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Explore how electromagnetic radiation, photons, and quantized energy illuminate the electronic structure of atoms. Learn about line spectra, Bohr's model, and the wave-particle duality in atomic theory.
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The electronic structure of an atom refers to its number of electrons, how these electrons are distributed around the nucleus, and to their energies. • Much of our understanding of the electronic structure of atoms has come from the analysis of light either absorbed or emitted by substances.
6.1 The Wave Nature of Light • To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation (EMR). • Because EMR carries energy through space, it is also known as radiant energy. • There are many forms of EMR, to include visible light, radio waves, infrared waves, X-rays, etc. (See fig 6.4). • All EMR consists of photons, the smallest increments of radiant energy.
Different forms of EMR share characteristics: • All have wavelike characteristics (much like waves of water). • The distance between corresponding points on adjacent waves is the wavelength(). • The amplitude – or, maximum extent of oscillation of the wave -- is related to the intensity of the radiation
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.
Electromagnetic Radiation Spectrum • All EMR moves through travels at the same velocity: the speed of light (c), 3.00 108 m/s. • Therefore, c =
As you can see from the electromagnetic spectrum, there are many forms of EMR. • The difference in the forms are due to their different wavelengths, which are expressed in units of length. • Wavelengths vary from10-11 m to 103 m. • Frequency is expressed in cycles per second, also called a hertz. • Units of frequency are usually given simply as “per second,” denoted as s-1 or /s. As in 820 kilohertz (kHz), written as 820,000 s-1 or 820,000/s • See Table 6.1 for types of radiation and associated wavelength.
6.2 Quantized Energy and Photons • The wave nature of light does not explain how an object can glow when its temperature increases. • Max Planck explained it by assuming that energy comes in packets called quanta.
Einstein used this assumption to explain the photoelectric effect. • When photons of sufficiently high energy strike a metal surface, electrons are emitted from the metal. • Electrons are not emitted unless photons exceed a certain minimal energy. • E.g., light with a frequency of 4.60 x 1014 s-1 or greater will cause cesium atoms to emit electrons, but light of lower frequency has no effect. • He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.626 10−34 J-s.
Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c = E = h
6.3 Line Spectra and the Bohr Model Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.
One does not observe a continuous spectrum, as one gets from a white light source. • Only a line spectrum of discrete wavelengths is observed.
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). • Electrons in permitted orbits have specific, “allowed” energies; these energies are not radiated from the atom. • 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
1 nf2 ( ) - E = −RH 1 ni2 • The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: 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.
Limitations of the Bohr Model • The Bohr model explains the line spectrum of the hydrogen atom, but not (accurately) the spectra of other atoms. • Also, the Bohr model assumes the electron behaves as a particle. • Electrons also have wave-like properties. • However, Bohr model is important because: • It shows electrons as existing in only certain discrete energy levels, which are described by quantum numbers. • Energy is involved in moving an electron from one level to another.
h mv = 6.4 The Wave Nature of Matter • In the years after development of the Bohr model, the dual nature of light became known: EMR (i.e., light) can exhibit both particle-like (photon) character as well as wave-like character. • Louis de Broglie (in 1924) extended this idea to electrons, proposing a relationship between the wavelength of an electron (or any other particle), its mass, and velocity: • h = Planck’s constant
h 4 (x)(mv) 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! • In sum, you cannot accurately know both an electron’s position and momentum at the same time.
6.5 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.
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.
Quantum Numbers • Solving the wave equation gives a set of wave functions, or 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.
Principal Quantum Number, n • The principal quantum number, n, describes the energy level on which the orbital resides. • The values of n are integers ≥ 0.
Azimuthal 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.
Magnetic Quantum Number, ml • Describes the three-dimensional orientation of the orbital. • Values 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.
Orbitals with the same value of n form a shell. • Different orbital types within a shell are subshells.
6.6 Representations of Orbitals s Orbitals • Value of l = 0. • Spherical in shape. • Radius of sphere increases with increasing value of n.
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.
p Orbitals • Value of l = 1. • Have two lobes with a node between them.
d Orbitals • Value of l is 2. • Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.
f orbitals • When n = 4 or greater, there are seven equivalent f orbitals for which l= 3. • F orbital shapes are very complicated:
Links to atomic orbital videos • A depiction of the orbitals for scandium: • https://www.youtube.com/watch?v=sMt5Dcex0kg • Electrons in orbitals: • https://www.youtube.com/watch?v=4WR8Qvsv70s • Orbitals, the basics: • https://www.youtube.com/watch?v=Ewf7RlVNBSA • Quantum Theory – documentary (1 hour): • https://www.youtube.com/watch?v=CBrsWPCp_rs
6.7 Many-Electron AtomsOrbitals and Their Energies • For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. • That is, they are degenerate.
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.
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.
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.
Pauli Exclusion Principle • No two electrons in the same atom can have exactly the same energy. • For example, no two electrons in the same atom can have identical sets of quantum numbers.
6.8 Electron Configurations • Distribution of all electrons in an atom. • Electrons are in lowest possible energy states. • Per the Pauli exclusion principle, there can be no more than two electrons per orbital. • Orbitals are filled in order of increasing energy. (Some exceptions after element 18.) • Consist of • Number denoting the energy level. 4 • Letter denoting the type of orbital. p • Superscript denoting the number of electrons in those orbitals. 5
Orbital Diagrams • Each box represents one orbital. • Half-arrows represent the electrons. • The direction of the arrow represents the spin of the electron.
Hund’s Rule “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”
6.9 Electron Configurations and the Periodic Table • Orbitals are filled in increasing order of energy. • Different blocks on the periodic table, then, correspond to different types of orbitals.
For representative elements (Grps 1, 2 13-18), d and f subshells are not considered valence electrons. • For transition elements, completely filled f subshells are not among the valence electrons. • Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row. • For instance, the electron configuration for chromium: [Ar] 4s1 3d5 rather than the expected [Ar] 4s2 3d4. • Another example is copper: [Ar] 4s1 3d10 rather than the expected [Ar] 4s2 3d9 • This occurs because the 4s and 3d orbitals are very close in energy. • These anomalies occur in f-block atoms, as well.
