**Electronic Structure of Atoms**

**Quantum Mechanics** • Or why mad scientists have all the fun • Quantum Mechanics describes the behavior of electrons in an atom. • The arrangement of electrons in atoms is termed the electronic structure of atoms. • We will examine how quantum theory is used to explain the trends in the periodic table and the formation of bonds in molecules

**The wave nature of light** • The light we see with our eyes makes a small portion of the electromagnetic spectrum called visible light. • All electromagnetic radiation travels in a vacuum at 299 792 458 m / s. That’s fast. • Wavelength is the distance between two successive peaks. Frequency is the number of wavelengths that pass a given point per second. • Light carries energy that is inversely proportional to its wavelength and directly proportional to frequency.

**The Wave Nature of Light**

**Common Wavelength Units**

**Wavelength and Frequency** • The electromagnetic spectrum is a chart of increasing wavelength. • The spectrum spans an enormous range, from the size of atoms to more than a mile (km) • Frequency is expressed in cycles per second in a unit called the hertz (Hz) • WBAP radio station at 820 on your AM radio dial is 820 kHz or 820,000 Hz or 820,000 wavelengths per second.

**Quantized Energy & Photons** • The wave/particle duality of light • In 1900 a German physicist named Max Plank (1858-1947) discovered that energy can be absorbed or emitted in discrete chunks or quanta. • E = hv • The constant h is called Plank’s constant and has a value of 6.626 x 10-34 J-s

**Quantized Energy & Photons** • According to Plank’s theory matter can emit or absorb light in only whole-number multiples of hv. • Each energy packet of electromagnetic radiation is called a photon – the particle aspect of the wave/particle nature of light. • In the Photoelectric effect there is a minimum energy requirement to eject an electron, called the work function.

**Photoelectric Effect**

**Line Spectra and the Bohr Model**

**Line Spectra**

**Bohr’s Model** • Rutherford’s discovery of the nuclear nature of the atom suggested that the atom can be thought of as a microscopic solar system. • Bohr based his model on three postulates • Only orbits of certain radii or energy level are permitted • An electron in a permitted orbit has a “allowed” energy state. An electron in an “allowed” energy state will not radiate energy. • Energy is emitted or absorbed by the electron only as the electron changes from one allowed energy state to another.

**Energy States of the Hydrogen Atom**

**Energy States of the Hydrogen Atom** • Bohr calculated the energies corresponding to each allowed orbit for the electron in the hydrogen atom. • E = (-2.18 x 10-18 J)(1/n2) • The number -2.18 x 10-18J is a product of three constants. • The number n is called the principal quantum number and ranges from 1 to ∞

**Energy States of the Hydrogen Atom** • The lower (more negative) the energy the more stable the atom will be. • N = 1 is the lowest energy state and is called the ground state of the atom. • When n > 1 the atom is said to be in an excited state. • When n = ∞ the energy is zero and the electron is completed separated from the atom.

**Energy states of the hydrogen atom** • Energy must be absorbed for an electron to be moved into a higher orbit. (higher value of n) • Energy is emitted when an electron falls from a higher orbit to a lower orbit. • From Bohr’s postulates only specific frequencies of light can be absorbed or emitted by the atom. • ΔE = Ef – Ei = Ephoton = hv

**Limitations of Bohr Model** • The Bohr Model only explains the hydrogen atom • Subsequent atoms get further away from Bohr’s model. • But Bohr’s model introduces two very important aspects • Electrons exist only in certain discrete energy levels • Energy is involved in moving at electron from one level to the next

**The wave behavior of matter** • Louis de Broglie suggested that all matter has both wavelike and particle behavior. • λ = h/mv • where h is Plank’s constant, m is mass of the object and v is the velocity,

**The Heisenberg Uncertainty Principle** • German physicist Wener Heisenberg proposed that the dual nature of matter places a fundamental limitation on how precisely we can know both the location and the momentum of any object. • When applied to electrons we determine that it is impossible to know simultaneously both the exact momentum and exact position. • Δx Δ(mv) ≥ h/4π(The uncertainty of an electron is 10-9 m)

**Quantum mechanics and atomic orbitals** • Erwin Schrödinger proposed his wave equation that incorporates both the wavelike behavior and the particle-like behavior of the electron. • If Schrödinger’s equations leads to a series of mathematical functions called wave functions. • Wave functions yield a probability of electron density distribution

**Orbitals and Quantum Numbers** • The solution to Schrodinger’s equation for the hydrogen atom yields a set of wave functions and energies called orbitals. • There are three quantum numbers, n, l, m to describe an orbital.

**Orbitals and Quantum Numbers** • Principal quantum number n can have a value of 1,2,3 … ∞ • The second quantum number l is the angular quantum number and can have values from 0 to n – 1 • The magnetic quantum number m can have values ranging from –l to l

**Electron Shells and Subshells** • The collection of orbitals with the same value of n is called an electron shell. • The set of orbitals that have the same n and l values is called a subshell • Each subshell is designated by a number (the value of n) and a letter (s, p, d, f corresponding to the value of l.

**Observations about quantum numbers** • The shell with principal quantum number n will consist of exactly n subshells. Each subshell corresponds to a different allowed value of l from 0 to n – 1. • Each subshell consists of a specific number of orbitals. Each orbital corresponds to a different allowed value of ml • The total number of orbitals is a shell is n2 where n is the principal quantum number.

**The electron shell** • The collection of orbitals with the same value of n is called an electronic shell. • The set of orbitals that have the same n and l is called a subshell.

**Representations of orbitals** • The s orbital is spherical symmetric • Plotting a radial probability function yields the probability of finding an electron versus the distance from the nucleus.

**Orbital diagrams**

**Many-Electron Atoms** • In a many electron atom, for a given value of n, the energy of an orbital increases with increasing value of l.

**Electron Spin** • Each electron has an intrinsic property called electron spin that causes each electron to behave as if it were a tiny sphere spinning on its own axis. • Electron spin is quantized and is denoted ms • The only two possible values for ms are +1/2 and -1/2

**Pauli exclusion principle** • No two electrons in an atom can have the same set of four quantum numbers n, l, ml, ms

**Electron Configurations** • The way the electrons are distributed among the various orbitals of an atom is termed electronic configuration of the atom. • Using the Pauli exclusion principle we can state that orbitals are filled in order of increasing energy with no more than two electrons per orbital. • Hund’s rule states that for degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.

**Condensed Electron Configuration** • He -2s2 • C - 1s2 2s2 2p2 or [He] 2s2 2p2 • Ne - 1s2 2s2 2p6 • Na – [Ne] 3s1 • Mn – [Ar] 4s2 3d5 • Zn – [Ar] 4s2 3d10 • After the d orbitals are filled the p orbitals are filled.

**Electronic Configurations and the Periodic Table** • The periodic table is the best choice for selecting the order in which orbitals are filled. • Exceptions to the rule – chromium, copper, molybdenum and silver • The exceptions occur when there enough electrons to lead to precisely half-filled sets of degenerate orbitals or to completely fill a d subshell as in copper.