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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.

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Electronic Structure of Atoms

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Electronic structure of atoms l.jpg

Electronic Structure of Atoms


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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


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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.


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The Wave Nature of Light


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Common Wavelength Units


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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.


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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


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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.


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Photoelectric Effect


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Line Spectra and the Bohr Model


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Line Spectra


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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.


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Energy States of the Hydrogen Atom


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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 ∞


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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.


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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


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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


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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,


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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)


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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


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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.


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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


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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.


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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.


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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.


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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.


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Orbital diagrams


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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.


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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


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Pauli exclusion principle

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


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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.


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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.


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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.


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