + ½ or – ½ for the direction of the electron spin • Pauli Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers n, l, ml, and ms • This also draws us to the conclusion that each orbital can hold up to two electrons, each with an opposite spin • This helps us define the region in space where electrons may lie

28. Electron Configurations • The way in which electrons are distributed among the various orbitals of an atom is called its electron configuration • Orbitals are filled by increasing energy due to the Pauli Exclusion Principle with no more than two electrons per orbital www.btinternet.com

29. Electron Configurations • The orbitals fill by row, going from 1s to 2s to 2p to 3s to 3p to 4s to 3d to 4p to 5s to 4d to 5p to 6s to 4f to 5d to 6p to 7s to 5f to 6d • For example, the electron configuration for zinc is 1s2 2s2 2p6 3s2 3p6 4s2 3d10 • In noble gas configuration you take the closest noble gas and start the configuration from there so zinc would be [Ar] 4s2 3d10

30. Electron Configurations and the Periodic Table • The periodic table is set up so that elements of the same pattern of outer-shell electron configuration are arranged in columns • The table is broken up into 4 groups, s, p, d, and f blocks

31. Electron Configurations and the Periodic Table • Each element groups have their own sublevels, so alkali and alkaline earth metals (and helium) make up the S block. The p block is made up by noble gasses, halogens, non metal, and far right elements in columns 13-18. The d block is all the central transition metals from columns 3-12. Finally the F block is made up by the lanthanides and actinides below all the other elements (4f and 5f).

32. Electron Configurations and the Periodic Table • Here is a visual to help you understand how it is broken up www.btinternet.com