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Chapter 11 Atomic Theory: The Quantum Model of the Atom. Dual Characteristics of Light. Light has both wavelike properties and particle-like properties . In one hand, light can be considered as an electromagnetic radiation characterized by
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Dual Characteristics of Light Light has both wavelike properties and particle-like properties. In one hand, light can be considered as an electromagnetic radiation characterized by its velocity c (velocity in vacuum is 2.998 x 10 8 m/s ) its wavelength λ (lambda) or its frequency ν (nu) Wavelength of blue light is 470 nm Wavelength of red light is 700 nm c = λ . ν Long-wavelength has lower frequency than short-wavelength
Dual Characteristics of Light On the other hand, light can be considered as a stream of “particles” called photon , with energy given by E = h ν h is the Planck constant. Photons of blue light (higher frequency) are more energetic than red light (lower frequency).
Continuous Spectrum When white light is passed through a prism, it produces a spectrum which contains all wavelengths. A spectrum that contains all the wavelengths is called continuous spectrum.
Line Spectrum of Hydrogen When light emitted by hydrogen atoms is passed through a prism, we see only a few lines, each of which corresponds to discrete wavelength. The hydrogen spectrum is called a line spectrum.
Line Spectrum of Hydrogen The line spectrum of hydrogen indicates that only certain energies are allowed for the electron in the hydrogen atom.
Bohr Model of Hydrogen Atom In 1913 Niels Bohr proposed that the electron in a hydrogen atom moves around the nucleus only on certain allowed orbits and thus the energy of the electron in the hydrogen atom is quantized (electron energy can only have discrete set of values)
Bohr Model of Hydrogen Atom When an electron jumps from an excited state to a lower energy state, it releases the energy by emitting a photon of electromagnetic radiation. The energy of this photon is quantized, and thus corresponds to a line in the spectrum of the element.
Quantum Mechanical Model In 1927 Werner Heisenberg derived the uncertainty principle, which states that it is impossible to know simultaneously both the momentum (mv ) and the position of a particle with certainty. Therefore we cannot speak of the orbit of an electron around the nucleus
Quantum Mechanical Model In 1926, Ervin Schrodinger advanced the famous wave equation Hψ = E ψ E is the energy of the atom, and ψ(x,y,z) is called the wave function. The wave function ψ that describes the state of one electron is called orbital.
Quantum Mechanical Model The square of the orbital │ψ(x,y,z)│2is a direct measure of the probability density of finding the electron in that orbital at any particular point. The region of space in which an electron is most likely to be found can be visualized as the orbital itself.
Three orbital quantum numbers Atomic orbital are specified by three orbital quantum numbers: a) The principal quantum number n. n has integral values 1, 2, 3.... Orbitals with the same quantum number n are said to belong to the same shell. Each shell has n2orbitals As n increases, the orbital becomes larger and the electron spends more time further from the nucleus and the electron is less tightly bound to the nucleus.
Quantum number specification of orbital b) The orbital shape quantum number l (also called the angular momentum quantum number). For each value of n, l can have n integral values from 0 to n-1. Orbital with l = 0 is called orbital s Orbital with l = 1 is called orbital p Orbital with l = 2 is called orbital d Orbital with l = 3 is called orbital f Orbitals with the same quantum numbers n and l are said to belong to the same subshell
Quantum number specification of orbital c) orbital orientation quantum number ml For a given value of l, ml can have (2l+1) integral values between l and -l, including zero There are 2l+1 orbitals in each subshell Thus we have l = 0, one orbital ns l = 1, three orbitalsnp l = 2, five orbitalsnd l = 3, seven orbital nf.
Electron spin quantum number Spectral data indicate that electron has a magnetic moment with two possible orientations relative to an external magnetic field. Electron spin quantum number mshas been introduced to describe the two spin states of the electron. (ms can have only one of two values +1/2 and -1/2) The state of the electron is thus specified by four quantum numbers : n, l, ml and ms.
THE PAULI PRINCIPLE In an atom no two electrons can have the same set of four quantum number. Since electrons in the same orbital have the same values of n, l, ml they must have different values of ms. Thus an orbital can only hold two electrons with opposite spin(two different values of ms )
THE PAULI PRINCIPLE An orbital can only hold two electrons. Therefore the maximum number of electrons in a sublevel l is twice the number of orbitals in the sublevel, 2 (2l+1). The maximum number of electrons on level n is 2 n2
ORBITAL ENERGY Orbital energy depends on quantum numbers n and l. Energy levels with the same principal quantum number n are said to belong to a same principal level. Energy increases with increasing n. For each principal level there are one or more sublevels, which are ns, np, nd, nf... In general the energy order is ns< np < nd < nf
Electron Configuration Electron Configuration: A list of the number of electrons in each energy level in an atom. Two principles are used • At ground state the electrons fill the lowest-energy orbitals available. 2. No orbital can have more than two electrons.
Electron Configuration The number of electrons at any sublevel is shown by a superscript number.
Electron Configuration Example: Write the electron configuration of aluminum. Solution: First, locate Al in the periodic table. It is Group 3A and Period 3, the first element in the 3p block. Now write the electron configuration of its highest occupied energy sublevel: 3p1 (continued on the next slide)
Electron Configuration 3p1 To the left of what is written, we next list all lower-energy sublevels in order of increasing energy. 1s 2s 2p 3s 3p1 Now write the number of electrons that fill each sublevel. 1s22s22p63s23p1 Finally, check for the correct number of electrons: 2 + 2 + 6 + 2 + 1 = 13 = Z for Al
Electron Configuration Let’s compare the electron configuration of Al with the electron configuration of Ne: Al: 1s22s22p63s23p1 Ne: 1s22s22p6 Note that they are the same through the first 10 electrons, which are the n = 1 and n = 2 electrons.
Electron Configuration The Al configuration contains a Ne core: Al: 1s22s22p63s23p1 Since the n = 1 and n = 2 electrons are in the inner part of the atom and therefore not involved in bonding, we don’t need much detail about their configurations.
Electron Configuration A noble-gas core is commonly used in writing electron configurations Al: 1s22s22p63s23p1 Al: [Ne]3s23p1
Electron Configuration To Write an Electron Configuration Using a Noble-Gas Core: • Find the noble gas (Group 8A/18 element) with the highest atomic number that is less than the atomic number of the element for which the electron configuration is being written (last element of previous period). • Write the elemental symbol of the noble gas in square brackets. • Write the remainder of the electron configuration using the previously-described procedure.
Electron Configuration Exceptions There are two exceptions to the filling order of 4s and 3d • Chromium (Z = 24) Instead of [Ar]4s23d4 More stability if five dorbitals are half-filled. Electron configuration of chromium [Ar]4s13d5.
Electron Configuration Exceptions • Copper (Z = 29) Systematic prediction: [Ar]4s23d9 There is a special stability when all five dorbitals are filled. Electron configuration of copper: [Ar]4s13d10
Valence Electrons Valence Electrons: The s and p electrons of the highest-occupied energy level; the outermost electrons of an atom. Lewis Symbol:Element symbol surrounded by dots that represent the valence electrons of an atom of that element.
The Atomic Radii General Trends in Atomic Radii
First Ionization Energy First Ionization Energy: The energy required to remove one electron from a neutral gaseous atom of an element. Mg + 738 kJ Mg+ + e
Trends in the Periodic Table General Trends in Metallic Character
Homework Homework : 21, 31, 39, 43, 45, 47, 49, 57
