Inorganic Chapter1

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    Chapter 1 - Basic Concepts: atoms

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    Charge Symbol Mass (kg)Charge Symbol Mass (kg) Mass (Amu) DiscoveryMass (Amu) Discovery

    Proton +1 p+ 1.67310-27 1.00732 1919, Rutherford

    Neutron 0 n0 1.67510-27 1.00870 1932, Chadwick

    Electron -1 e- 9.11010-31 0.000549 1897, Thomson

    Atomic and Mass Numbers

    12

    6C

    SymbolMass number

    Atomic number(optional)

    Atomic number: equal to the number of protons in the

    nucleus. All atoms of the same element have the samenumber of protons. Denoted by Z.

    Mass number: equal to the sum of the number ofprotons and neutrons for an atom.

    Atomic mass unit (amu) is 1/12 the mass of12C (1.660 10-27 kg)

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    The atomic mass is the weighted average mass, of the naturally

    occurring element. It is calculated from the isotopes of an element

    weighted by their relative abundances.

    atomic mass = fractionAmA + fractionBmB + . . .

    Allotropes

    element's atoms are bonded together in a different manner

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    Successes in early quantum theory

    ==

    22

    '

    111

    nn

    R

    where R is theRydberg constant forH, 1.097105 cm-1

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    =h

    mv

    where h is Plancksconstant,6.62610-34 Js

    (x) (mv) h

    4

    Uncertainty Principle

    Wave Nature of Matter

    Schrdinger wave equation

    The probability of finding an electron at a given point in space isdetermined from the function 2 where is the wavefunction.

    0)(8

    2

    2

    2

    2

    =+

    VEh

    m

    dx

    dwhere m = mass, E= totalenergy, and V= potentialenergy of the particle

    1d

    3d 0)(8

    2

    2

    2

    2

    2

    2

    2

    2

    =+

    +

    +

    VE

    h

    m

    zyx

    where m = mass, E= totalenergy, and V= potentialenergy of the particle

    It is convenient to use spherical polar coordinates, withradial and angular parts of the wavefunction.

    ),()(),()(),,( ArRrzyx angularradialCartesian =

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    Atomic Orbitals

    A wavefunction is a mathematical function that contains detailedinformation about the behavior of an electron. An atomicwavefunction consists of a radial component R(r), and an angularcomponentA(,). The region of space defined by a wavefunction iscalled an atomic orbital.

    Degenerate orbitals possess the same energy.

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    -1122py

    0122pz

    +1122px

    0022s

    0011s

    Angular part of

    the wavefunction,

    A(,)

    Radial part of the

    wavefunction,

    R(r)

    mllnAtomic

    Orbital

    re2

    2/)2(22

    1 rer

    2/

    62

    1 rre

    2/

    62

    1 rre

    2/

    62

    1 rre

    2

    1

    2

    1

    2

    )cos(sin3

    2

    )(cos3

    2

    )sin(sin3

    1s 2s

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    ns orbitals have (n-1 radial nodes), np orbitals have (n-2 radial nodes),ndorbitals have (n-3 radial nodes), nforbitals have (n-4 radial nodes).

    Radial Distribution Function,

    4r2R(r)2

    =1* d

    =12 d

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    Boundary surfaces for angular part of wavefunction, A(,)

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    Orbitals energies in hydrogen-like species

    2

    2

    nkZE = k = 1.312103 kJ mol-1

    Z = atomic number

    E

    n =3

    n =2

    n =1

    shell

    3s

    2s

    1s

    3p

    2p

    3d

    In the absence of an electric or magnetic field these atomic orbitalenergy levels are degenerate; that is they are identical in energy.

    Radial probability functions

    Probability density

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    Spin Quantum Number,Spin Quantum Number, mmss

    Spin angular number, s,determines the magnitude of thespin angular momentum of aelectron and has a value of .

    Since angular momentum is avector quantity, it must havedirection

    Magnetic spin quantumnumber, ms, can have values+1/2 or -1/2.

    An orbital is fully occupied when it contains two electrons which arespin paired; one electron has a value of ms = +1/2 and the other -1/2

    ml= 2 +2(h/2)

    ml= 1 +(h/2)

    ml= 0 0

    ml = -1 -(h/2

    )

    )2/(6 h

    )2/(6 h

    )2/(6 h

    )2/(6 h

    )2/(6 hm

    l= -2 -2(h/2)

    Resultantangularmomentum

    Resultantmagnetic

    moment

    Angular momentum, the inner quantum number, j, spin-orbit coupling

    z component of orbitalangular momentum

    orbital angularmomentum

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    1H ground state Many-electron atom

    Ground State Electronic ConfigurationsGround State Electronic Configurations

    Some irregularities: seeTable 1.3 in textbook

    The sequence thatapproximately describesthe relative energies ororbitals in neu t r a l atoms:

    1s < 2s < 2p < 3s < 3p