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CHEM 10First Semester, SY 2015-2016

UNIT 3ELECTRONIC STRUCTURE AND THE PERIODIC TABLE

From Classical Physics to Quantum TheoryBy assuming that molecules behave like rebounding balls, physicists were able to predict and explain some macroscopic phenomena, such as the pressure exerted by a gas. However, their model did not account for the stability of molecules; that is, it could not explain the forces that hold atoms together. The properties of atoms and molecules are not governed by the same laws that work so well for larger objects.

3.1 Light, Photon Energies, and Atomic Spectra

The Wave Nature of Light: Wavelength and FrequencyLight travels through space as a wave, consisting of successive crests which rise above the midline and a trough which sink below it.

Two of the three primary characteristics of waves:Figure 3. 1 Characteristics of waves.

1. Amplitude (), the height of a crest or the depth of a tough.2. Wavelength (), the distance between two consecutive crests or troughs, most often measured in meters or nanometers (1 nm = 10-9m).3. Frequency (), the number of wave cycles (successive crests or troughs) that pass a given point in unit time. If 108 cycles pass a particular point in one second, HzThe frequency unit hertz (Hz) represents one cycle per second.

The speed at which a wave moves through space can be found by multiplying the length of a wave cycle (l) by the number of cycles passing a point in unit time (n). For light,

where c, the speed of light in a vacuum, is 2.998 x 108 m/s.

Example:

Solution:

Light visible to the eye is only a tiny portion of the entire electromagnetic spectrum (Figure 6.2) covering only the narrow wavelength region from 400 to 700 nm..

The colors of gases and liquids are due to the selective absorption of certain components of visible light. Bromine, for example, absorbs in the violet and blue regions of the spectrum (Table 6.1). The subtraction of these components from visible light accounts for the red color of bromine liquid or vapor.

The Particle Nature of Light: Photon Energies

We consider light to be generated as stream of particles called photons, whose energy is given by the equation:

Plancks equation To express energy, the SI unit Joule, J (1 kg) will be used. The quantity appearing in the equation is referred to as the Plancks constant.

Example:

Solution:(a) (b) (c)

Atomic Spectra

light from the Sun can be broken down into its various color components by a prism. It contains essentially all wavelengths between 400 and 700 nm. This rainbow of colors, containing light of all wavelengths, is called a continuous spectrum. The situation with high-energy atoms of gaseous elements is quite different. Here the spectrum consists of discrete lines given off at specific wavelengths. A spectrum containing radiation of only specific wavelengths is called a line spectrum. Each element has a characteristic spectrum that can be used to identify it. The fact that the photons making up atomic spectra have only certain discrete wavelengths implies that they can have only certain discrete energies. Since these photons are produced when an electron moves from one energy level to another, the electronic energy levels in an atom must be quantized, that is, limited to particular values.

3.2 The Hydrogen Atom

Bohr Model Bohr assumed that a hydrogen atom consists of a central proton about which an electron moves in a circular orbit He related the electrostatic force of attraction of the proton for the electron to the centrifugal force due to the circular motion of the electron. To this point, his analysis was purely classical, based on Coulombs law of electrostatic attraction and Newtons laws of motion Bohr postulated that the electron is allowed to occupy only certain orbits of specific energies. In other words, the energies of the electron are quantized. Bohr obtained the following equation for the energy of the hydrogen electron:

Where is the energy of the electron, and is a quantity called Rydberg constant.

and n is an integer called principal quantum number.

Ordinarily the hydrogen electron is in its lowest energy state, referred to as the ground state or ground level, for which n=1. When an electron absorbs enough energy, it moves to a higher, excited state. In a hydrogen atom, the first excited state has n=2, the second n=3, and so on.When an excited electron gives off energy as a photon of light, it drops back to a lower energy state. The electron can return to the ground state (from n=2 to n=1, for example) or to a lower excited state (from n=3 to n=2). In every case, the energy of the photon () evolved is equal to the difference in energy between the two states

Quantum Mechanical ModelBohrs theory for the structure of the hydrogen atom was highly successful. However, the extension of Bohrs ideas to atoms with two or more electrons gave, at best, only qualitative agreement with experiment. There appeared to be no way the theory could be modified to make it work well with helium or other atoms. Indeed, it soon became apparent that there was a fundamental problem with the Bohr model. The idea of an electron moving about the nucleus in a well-defined orbit at a fixed distance from the nucleus had to be abandoned. Scientists in the 1920s, speculating on this problem, became convinced that an entirely new approach was required to treat electrons in atoms and molecules.

Louis de Broglie reasoned that if light could show the behavior of particles (photons) as well as waves, then perhaps an electron, which Bohr had treated a particle, could behave like a wave. In a few years, de Broglies postulate was confirmed experimentally.

The dual nature of electrons was particularly troublesome because of the electrons exceedingly small mass. To describe the problem of trying to locate a subatomic particle that behaves like a wave, the German physicist Werner Heisenberg formulated what is now known as the Heisenberg uncertainty principle: It is impossible to know simultaneously both the momentum (mass times velocity) and the position of a particle with certainty. In other words, to get a precise measurement of the momentum of a particle we must settle for less precise knowledge of the particles position, and vice versa. Applying the Heisenberg uncertainty principle to the hydrogen atom, we see that it is inherently impossible to know simultaneously both the precise location and precise momentum of the electron. Thus, it is not appropriate to imagine the electron circling the nucleus in well-defined orbits. The best we can do is to estimate the probability of finding the electron within a particular region.

Erwin Schrdinger wrote down a rather complex differential equation to express the wave properties of an electron in an atom. This equation (Schrdinger equation) can be solved, at least in principle, to find the amplitude (height) of the electron wave at various points in space. The quantity (psi) is known as the wave function. Although quantum mechanics tells us that we cannot pinpoint an electron in an atom, it does define the region where the electron might be at a given time. The concept of electron density gives the probability that an electron will be found in a particular region of an atom. The square of the wave function, 2, is directly proportional to the probability of finding the electron at a particular point. If 2 at point A is twice as large as at point B, then we are twice as likely to find the electron at A as at B. Putting it another way, over time the electron will turn up at A twice as often as at B.

3.3 Quantum Numbers

(1st) Principal Quantum Number, n; Principal Energy LevelsThe first quantum number, given the symbol n, is of primary importance in determining the energy of an electron. For the hydrogen atom, the energy depends upon only n. In other atoms, the energy of each electron depends mainly, but not completely, upon the value of n. As n increases, the energy of the electron increases and, on the average, it is found farther out from the nucleus.The quantum number n can take on only integral values, starting with 1:

An electron for which n = 1 is said to be in the first principal level. If n = 2, we are dealing with the second principal level, and so on.

(2nd) Angular Momentum Quantum Number, l ; Sublevels (s, p, d, f) Each principal energy level includes one or more sublevels The sublevels are denoted by the second quantum number,l l can take on any integral value starting with 0 and going up to a maximum of (n-1). That is,

l

If n = 1, there is only one possible value of l namely 0. This means that in the first principal level, there is only one sublevel. In the same way,n = 1:l = 0 (one sublevel)n = 2:l = 0, 1, or 2 (three sublevels)n = 3:l = 0, 1, 2, or 3 (four sublevels)

In general, in the nth principal level, there are n different sublevels. Another method in designating sublevels is assigning l to the letters s, p, d, f, respectively. General shape of the electron cloud (or orbital) associated with an electron is determined by l.

Quantum number, l0123Type of sublevelspdf

Usually, in designating a sublevel, a number is included to indicate the principal level (Table 6.3).

For atoms containing more than one electron, the energy is dependent on l, as well as n. Within a given principal level (same value of n), sublevels increase in energy in the orderns < np < nd < nf

(3rd) Magnetic Quantum Number, ; Orbitals Each sublevel contains one or more orbitals These orbitals differ from one another in the value assigned to the third quantum number . This quantum number determines the direction in space of the electron cloud surrounding the nucleus. For a given value of l, there are (2l + 1) integral values of that is

- l, (-l +1), 0, (+l +1), + l

For an s sublevel, (l = 0), can have only one value (2(0)+1=1),that is 0. This means that the sublevel contains only one orbital, referred to as an s orbital. In the same wayp sublevel:l = 12(1) + 1 = 3d sublevel:l = 22(2) + 1 = 5f sublevel:l = 32(3) + 1 = 7Here again all the orbitals in a given d or f sublevel have the same energy.

(4th) Electron Spin Quantum Number, ms; Electron Spin The fourth quantum number is associated with electron spin. Either of the two spins is possible: clockwise or counterclockwise This quantum number is not related to n, l, or It can have either of the two values:

Electrons that have the same value of ms (i.e., both or both) are said to have parallel spins. Electrons that have different ms values (i.e., one and the other ) are said to have opposed spins.

Pauli Exclusion Principle This rule relates to all the quantum numbers It requires that no two electrons in an atom can have the same set of four quantum numbers. It requires that only two electrons can fit into an orbital, since there are only two possible values of ms. if two electrons occupy the same orbital, they must have opposed spins.

Example 1:

Solution:

Example 2:

Solution:

3.4 Atomic Orbitals; Shapes and Sizes an orbital occupied by an electron in an atom can be represented physically by showing the region of space in which there is a 90% probability of finding the electron Orbitals are commonly designated by citing the corresponding sublevels. Thus we refer to 1s, 2s, 2p, 3s, 3p, 3d, . . . orbitals.

One of the important questions we ask when studying the properties of atomic orbitals is what are the shapes of the orbitals? Strictly speaking, an orbital does not have a well-defined shape because the wave function characterizing the orbital extends from the nucleus to infinity. In that sense, it is difficult to say what an orbital looks like. On the other hand, it is certainly convenient to think of orbitals as having specific shapes, particularly in discussing the formation of chemical bonds between atoms. We can represent the orbitals by drawing a boundary surface diagram that encloses about 90 percent of the total electron density in an orbital.

s Orbitals All s orbitals are spherical in shape but differ in size, which increases as the principal quantum number increases.

p Orbitals The three p orbitals are identical in size, shape, and energy; they differ from another only in orientations. Note, however, that there is no simple relation between the values of and the x, y, and z directions. For our purpose, you need to remember only that because there are three possible values of , there are three p orbitals with different orientations. The boundary surface diagrams of p orbitals show that each can be thought of as two lobes on opposite sides of the nucleus. p orbitals increase in size from 2p to 3p to 4p and so on.

d Orbitals As in the case of the p orbitals, the different orientations of the d orbitals correspond to the different values of but again there is no direct correspondence between a given orientation and a particular value. All 3d orbitals in an atom are identical in energy.

The Energy of Orbitals the energies of hydrogen orbitals increase as follows

Although the electron density distributions are different in the 2s and 2p orbitals, hydrogens electron has the same energy whether it is in the 2s orbital or a 2p orbital. The 1s orbital in a hydrogen atom corresponds to the most stable condition, the ground state. An electron residing in this orbital is most strongly held by the nucleus because it is closest to the nucleus. An electron in the 2s, 2p, or higher orbitals in a hydrogen atom is in an excited state.

The energy picture for many-electron atoms is more complex than for hydrogen For many-electron atoms, the 3d energy level is very close to the 4s energy level. It turns out that the total energy of an atom is lower when the 4s subshell is filled before a 3d subshell

3.5 Orbital Diagrams of Atoms Orbital diagrams show how electrons are distributed among orbitals. Each orbital is represented by parentheses () or and electrons are shown by arrows or , depending on spin.

Hunds Rule -the most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins. when several orbitals of equal energy are available, as in a given sublevel, electrons enter singly with parallel spins. Only after all the orbitals are half-filled do electrons pair up in orbitals. in all filled orbitals, the two electrons have opposed spins. in accordance with Hunds rule, within a given sublevel there are as many half-filled orbitals as possible.

Paramagnetism and DiamagnetismParamagnetic substances are those that contain net unpaired spins and are attracted by a magnet.Diamagnetic substances do not contain net unpaired spins and are slightly repelled by a magnet.

Shielding Effect in Many-Electron Atoms Because the 2s and 2p orbitals are larger than the 1s orbital, an electron in either of these orbitals will spend more time away from the nucleus than an electron in the 1s orbital. Thus, we can speak of a 2s or 2p electron being partly shielded from the attractive force of the nucleus by the 1s electrons. The important consequence of the shielding effect is that it reduces the electrostatic attraction between the protons in the nucleus and the electron in the 2s or 2p orbital. for the same principal quantum number n, the penetrating power decreases as the angular momentum quantum number l, increases, ors > p > d >f

3.6 Electron Configurations in Atoms Electron configuration describes the how the electrons are distributed among the various atomic orbitals, which shows the number of electrons, indicated by a superscript, in each sublevel It should be emphasized that, throughout this discussion, we refer to isolated gaseous atoms in the ground state. (In excited states, one or more electrons are promoted to a higher energy level.)

Electron Configuration from Sublevel Energies Electrons enter the available sublevels in order of increasing sublevel energy Aufbau Principle - electrons orbiting one or more atoms fill the lowest available energy levels before filling higher levels (e.g., 1s before 2s)

Examples:

Beyond neon, electrons enter the third principal level. The 3s sublevel is filled at magnesium:

Six more electrons are required to fill the 3p sublevel with argon:

After argon, an overlap of principal energy levels occurs. The next electron enters the lowest sublevel of the fourth principal level (4s) instead of the highest sublevel of the third principal level (3d). Potassium (Z =19) has one electron in the 4s sublevel; calcium (Z=20) fills it with two electrons:

Now the 3d sublevel starts to fill with scandium (Z=21). Recall that a d sublevel has a capacity of ten electrons. Hence the 3d sublevel becomes filled at zinc (Z 5 30):

The next sublevel, 4p, is filled at krypton (Z=36):

Exercise:Find the electron configurations of the sulfur and nickel atoms.

Often, to save space, electron configurations are shortened; the abbreviated electron configuration, referred as noble gas core, starts with the preceding noble gas in brackets followed by the symbol for the highest filled subshells in the outermost shells. For the elements sulfur and nickel,

Filling of Sublevels and the Periodic Table

The atoms of elements in a group of the periodic table have the same distribution of electrons in the outermost principal energy level.

The elements in Groups 1 and 2 fill s sublevels. The elements in Groups 13 through 18 (six elements in each period) fill p sublevels. The transition metals, in the center of the periodic table, fill d sublevels with a principal quantum number one less than the period number. The two sets of 14 elements listed separately at the bottom of the table are filling f sublevels with a principal quantum number two less than the period number 14 elements in Period 6 fill the 4f sublevel. These elements are commonly called as rare earth or lanthanides 14 elements in Period 7 fill the 5f sublevel. These elements are commonly called as actinides

Electron Configuration from the Periodic Table

Example:For the iodine atom, write(a) the electron configuration(b) the abbreviated electron configuration.

Solution:

As you can see, the electron configurations of several elements (marked *) differ slightly from those predicted. In every case, the difference involves a shift of one or, at the most, two electrons from one sublevel to another of very similar energy. For example, in the first transition series, two elements, chromium and copper, have an extra electron in the 3d as compared with the 4s orbital.

These anomalies reflect the fact that the 3d and 4s orbitals have very similar energies. Beyond that, it has been suggested that there is a slight increase in stability with a half-filled (Cr) or completely filled (Cu) 3d sublevel

3.7 Electron Arrangements in Monoatomic IonsIt is also possible to assign electronic structures to monatomic ions, formed from atoms by gaining or losing electrons. In general, when a monatomic ion is formed from an atom, electrons are added to or removed from sublevels in the highest principal energy level.

Ions with Noble-gas StructuresElements close to a noble gas in the periodic table form ions that have the same number of electrons as the noble-gas atom. This means that these ions have noble-gas electron configurations. Thus, the three elements preceding neon (N, O, and F) and the three elements following neon (Na, Mg, and Al) all form ions with the neon configuration, 1s22s22p6.

The three nonmetal atoms achieve this structure by gaining electrons to form anions:

The three metal atoms acquire the neon structure by losing electrons to form cations:

Isoelectronic species that have the same electron configuration

Transition Metal Cations The transition metals to the right of the scandium subgroup do not form ions with noble-gas configurations. To do so, they would have to lose four or more electrons. these metals do form cations with charges of +1, +2, or +3. Applying the principle that, in forming cations, electrons are removed from the sublevel of highest n, you can predict correctly that when transition metal atoms form positive ions, the outer s electrons are lost first.

6.8 Periodic Trends in the Properties of AtomsOne of the most fundamental principles of chemistry is the periodic law, which states that The chemical and physical properties of elements are a periodic function of atomic number. This is, of course, the principle behind the structure of the periodic table. Elements within a given vertical group resemble one another chemically because chemical properties repeat themselves at regular intervals of 2, 8, 18, or 32 elements.

Atomic Radius decrease across a period from left to right in the periodic table. increase down a group in the periodic table. effective nuclear charge Ionic Radius

Ionization EnergyElectronegativitynfea2015