1. AP Chemistry 2014-2015 CH 7 ATOMIC STRUCTURE AND PERIODICITY

2.  Electromagnetic radiation: radiant energy that exhibits wavelike behavior and travels through space at the speed of light in a vacuum  Wavelength: the distance between two consecutive peaks or troughs in a wave.  Frequency: the number of waves in a cycle that pass a given point in space each second. TERMS 7.1-7.4

5.  Planck’s constant: the constant relating the change in energy for a system to the frequency of the electromagnetic radiation absorbed or emitted; equal to 6.626 x 10 -32 Js. TERMS

6.  Quanta  Quantization is the concept that energy can only occur in discrete packets, called quantum. “Quanta” is the plural of quantum.  Photon: a quantum of electromagnetic radiation.

7.  Photoelectric effect: the phenomenon in which electrons are emitted from the surface of a metal when light strikes it.  This light must meet or exceed a threshold frequency in order for the effect to occur.  If the effect occurs, the number of electrons and kinetic energy of the electrons emitted both increase as the intensity of the light increases (for KE, the relationship is linear)

8.  Dual nature of light: light exhibits both wave-like and particulate characteristics.  A photon only has mass in a relative sense; it cannot be weighed but it exhibits mass experimentally.

9.  Diffraction: the scattering of light from a regular array of points or lines.  Diffraction patterns are patterns of bright spots and dark areas that form when scattered light interferes constructively and destructively (respectively). This phenomenon demonstrates that particles such as electrons have wavelengths.

10.  All matter exhibits both particulate and wave properties.  EMR has been shown to behave like a particle; electrons have been shown to have wavelengths. Science is solved, everyone go home.

11.  Atomic spectra  The continuous spectrum contains all the wavelengths of visible light and is obtained by passing white light through a prism.  Line spectra  An emission spectrum shows lines with wavelengths corresponding to discrete energy levels in a substance.  The opposite of an emission spectrum is an absorption spectrum, which shows light at all wavelengths except the wavelengths corresponding to discrete energy levels in a substance.  The wavelengths at which light can be absorbed or emitted correspond to the energy levels that are allowed for a substance, which in turn are related to its electron structure. Neat! So electron structure determines the energy found in each possible quantum which determines color!

16.  Quantum model (the Bohr Model)  Niels Bohr developed a quantum model for the hydrogen atom (see Equations section). The meaning of this model is that the electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.  This model only works for the electron in hydrogen. It does not work for any other element.

17.  Ground state: the lowest possible energy level for an electron in an atom.

19. EQUATIONS

20.  1, 2, 3, 4 PRACTICE PROBLEMS

21. The brilliant red colors seen in fireworks are due to the emission of light with wavelengths around 650 nm when strontium salts such as Sr(NO 3 ) 2 and SrCO 3 are heated. Calculate the frequency of red light of wavelength 6.50 × 10 2 nm.

22.  Quantum mechanics (or wave mechanics) is the result of Heisenberg, de Broglie, and Schrodinger’s efforts to find a model superior to the Bohr model. This model emphasizes the wave properties of the electron.  The electron bound the nucleus is similar to a standing wave (a stationary wave; its ends are fixed). There are limitations on the allowed wavelengths of standing waves since they have definite length. Nodes (N) have zero displacement while antinodes (A) exhibit the amplitude of the wave. There must be a whole number of half wavelengths in any of the allowed motions of a standing wave. TERMS 7.5-7.8

23.  Only certain circular orbits in an atom have a circumference into which a whole number of wavelengths of a standing electron will “fit”.  All other orbits produce destructive interference and are not “allowed”. Schrodinger used this model to derive the equation to the right. The Ψ (psi) is called the wave function. A specific wave function (solution) for Ψ is called an orbital.  The wave function does not actually tell us how an electron moves.

24.  The Heisenberg uncertainty principle states that there is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a given time. The more accurately we know about a particle’s position, the less accurately we can know its momentum, and vice-versa.  This limitation is negligibly small for large objects like baseballs but is much more significant for small particles like electrons-- which is another inadequacy of the Bohr model (it assumes we know more than we can).  Δx = uncertainty in a particle’s position, Δp = uncertainty in a particle’s momentum (also calculated as Δmv), h = Planck’s constant 6.626 x 10 -34 Js

26.  The square of a wave function indicates the probability of finding an electron near a particular point in space (probability distribution).  A graph of the total probability of finding an electron in each spherical shell vs. distance from the nucleus is called its radial probability distribution. The maximum in this curve occurs because of two opposing effects: the probability of finding an electron at a particular position is greatest near the nucleus, but the volume of the spherical shell increases with distance from the nucleus. Therefore, the total probability increases to a certain radius and then decreases past it.  The size of an orbital (as we usually use the term) is the radius of the sphere that encloses 90% of the total electron probability.

30.  Principal quantum number (n)  Has integral values 1, 2, 3…  Related to the size and energy of the orbital; as n increases, energy increases  Angular momentum quantum number (l)  Has integral values from 0 to n - 1 for each value of n.  Related to shape of atomic orbital  s orbitall = 0  p orbitall = 1  d orbitall = 2  f orbitall = 3  Each set of orbitals with a given value of l is called a subshell. These subshells are described using the principal quantum number and the angular momentum quantum number.  Magnetic quantum number (m l )  Has integral values between l and -l, including zero.; related to the orientation of the orbital in space relative to the other orbitals in the atom.  Spin quantum number (m s )  ½ or -½ (positive is “filled” before negative); two electrons with opposite spin can occupy any one orbital. EACH ORBITAL IS CHARACTERIZED BY A SET OF QUANTUM NUMBERS.

33.  Orbital Shapes and Energies  Nodal surface: an area of low probability in  a probability distribution (also called a node).  s orbital = spherical, found in all n  p orbital = peanut, found in n >1  d orbital = daisy, found in n > 2  f orbital = fancy, found in n >3

35.  All orbitals with the same n have the same energy and are said to be degenerate.  All 3 p orbitals in a given level have the same energy as each other, etc.

36.  Electron spin and the Pauli Exclusion Principle  An electron has a magnetic moment with two possible orientations when the atom it is found in is placed in an external magnetic field. Therefore, electrons have two (opposite) spin states.  Pauli Exclusion Principle: in a given atom no two electrons can have the same set of four quantum numbers.

37. 55 PRACTICE PROBLEM

38.  Polyelectronic atoms: atoms with more than one electron  Three energy contributions are considered in the description of polyelectronic atoms  KE of the electrons as they move around the nucleus  PE of attraction between the nucleus and the electrons  PE of repulsion between two electrons  Since the results of the Schrodinger equation cannot be solved exactly, electron repulsion cannot be calculated exactly. This is called the electron correlation problem, and requires that we make approximations in describing the movements of electrons. TERMS 7.9-7.11

39.  Shielding (or screening) occurs when an electron in a polyelectronic atom is repelled away from the nucleus due to the other electrons in the atom. This leads to the electron binding to not be as tight as it would have been if the atom was not polyelectronic.

41.  When electrons are placed in a particular quantum level, they “prefer” the orbitals in the order s, p, d, and then f. This is due to the energy of each sublevel (s = lowest, f = highest).  Aufbau principle: as protons are added one by one to the nucleus to build up the elements, electrons are similarly added to orbitals (starting with the lowest- energy orbital and working upwards). By the way, “aufbau” is German for “building up” and not someone’s last name.

45.  Hund’s rule: the lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli Exclusion Principle in a particular set of degenerate orbitals. (these images are called orbital diagrams)

46.  Electrons can be grouped together in many ways, including  Valence electrons, which are found in the outermost principal quantum level of an atom; important to chemists because they are involved in bonding; the elements in the same group have the same number of valence electrons  Core electrons, the inner electrons

48.  Electron configuration: description of electronic structure of an atom that uses the principal quantum number, the angular momentum quantum number, and the number of electrons in a subshell. Can be written longhand or using noble gas configuration. When writing the electron configuration for an ion, take the number of electrons lost or gained into account.

49.  Orbital diagram: description of electronic structure of an atom that displays the number electrons in each orbital. Cannot be written shorthand.

51.  Parts of the periodic table to know  Group 1A = alkali metals  Group 2A = alkaline earth metals  Group 7A = halogens  Group 8A = noble gases  d-block = transition metals  f-block = lanthanides (4f) and actinides (5f)  s-block + p-block = representative elements

53.  6 and 7 PRACTICE PROBLEMS

54.  Ionization energy is the energy required to remove an electron from a gaseous atom or ion (assumed to be in its ground state).  The first ionization energy, I 1, is the energy required to remove the highest-energy electron of an atom.  The second ionization energy, I 1, is the energy required to remove the next highest-energy electron of an atom after the highest-energy electron has been removed.  Ionization energy increases from left to right, and decreases going down a group.  Electrons added in the same principal quantum level do not completely shield the increasing nuclear charge caused by added protons. Thus electrons in the same principal quantum level are generally more strongly bound as we move to the right on the periodic table.  The main reason for the decrease in ionization energy in going down a group is that the electrons being removed are, on average, farther from the nucleus. TERMS 7.12

59.  Electron affinity is the energy change associated with the addition of an electron to a gaseous atom. If the addition is exothermic, the corresponding value for electron affinity will carry a negative sign.  Becomes more exothermic from left to right across a period until group 8A.  Sort of becomes less exothermic down a group, but there are a lot of exceptions and the change going down a group is relatively small.

61.  The atomic radius is measured indirectly (by measuring the distances between atoms in chemical compounds— often called covalent atomic radii because of the way they are determined; the radii for metal atoms, called metallic radii, are obtained from half the distance between metal atoms in solid metal crystals).  Smaller than might be expected from the 90% electron density volumes of isolated atoms, because when atoms form bonds, their electron “clouds” interpenetrate.  Decreases from left to right across a period, due to increase in effective nuclear charge.  Increases down a group because of the increases in the orbital sizes in successive principal quantum levels.

66.  8, 9, 10, 43 EXERCISES