Chapter 6 Electronic Structure of Atoms Chemistry, The Central Science, 11th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten Chapter 6 Electronic Structure of Atoms John D. Bookstaver St. Charles Community College Cottleville, MO © 2009, Prentice-Hall, Inc.

6.1 The Wave Nature of Light • The electronic structure of an atom refers to the arrangement of electrons. • Visible light is a form of electromagnetic radiation or radiant energy. • Radiation carries energy through space. • Electromagnetic radiation is characterized by its wave nature. • All waves have a characteristic wavelength, (). (lambda), and amplitude, A. • The frequency, (). (nu), of a wave is the number of cycles which pass a point in one second. • The units of (). are Hertz (1 Hz = 1 s–1). • The speed of a wave is given by its frequency multiplied by its wavelength. • For light, speed, c =   • Electromagnetic radiation moves through a vacuum with a speed of 3.00 x 108 m/s. • Electromagnetic waves have characteristic wavelengths and frequencies. • The electromagnetic spectrum is a display of the various types of electromagnetic radiation arranged in order of increasing wavelength. •Example: visible radiation has wavelengths between 400 nm (violet) and 750 nm (red). © 2009, Prentice-Hall, Inc.

Characteristics of water waves. Caption: Title: Characteristics of water waves. Caption: The distance between corresponding points on each wave is called the wavelength. In this drawing, the two corresponding points are two peaks, but they could be any other two corresponding points, such as two adjacent troughs. (b) The number of times per second that the cork bobs up and down is called the frequency of the wave. © 2009, Prentice-Hall, Inc.

Characteristics of electromagnetic waves. Title: Characteristics of electromagnetic waves. Radiant energy has wave characteristics; it consists of electromagnetic waves. Notice that the shorter the wavelength, λ, the higher the frequency, ν. The wavelength in (b) is half as long as that in (a), and the frequency of the wave in (b) is therefore twice as great as the frequency in (a). The amplitude of the wave relates to the intensity of the radiation, which is the maximum extent of the oscillation of the wave. In these diagrams amplitude is measured as the vertical distance from the midline of the wave to its peak. The waves in (a) and (b) have the same amplitude. The wave in (c) has the same frequency as that in (b), but its amplitude is lower. © 2009, Prentice-Hall, Inc.

Waves To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. The distance between corresponding points on adjacent waves is the wavelength (). © 2009, Prentice-Hall, Inc.

Waves 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. © 2009, Prentice-Hall, Inc.

Electromagnetic Radiation All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00  108 m/s. Therefore, c =  Title: The electromagnetic spectrum. Wavelengths in the spectrum range from very short gamma rays to very long radio waves. Notice that the color of visible light can be expressed quantitatively by wavelength. © 2009, Prentice-Hall, Inc.

Concepts of Wavelength and Frequency Two electromagnetic waves are represented in the figure. (a) Which wave has the higher frequency? (b) If one wave represents visible light and the other represents infrared radiation, which wave is which? The lower wave has a longer wavelength (greater distance between peaks). The longer the wavelength, the lower the frequency (v = c/λ). Thus, the lower wave has the lower frequency, and the upper wave has the higher frequency. (b) The electromagnetic spectrum (Figure 6.4) indicates that infrared radiation has a longer wavelength than visible light. Thus, the lower wave would be the infrared radiation. © 2009, Prentice-Hall, Inc.

Sample Exercise 6.2 Calculating Frequency from Wavelength The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589 nm. What is the frequency of this radiation? Analyze: We are given the wavelength, λ, of the radiation and asked to calculate its frequency, v. Plan: The relationship between the wavelength (which is given) and the frequency (which is the unknown) is given by Equation 6.1. We can solve this equation for v and then use the values of and c to obtain a numerical answer. (The speed of light, c, is a fundamental constant whose value is 3.00 × 108 m/s.) Solve: Solving Equation 6.1 for frequency gives v = c/λ. When we insert the values for c and λ, we note that the units of length in these two quantities are different. We can convert the wavelength from nanometers to meters, so the units cancel: Check: The high frequency is reasonable because of the short wavelength. The units are proper because frequency has units of “per second,” or s–1. © 2009, Prentice-Hall, Inc.

The wavelength of electromagnetic energy multiplied by its frequency equals: c, the speed of light h, Planck’s constant Avogadro’s number 4.184 Practice Exercise (a) A laser used in eye surgery to fuse detached retinas produces radiation with a wavelength of 640.0 nm. Calculate the frequency of this radiation. (b) An FM radio station broadcasts electromagnetic radiation at a frequency of 103.4 MHz (megahertz; MHz = 106 s–1). Calculate the wavelength of this radiation. The speed of light is 2.998 × 108 m/s to four significant digits. Answers: (a) 4.688 × 1014 s–1, (b) 2.901 m © 2009, Prentice-Hall, Inc.

The Nature of Energy 6.2 Quantized Energy and Photons The wave nature of light does not explain how an object can glow (shine) when its temperature increases. Heated solids emit radiation (black body radiation) The wavelength distribution depends on the temperature (i.e., “red hot” objects are cooler than “white hot” objects). Max Planck proposed that energy can only be absorbed or released from atoms in certain amounts. These amounts are called quanta He explained it by assuming that energy comes in packets called quanta. © 2009, Prentice-Hall, Inc.

Einstein used this assumption to explain the photoelectric effect. • A quantum is the smallest amount of energy that can be emitted or absorbed as electromagnetic radiation. Einstein used this assumption to explain the photoelectric effect. Einstein assumed that light traveled in energy packets called photons. The energy of one photon is E = h He concluded that energy is proportional to frequency: where h is Planck’s constant, 6.626  10−34 J-s. Title: The photoelectric effect. Caption: When photons of sufficiently high energy strike a metal surface, electrons are emitted from the metal. © 2009, Prentice-Hall, Inc.

Sample Exercise 6.3 Energy of a Photon Calculate the energy of one photon of yellow light with a wavelength of 589 nm. If one photon of radiant energy supplies 3.37 × 10–19 J, then one mole of these photons will supply A laser emits light with a frequency of 4.69 × 1014 s–1. What is the energy of one photon of the radiation from this laser? (b) If the laser emits a pulse of energy containing 5.0 × 1017 photons of this radiation, what is the total energy of that pulse? (c) If the laser emits 1.3 × 10–2 J of energy during a pulse, how many photons are emitted during the pulse? Answers: (a) 3.11 × 10–19 J, (b) 0.16 J, (c) 4.2 × 1016 photons © 2009, Prentice-Hall, Inc.

The energy of a photon of electromagnetic energy divided by its frequency equals: c, the speed of light h, Planck’s constant Avogadro’s number 4.184

6.3 Line Spectra and the Bohr Model Line spectra : a particular source of radiant energy may emit a single wavelength as in the light of laser. Radiation composed of a single wavelength is said to be monochromatic However most common radiation sources including light bulbs and stars produce radiation containing many different wave length Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c =  E = h © 2009, Prentice-Hall, Inc.

The Nature of Energy A spectrum is produced when radiation from light sources is separated into different wavelength component as shown in the figure which is called continues spectrum For atoms (Na) (H) figure below and molecules one does not observe a continuous spectrum, as one gets from a white light source. Only a line spectrum of specific wavelengths is observed. As shown © 2009, Prentice-Hall, Inc.

The Nature of Energy The emission spectra observed from energy emitted by atoms and molecules. Not all radiation sources produce a continuous spectrum when a high voltage is applied to tubes that contain different gases. The light emitted by neon gases is the familiar is the red orange glow as shown in figure A formula that calculate the wavelengths of all the spectral lines of hydrogen is called Rydberg equation © 2009, Prentice-Hall, Inc.

The Energy state of the hydrogen atom Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: Electrons in an atom can only occupy certain orbits (corresponding to certain energies). The energy that the electron will be depending on which orbit it is in. page 220 The lower the energy the more stable the atom will be n=1 ,2, 3,……. The lowest energy state n=1 is called the ground state When the electron is in a higher energy state n=2 or higher the atom is said to be I an excited state As shown in figure © 2009, Prentice-Hall, Inc.

The Nature of Energy Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom. © 2009, Prentice-Hall, Inc.

The Nature of Energy Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 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 © 2009, Prentice-Hall, Inc.

The Nature of Energy The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: E = −RH ( ) 1 nf2 ni2 - where RH is the Rydberg constant, 2.18  10−18 J, and ni and nf are the initial and final energy levels of the electron. © 2009, Prentice-Hall, Inc.

Light that contains colors of all wavelengths is called: a continuous spectrum. monochromatic. a line spectrum. a Balmer series.

The Wave Nature of Matter Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties. He demonstrated that the relationship between mass and wavelength was  = h mv © 2009, Prentice-Hall, Inc.

The Uncertainty Principle 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! (x) (mv)  h 4 © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

Quantum Mechanics The wave equation is designated with a lower case Greek psi (). The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time. © 2009, Prentice-Hall, Inc.

Quantum Numbers Solving the wave equation gives a set of wave functions, called 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. n, l, and m © 2009, Prentice-Hall, Inc.

Principal Quantum Number (n) The principal quantum number, n, describes the energy level on which the orbital resides. The values of n are integers ≥ 1. as 1,2,3,…… As n increases the orbital becomes larger © 2009, Prentice-Hall, Inc.

Angular Momentum 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. Value of l 1 2 3 Type of orbital s p d f © 2009, Prentice-Hall, Inc.

Magnetic Quantum Number (ml) The magnetic quantum number describes the three-dimensional orientation of the orbital. Allowed values of ml 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. © 2009, Prentice-Hall, Inc.

Magnetic Quantum Number (ml) Orbitals with the same value of n form a shell. Different orbital types within a shell are subshells. © 2009, Prentice-Hall, Inc.

s Orbitals The value of l for s orbitals is 0. They are spherical in shape. The radius of the sphere increases with the value of n. © 2009, Prentice-Hall, Inc.

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. © 2009, Prentice-Hall, Inc.

p Orbitals The value of l for p orbitals is 1. They have two lobes with a node between them. © 2009, Prentice-Hall, Inc.

d Orbitals The value of l for a d orbital is 2. Four of the five d orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center. © 2009, Prentice-Hall, Inc.

Energies of Orbitals For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. That is, they are degenerate. © 2009, Prentice-Hall, Inc.

Energies of Orbitals As the number of electrons increases, though, so does the repulsion between them. Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate. © 2009, Prentice-Hall, Inc.

Spin Quantum Number, ms In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy. The “spin” of an electron describes its magnetic field, which affects its energy. © 2009, Prentice-Hall, Inc.

Spin Quantum Number, ms This led to a fourth quantum number, the spin quantum number, ms. The spin quantum number has only 2 allowed values: +1/2 and −1/2. © 2009, Prentice-Hall, Inc.

Pauli Exclusion Principle No two electrons in the same atom can have exactly the same energy. Therefore, no two electrons in the same atom can have identical sets of quantum numbers. © 2009, Prentice-Hall, Inc.

Electron Configurations This shows the distribution of all electrons in an atom. Each component consists of A number denoting the energy level, © 2009, Prentice-Hall, Inc.

Electron Configurations This shows the distribution of all electrons in an atom Each component consists of A number denoting the energy level, A letter denoting the type of orbital, © 2009, Prentice-Hall, Inc.

Electron Configurations This shows the distribution of all electrons in an atom. Each component consists of A number denoting the energy level, A letter denoting the type of orbital, A superscript denoting the number of electrons in those orbitals. © 2009, Prentice-Hall, Inc.

Orbital Diagrams Each box in the diagram represents one orbital. Half-arrows represent the electrons. The direction of the arrow represents the relative spin of the electron. © 2009, Prentice-Hall, Inc.

Hund’s Rule “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.” © 2009, Prentice-Hall, Inc.

Periodic Table We fill orbitals in increasing order of energy. Different blocks on the periodic table (shaded in different colors in this chart) correspond to different types of orbitals. © 2009, Prentice-Hall, Inc.

Some Anomalies Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row. © 2009, Prentice-Hall, Inc.

Some Anomalies For instance, the electron configuration for copper is [Ar] 4s1 3d5 rather than the expected [Ar] 4s2 3d4. © 2009, Prentice-Hall, Inc.

Some Anomalies This occurs because the 4s and 3d orbitals are very close in energy. These anomalies occur in f-block atoms, as well. © 2009, Prentice-Hall, Inc.