Atomic Structure Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology
6/17/2015 Heated cathodes emitted cathode "rays" + - Deflected by either magnetic or electric fields Cathode Ray Tube J.J. Thomson, 1897
6/17/2015 The "beam" carried a negative charge. + - J. J. THOMSON (1897) British Physicist The ratio of charge to mass (e/m) was independent of the cathode material. Why does this indicate that cathode rays (electrons) are an integral part of each element? How did he know that?
6/17/2015 Photoelectric Effect + - Albert Einstein (1905) German Physicist Interpreted the Photoelectric Effect Confirmed that light is corpuscular (possess particle-like properties)
6/17/2015 Gold Foil Experiment ( cm thick) Kotz & Purcell (1987) Rutherford, 1911
6/17/2015 Ernest Rutherford (1911) British Chemist Most of the alpha particles (a, 4 He 2+ ) passed straight through, but a few were deflected or reflected straight backwards. Since alpha particles were known to have a positive charge, this indicated that the nucleus of an atom contained most of the mass, and that it was positive in charge Diagram source unknown
6/17/2015 The Atom Before 1913 Smallest unit of matter which maintains the physical and chemical properties of the element. Combines with other atoms to form molecules, but it itself is not destroyed. Consists of a positive nucleus of very small size containing most of the mass of the atom. Exhibits a volume much larger than the nucleus due to the presence of electrons.
Other physical properties had to be accounted for All the mass of the atom cannot be accounted for by only protons and electrons.
hydrogen prism white light source If white light is passed through a sample of hydrogen gas, certain selected wavelengths of light are absorbed by the gas. If the gas is heated until it glowed, the same wavelengths of light are emitted by the gas. Dark and Bright Line Spectra
6/17/2015 A Possible Solution A unified theory explaining these facts was proposed by Niels Bohr in An atom consists of a positive nucleus surrounded by electrons moving in spherical orbits. “planetary model” of the atom
6/17/2015 The Bohr Model of the Atom A Break From Classical Mechanics The electrons continuously circle the nucleus without losing energy. The electron does not lose energy in a degenerating orbit until it crashes into the nucleus. This represents a break from classical physics since any acceleration (including centripetal) is expected to require some energy.
6/17/2015 The Bohr Model of the Atom Radiation (light) is emitted when an electron in a higher energy orbit moves to a lower energy orbit If energy is absorbed the electron moves from a lower to a higher energy orbit. energy difference = energy absorbed or emitted
6/17/2015 Energy associated with a spectral line = - R nn H () Other Things To Consider integers The spectral lines of hydrogen can be explained by the Rydberg equation. (1899) If white light is passed through a sample of hydrogen gas, certain selected wavelengths of light are absorbed by the gas. prism Rydberg constant for hydrogen
6/17/2015 Bohr Theory (1913) Accounted for two important developments Rutherford's experiment demonstrating the concept of the nucleus. + - Einstein's theory concerning the energy of a photon. E = h h = x 10 –27 erg·s = x 10 –34 J·s
6/17/2015 Bohr Theory (1913) Because only certain frequencies are absorbed or emitted only certain energy changes are allowed within the atom.
6/17/2015 Bohr Model of the Hydrogen Atom Planetary Model Only integral multiples of h/2 are allowed integer principal quantum number (1, 2, 3,..., ) 2 n h
6/17/2015 Bohr Model of the Hydrogen Atom Planetary Model electrons are allowed here electrons are not allowed here
6/17/2015 Bohr Model of the Hydrogen Atom Planetary Model Different orbits have different energies Lowest energy (most stable) 2nd most stable (n = 2) 3rd most stable (n = 3)
The energy difference between levels corresponds to the observed lines in the hydrogen spectrum Emission and Absorption are Opposite Processes Emission Absorption
Emission and Absorption are Opposite Processes Big absorption What happens if an electron moves to an orbit infinitely distant from the nucleus? IONIZATION
6/17/2015 Hydrogen Atom Energy Levels 4 1 2 3 Balmer Series RedViolet Frequency Visible Emission Spectrum of Hydrogen
6/17/2015 Horsehead Nebula in Orion 48 inch Schmidt Telescope - Hale Observatories
6/17/2015 Visible Solar Spectrum 13-foot Heliospectrograph, Mt. Wilson Observatory 11 22 33 44 5 Å Å Å 6900 Å6100
6/17/2015 A Caveat (Note of Caution) The Bohr Atom calculations and the Rydberg equation for electronic transitions only work for “hydrogen-like” species. One electron species: H, He +, Li 2+,...
6/17/2015 Niels Bohr (1913) (Danish Physicist) Postulated that electrons spin around the nucleus in an orbit. The energy differences between these orbits can be used to explain the various colors of light emitted and absorbed by gaseous elements.
6/17/2015 Erwin Schrodinger (1926) (Austrian Physicist) Developed the modern view of the atom, treating electrons as mathematical functions. sine and cosine wave functions. Louis de Broglie (1926) (French Physicist) Proposed that matter has both wave and particle properties.
6/17/2015 Standing Wave (General Equation - One Dimension) = wavelength = amplitude = displacement of the wave from origin d dd 44
6/17/2015 Schrödinger Equation (One Dimension) hh dd 8m8m dd + V = E Energy of a Particle mass position potential energy is a wave function which describes the particle
6/17/2015 Schrödinger Wave Equation (Three Dimensions) ( 2 x 2 2 y 2 2 z 2 mE h2h2 + ( = 0 To solve this equation in three dimensions for hydrogen, the energy (E) of the electron must take on certain (quantized) values related by integers. These integers are known as QUANTUM NUMBERS. Quantum numbers need not be assumed (as was done by Bohr), but are required by the mathematics of the system.
6/17/2015 Wave Functions are composed on sine and cosine terms 2 is the probability of finding an electron at a specific location What is the probability of finding an electron at a node? The wave function ( ) has no physical significance
6/17/2015 A Mathematical Model of the Atom These wave equations give a "mathematical model" for the electron. the electron can be at many different places The likelihood (probability) of "finding" the electron at any point depends on Radial function (distance) Angular function (direction)
6/17/2015 Orbitals The region around a nucleus in which an electron has a probability of being located is called an orbital. Orbitals can vary in distance from the nucleus (radial function) direction (angular function)
6/17/2015 Wave Function ( 2 x 2 2 y 2 2 z 2 + V 2 m E = h2h2 The shape of the orbital and the energy of the electron is related to the wave function ( ). The electron is mathematically described by the wave function, the Schrödinger Equation is used to calculate the energy of that electron. The wave function is composed of radial and angular functions (in three dimensions).
6/17/2015 Orbitals With No Angular Dependence 1s 2s s orbitals have a spherical shape isotropic orbitals
6/17/2015 Orbitals With Angular Dependence p orbitals have a propeller shape 2p x x y z x y z 2p y x y z 2p z How can you distinguish p x from p y or p z ? Anisotropic orbitals the angular probability function is not the same in all directions
6/17/2015 Higher Energy Orbitals Higher energy levels correspond to higher wave functions including 3s, 3p x, 3p y, 3p z and d orbitals.
6/17/2015 d Orbitals x y z 3d xy x y z 3d yz x y z 3d xz x y z 3d x 2 -y 2 3d z 2 x y z
6/17/2015 Quantum Numbers Each electron in the orbital of the atom can be described by an unique combination of values known as quantum numbers. There are four different quantum numbers n, , m, m s
6/17/2015 Principal Quantum Number n=1 n=2 n=3 n=4 n=5 n=6 n=7 principal quantum number Larger values of n refer to higher energy orbitals (further from the nucleus) range: n = 1, 2, 3, …, The principal quantum number is related to the rows of the periodic table.
Angular Quantum Number = 0 s orbital (no angular dependence) = 1 p orbital = 2 d orbital = 3 f orbital range: = 0, …, n-1 Is it possible to have a 2f orbital? Is it possible to have a 3p orbital? This is the principal quantum number
6/17/2015 Magnetic Quantum Number What would be the names of these orbitals? m = - , …, 0, …, + Differentiates between orbitals with the same n and quantum numbers In a magnetic field aligned along the z-axis, an electron in the 2p z orbital will behave differently than an electron in the 2p x or 2p y orbitals. p-1p-1 p0p0 p+1p+1 How many f-orbitals are there in an f-orbital set?
6/17/2015 Spin Quantum Number m s = -1/2, +1/2 Each orbital can contain up to two electrons one aligned with an external field one aligned against an external field Which electron has lower energy?
6/17/2015 Quantum Numbers and the Periodic Table Identify the regions of the periodic table that correspond to the s, p, d and f orbitals s p d f
6/17/2015 Four Quantum Numbers Each electron in an atom can be described uniquely by the four quantum numbers. Three rules involving quantum numbers Pauli Exclusion Principle Aufbau Principle Hund's Rule
6/17/2015 Pauli Exclusion Principle Only one electron in an atom may have the same four quantum numbers. it’s like a house address /2
6/17/2015 Aufbau Principle In the ground state, electrons fill in the lowest available energy state (orbital) first it’s like the best house on the block
6/17/2015 Hund's Rule If more than one electron occupies a degenerate set of orbitals (orbitals of the same energy), then the electrons will fill in such a way as to maximize the number of orbitals filled. each electron would prefer to be single rather than be doubled up It is more stable for the spin of the electrons to be aligned in the same direction.
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