AP CHEMISTRY CHAPTER REVIEW CHAPTER 6: ELECTRONIC STRUCTURE AND THE PERIODIC TABLE You should be familiar with the wavelike properties of light: frequency (), wavelength (), and energy (E) as well as the equations that show their relationships (E = h and c = ) You should be familiar with the electromagnetic spectrum and atomic spectra (bright-line spectra). You should understand the details of the Bohr model for the hydrogen atom. You should understand the differences between the quantum mechanical model of the atom and the Bohr model. You should understand how each orbital in the atom is assigned a unique set of quantum numbers (n, l, ml) as well as the significance of the spin quantum number (ms). You should understand the relationship between the principal quantum number (n) and orbital size. You should understand the relationship between the second quantum number (l) and orbital shape. You should know the order in which electrons are added to the orbitals in an energy level diagram. You should be able to draw the orbital diagram and write the electron configuration for any element, from Z = 1 to Z = 38 (including Z = 24 and Z = 29, which are exceptions to the Aufbau rule.) You should understand how the position in the periodic table relates to the filling of sublevels (See Figure 6.9 on p. 144) You should be able to write the electron configuration for any common monoatomic ion (including transition metal cations, with the “first in, first out” rule.) You should understand the horizontal and vertical trends of the periodic table, with respect to atomic radius, ionic radius, ionization energy, and electronegativity.
6.1
LIGHT, PHOTON ENERGIES, AND ATOMIC SPECTRA
You may wonder why we discuss the properties of light in chemistry class. It sounds like a topic for a physics lesson. The reason we talk about light is because electrons in atoms will absorb and emit energy in the form of electromagnetic radiation. Light travels through space as a wave. Waves have the following characteristics: wavelength (): distance from crest to crest frequency (): # or wave cycles per unit time amplitude: distance from midline to top of crest Wavelength is often measured in meters or nanometers (1 m = 109 nm) Frequency is usually measured in Hertz (Hz) which represents 1 cycle per second (1 Hz = 1 s-1) The speed of a wave can be found by multiplying wavelength x frequency x = c, where c is the speed of light in a vacuum c = 3.0 x 108 m/s = wavelength expressed in m = wavelength expressed in Hz (or s-1)
With the equation x = c, you can solve for either the frequency or the wavelength, if the other property is given.
Short High High Energy
rays
X- rays
UV
IR
microwaves
Long Low Low Energy
radio waves
Visible light ( = 400 – 700 nm) is only a tiny portion of the electromagnetic spectrum: Light certainly has wave-like properties. However, light also exhibits behavior that is similar to particles. Light can be described as bundles or packets of specific energy called photons. A given frequency () of light will correspond to a specific amount of energy, as calculated by the following equation: E = h
where E = energy measured in joules, and h = Planck’s constant, 6.63 x 10-34 J s
The equation can also be written as E = hc/ Energy is normally measured in joules (J) or kilojoules (kJ). If visible light (white light) is split by a prism, a continuous rainbow of colors is produced. However, if a high voltage is applied to a sample of hydrogen gas and the light produced is passed through a prism, a series of distinct bands of color appear. This is known as a bright line emission spectrum. H2 spectrum: (410 nm, 434 nm, 486 nm, 656 nm)
400 nm
700 nm
Each element has a characteristic spectrum that can be used to identify it. Where does the emitted light come from? Electrons in the atom travel up to excited states when they receive an input of energy (coming from electricity or from a flame.) When the electrons travel from excited energy levels back down to lower energy levels, they release energy in the form of electromagnetic radiation, which includes visible light. Why does the light emitted from an element result in individual lines instead of a continuous rainbow? This is because the photons emitted from the element can only have certain discrete wavelengths (and energy values.) The electronic energy levels in an atom are said to be quantized. When the emission spectrum of hydrogen was studied, a theory was developed about the energy levels available to the electron. This theory led to the Bohr model of the atom.
6.2
THE HYDROGEN ATOM
The following table lists a series of wavelengths (in nm) that correspond to line emissions from the hydrogen spectrum: Ultraviolet (Lyman Series) 121.53 102.54 97.23 94.95 93.75 93.05
Visible (Balmer Series) 656.28 486.13 434.05 410.18 397.01
Infrared (Paschen Series) 1875.09 1281.80 1093.80 1004.93
The following diagram represents the various energy levels that an electron may occupy in the hydrogen atom.
Notice that the larger the gap in energy, the more energy is given off by that transition.
In this set of electronic transitions, UV has the most energy, and IR has the least energy.
How can you calculate the energy that is absorbed (or emitted) when an electron makes a transition from one energy level to another?
The energy of an individual level, n, is given by the equation E = - 2.18 x 10-18 J n2 The energy of a transition between levels is calculated from this equation: E = (2.18 x10-18 J )
1 (nlo)2
-
1 (nhi)2
Once the energy of a specific transition is known, the wavelength or the frequency that energy can be calculated:
= E h
= hc E
For example, the energy of the transition from n = 2 to n = 1 would be (2.18 x 10-18 J)(1 – ¼) = 1.635 x 10-18 J The wavelength of light emitted would be equal to (6.63 x 10-34 J s)(3 x 108 m/s) = 1.22 x 10-7 m = 122 nm (1.635 x 10-18 J) The energy emitted with a wavelength of 122 nm would fall in the UV range (see “Lyman series” in the above diagram)
The following table represents the wavelengths of light emitted when electrons undergo various transitions. Electronic Transition 21 31 41 51 61 71
Ultraviolet (Lyman Series) 121.53 nm 102.54 nm 97.23 nm 94.95 nm 93.75 nm 93.05 nm
Electronic Transition 32 42 52 62 72
Visible (Balmer Series) 656.28 nm 486.13 nm 434.05 nm 410.18 nm 397.01 nm
Electronic Transition 43 53 63 73
Infrared (Paschen Series) 1875.09 nm 1281.80 nm 1093.80 nm 1004.93 nm
The Bohr model of the hydrogen atom worked very well for explaining the bright line spectrum of hydrogen, but this model was not very good at predicting the behavior of atoms with more than one electron. In 1924, Louis de Broglie proposed that if light could exhibit particle-like behavior (photons), then perhaps particles (like electrons) could exhibit wavelike behavior. His assumption was proved to be true with experimental evidence. This opened up a whole new field known as wave mechanics or quantum mechanics. How is the quantum mechanical model of the atom different than the Bohr model? Electrons are not confined to a circular orbit around the nucleus. Electrons are located in orbitals. Orbitals are regions in space around the nucleus of an atom in which there is a good probability of finding an electron. In 1926, Erwin Schrodinger came up with a complex differential equation to express the wave properties of an electron in an atom. This equation is known as a wave function. Wave functions help us to understand the shapes of the different orbitals that exist at various energy levels. At the first level (n = 1), the shape of the orbital is spherical.
6.3
QUANTUM NUMBERS
There are three quantum numbers that are used to describe each atomic orbital. Each number will be discussed. 1st Quantum number (n): Principal Energy Level The quantum number n corresponds to the energy level and has integer values beginning with 1, 2, 3, etc. As the value of n increases, the energy of the electron increases, and it can be found farther away from the nucleus. 2nd Quantum number (l): Sublevels (s, p, d, and f) Each principal energy level contains one or more sublevels. The general shape of the orbital is determined by l. The values of l can be integral values, beginning with 0 and going up to a maximum value of (n-1). l type of sublevel
0 s
1 p
2 d
3 f
The summary of the possible values for the 1st two quantum numbers is shown below.
n l Sublevel (orbital)
1 0
0
2 1
0
3 1
2
0
1
4 2
3
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
3rd Quantum number (ml): Orbitals Each sublevel contains one or more orbitals. The orientation of these orbitals in three-dimensional space is determined by the third quantum number, ml. The values of ml can be integral values, including zero, that fall in the range of - l to + l l
ml
0 1 2 3
0 -1, 0, 1 -2, -1, 0, 1, 2 -3, -2, -1, 0, 1 , 2, 3
Number of orbitals at this sublevel 1 3 5 7
4th Quantum number (ms): Electron Spin Each orbital can hold a maximum of two electrons. When two electrons occupy the same orbital, they have opposite spins. The possible values of the spin quantum number, ms, are +½ and -½. 6.4
ATOMIC ORBITALS; SHAPES AND SIZES
The s-orbitals are round in shape. The p-orbitals have two lobes along an axis, with a node in the origin. (See Figure 6.7 on p.141) The shape of d and f orbitals are complex, with donut shapes and cloverleaf patterns. You don’t need to know what these shapes look like. As the value of n increases, the radius of the orbital becomes larger. (See Figure 6.6 on p. 141) It is important that you know this fact. The higher the energy, the larger the orbital.
6.5
ELECTRON CONFIGURATIONS IN ATOMS
The following lists the electron configurations for the elements from Z = 1 through Z = 38 Element H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K
Long form 1s1 1s2 1s22s1 1s22s2 1s22s22p1 1s22s22p2 1s22s22p3 1s22s22p4 1s22s22p5 1s22s22p6 1s22s22p63s1 1s22s22p63s2 1s22s22p63s23p1 1s22s22p63s23p2 1s22s22p63s23p3 1s22s22p63s23p4 1s22s22p63s23p5 1s22s22p63s23p6 1s22s22p63s23p64s1
Short form [He]2s1 [He]2s2 [He]2s22p1 [He]2s22p2 [He]2s22p3 [He]2s22p4 [He]2s22p5 [He]2s22p6 [Ne]3s1 [Ne]3s2 [Ne]3s23p1 [Ne]3s23p2 [Ne]3s23p3 [Ne]3s23p4 [Ne]3s23p5 [Ne]3s23p6 [Ar]4s1
Element Ca Sc Ti V Cr** Mn Fe Co Ni Cu** Zn Ga Ge As Se Br Kr Rb Sr
Long form 1s22s22p63s23p64s2 1s22s22p63s23p63d14s2 1s22s22p63s23p63d24s2 1s22s22p63s23p63d34s2 1s22s22p63s23p63d54s1 1s22s22p63s23p63d54s2 1s22s22p63s23p63d64s2 1s22s22p63s23p63d74s2 1s22s22p63s23p63d84s2 1s22s22p63s23p63d104s1 1s22s22p63s23p63d104s2 1s22s22p63s23p63d104s24p1 1s22s22p63s23p63d104s24p2 1s22s22p63s23p63d104s24p3 1s22s22p63s23p63d104s24p4 1s22s22p63s23p63d104s24p5 1s22s22p63s23p63d104s24p6 1s22s22p63s23p63d104s24p65s1 1s22s22p63s23p63d104s24p65s2
Short form [Ar]4s2 [Ar]3d14s2 [Ar]3d24s2 [Ar]3d34s2 [Ar]3d54s1 [Ar]3d54s2 [Ar]3d64s2 [Ar]3d74s2 [Ar]3d84s2 [Ar]3d104s1 [Ar]3d104s2 [Ar]3d104s24p1 [Ar] 3d104s24p2 [Ar] 3d104s24p3 [Ar] 3d104s24p4 [Ar] 3d104s24p5 [Ar] 3d104s24p6 [Kr]5s1 [Kr]5s2
**the ground state electron configuration does not obey the aufbau rule
A simple way to figure out the electron configuration of an element is to be familiar with the blocks of the periodic table:
1s 2s 3s 4s 5s 6s 7s
1s 2p 3p 4p 5p 6p 7p
3d 4d 5d 6d 4f 5f
6.6
ORBITAL DIAGRAMS OF ATOMS
When the electrons are added to fill in the orbitals in an energy level diagram, the following rules are followed: aufbau (building up) principle: Electrons are added to the orbitals with the lowest energy first, and then sublevels are filled in order of increasing energy. Pauli exclusion principle: Each orbital can only hold a maximum of 2 electrons. Two electrons in the same orbital must have opposite spins. Hund’s Rule: If more than one orbital is present at the same energy level, put single electrons into each orbital (with parallel spins) before you put a second electron into an orbital.
One of the consequences of Hund’s Rule, is that within a given sublevel (p, d, f) there are as many half-filled orbitals as possible. These electrons are said to be unpaired. The number of unpaired electrons in an atom can be measured by experiment. A substance is placed in a magnetic field. If the substance is attracted into the field, then it should contain unpaired electrons and it is said to be paramagnetic. If the substance is slightly repelled by this field, it should contain only paired electrons and it is said to be diamagnetic. The words paramagnetic and diamagnetic may not make much sense to you. In any case, if you are given a list of electron configurations and you are asked to identify which substance is paramagnetic, then the answer should be the one with unpaired electrons in its electron configuration. A classic demonstration in chemistry is to show the difference between liquid nitrogen and liquid oxygen. For reasons that are two complex to explain (See pp. 619-622), liquid oxygen is paramagnetic. If liquid oxygen is poured between the poles of a strong magnet, the liquid will be attracted to the magnet for a few seconds before it evaporates. By contrast, liquid nitrogen does no do this and it is classified as diamagnetic. Remind me to show you a video of this demo.
6.7
ELECTRON ARRANGEMENTS IN MONOATOMIC IONS
When an ion is formed, electrons are either lost or gained. The focus will be on the electrons in the highest principal energy level. Consider these ions that are isoelectronic with each other: He (1s2)
Ne (1s22s22p6)
Ar (1s22s22p63s23p3d4s2)
H-, Li+, Be+2, B+3, C+4
N-3, O-2, F-, Na+, Mg+2, Al+3
P-3, S-2, Cl-, K+, Ca+2, Sc+3, Ti+2
The transition metals to the right of the scandium subgroup do not form ions with noble gas configurations. When transition metal atoms form positive ions, electrons are removed from the sublevel of highest n value first. In other words, when transition metal atoms form positive ions, the outer s electrons are lost first. For example: Mn = [Ar] 3d54s2
6.8
Mn+2 = [Ar] 3d5
PERIODIC TRENDS IN THE PROPERTIES OF ATOMS
The periodic law states that chemical and physical properties are a periodic function of atomic number. The important trends for you to understand include atomic radius, ionic radius, ionization energy, and electronegativity. Atomic radius decreases across a period from left to right. As you add electrons across a period, you are adding them to the same energy level. The effective nuclear charge should increase with atomic number. As effective nuclear charge increases, the outermost electrons are pulled in more tightly and atomic radius decreases. Atomic radius increases as you go down a group. This can be explained because the average distance of the electron from the nucleus increases with the principal quantum number n. Therefore the radius increases as you go down a group When an atom loses electrons to form a positive ion, the radius of the positive ion is smaller than the neutral atom. As electrons are lost, the excess of protons in the ion draws the outer electrons in closer to the nucleus. When an atom gains electrons to form a negative ion, the radius of the negative ion is larger than the neutral atom. The extra electron(s) will add to the repulsion between outer electrons making the ion larger than the atom. When you compare the ionic radius of two isoelectronic ions, the one with more protons will be smaller. Ionization energy (See p. 153) is a measure of how much energy is required to remove an electron from a gaseous atom. The more difficult it is to remove an electron, the larger the ionization energy. Ionization energy increases across a period from left to right. Ionization energy decreases as you go down a group. **Note that the 1st IE for B (801 kJ/mol) is actually less than for Be (900 kJ/mol). This can be explained because the electron to be removed from B is found in a 2p orbital and the outer electron for Be is located in a 2s orbital. Since 2p is higher energy than 2s, it should be easier to remove an electron from that sublevel. Electronegativity (See p. 154) is the ability of an atom to attract electrons within a covalent bond. The greater the EN, the greater the attraction for electrons. Electronegativity values increase across a period from left to right. Electronegativity values generally decrease or stay the same as you go down a group.
