Chapter 6: Electronic Structure of Atoms
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Chapter 6: Electronic Structure of Atoms. Light is a form of electromagnetic radiation (EMR) :. an oscillating charge, such as an electron, gives rise to electromagnetic radiation:. Electric Field. Magnetic Field. Chapter 6: Electronic Structure of Atoms.

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Chapter 6: Electronic Structure of Atoms

Light is a form of electromagnetic radiation (EMR):

  • an oscillating charge, such as an electron, gives rise to electromagnetic radiation:

Electric Field

Magnetic Field


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Chapter 6: Electronic Structure of Atoms

  • Both the Electric and the Magnetic field propagate through

  • space

  • In vacuum, both move at the speed of light(3 x 108 m/s)


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Chapter 6: Electronic Structure of Atoms

  • Electromagnetic radiation is characterized by

    • wavelength (), or frequency () and

    • amplitude (A)

l

A = intensity

l

l


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Chapter 6: Electronic Structure of Atoms

Frequency (n) measures how many wavelengths pass a point per second:

1 s


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Chapter 6: Electronic Structure of Atoms

Electromagnetic radiation travels at the speed of light:

c = 3 x 108 m s-1

Relation between wavelength, frequency, and amplitude:

c =l n



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Chapter 6: Electronic Structure of Atoms

RedOrangeYellowGreenBlueUltraviolet


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Chapter 6: Electronic Structure of Atoms

What is the wavelength, in m, of radiowaves transmitted by

the local radio station WHQR 91.3 MHz?


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Chapter 6: Electronic Structure of Atoms

A certain type of laser emits green light of 532 nm. What frequency does this wavelength correspond to?


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Chapter 6: Electronic Structure of Atoms

Classically, electromagnetic radiation (EMR) was thought to have only wave-like properties.

Two experimental observations challenged this view:

Blackbody radiation

Photoelectric Effect


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Chapter 6: Electronic Structure of Atoms

Blackbody radiation

  • Hot objects emit light

  • The higher T, the higher

  • the emitted frequency


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Chapter 6: Electronic Structure of Atoms

Blackbody radiation

prediction of classical theory

= there would be NO DARKNESS

Brightness

“ultraviolet catastrophe”

T2

T1

wavelength (l)

visible region


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Chapter 6: Electronic Structure of Atoms

Blackbody radiation

Max Planck (1858 - 1947)

  • light is emitted by oscillators

  • high energy oscillators require a minimum amount of energy to be excited:

    • E = h 

  • energy is not provided by temperature in “black body”


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    Chapter 6: Electronic Structure of Atoms

    Blackbody radiation

    frequency of oscillator

    E = h 

    Planck’s constant = 6.63 x 10-34 J s

    Energy of radiation is related to frequency, not intensity


    Slide15 l.jpg

    Chapter 6: Electronic Structure of Atoms

    What is the energy of a photon of electromagnetic radiation

    that has a frequency of 400 kHz?

    = 2.65 x 10-28 J


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    Chapter 6: Electronic Structure of Atoms

    Photoelectric Effect

    Albert Einstein (1879-1955)

    e-

    e-

    e-


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    Chapter 6: Electronic Structure of Atoms

    Photoelectric Effect

    Albert Einstein (1879-1955)

    e-

    e-

    e-

    e-

    • Light of a certain minimum frequency is required to dislodge electrons from metals


    Slide18 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Photoelectric Effect

    • Ability of light to dislodge electrons from metals is related to its frequency, not intensity

    E = h 

    • This means that light comes in “units” of h

    • Intensity is related only to the number of “units”

    • The h “unit” is called a quantum of energy

    • A quantum of light (EMR) energy = photon


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    Chapter 6: Electronic Structure of Atoms

    Relationship between Energy, Wavelength, and Frequency:


    Slide20 l.jpg

    Chapter 6: Electronic Structure of Atoms

    What is the energy of a photon of light of 532 nm?

    = 3.74 x 10-19 J


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    Chapter 6: Electronic Structure of Atoms

    Electromagnetic Radiation

    stream of particles

    (photons)

    wave

    or

    E = h n

    Whether light behaves as a wave or as a stream of photons depends on themethod used to investigate it !


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    Chapter 6: Electronic Structure of Atoms

    Understanding light in terms of photons helped understand atomic structure

    many light sources produce a continuous spectrum


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    Chapter 6: Electronic Structure of Atoms

    Thermally excited atoms in the gas phase emit line spectra

    continuous spectrum (all wavelengths together: white light)

    line spectrum (only some wavelengths: emission will have a color)


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    Rydberg constant

    1.097 x 107 m-1

    positive integers

    (e.g. 1,2,3, etc)

    Chapter 6: Electronic Structure of Atoms

    Photograph of the H2 line spectrum (Balmer series) in the visible region

    (1825-1898)

    Johann Balmer (1825-1898)


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    Chapter 6: Electronic Structure of Atoms

    Niels Bohr was the first to offer an explanation for line spectra

    Bohr Model of the Hydrogen Atom

    • Only orbits of defined energy and radii are permitted in the hydrogen atom

    • An electron in a permitted orbit has a specific energy and will not radiate energy and will not spiral into the nucleus

    • Energy is absorbed or emitted by the electron as the electron moves from one allowed orbit into another. Energy is absorbed or emitted as a photon of E = hn


    Slide26 l.jpg

    (1885-1962)

    Chapter 6: Electronic Structure of Atoms

    Niels Bohr was the first to offer an explanation for line spectra

    electron orbits

    n = 1

    n = 2

    n = 3

    n = 4

    n = 5

    n = 6

    nucleus

    Bohr’s Model of the Hydrogen Atom


    Slide27 l.jpg

    n = 6

    n = 5

    n = 4

    n = 3

    n = 2

    n = 1

    Chapter 6: Electronic Structure of Atoms

    Bohr’s Model of the Hydrogen Atom

    Energy

    absorption of a photon

    e

    Ground State

    nucleus


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    n = 6

    n = 5

    n = 4

    n = 3

    n = 2

    n = 1

    Chapter 6: Electronic Structure of Atoms

    Bohr’s Model of the Hydrogen Atom

    Energy

    e

    Ground State

    nucleus


    Slide29 l.jpg

    n = 6

    n = 5

    n = 4

    n = 3

    n = 2

    n = 1

    Chapter 6: Electronic Structure of Atoms

    Bohr’s Model of the Hydrogen Atom

    Energy

    “excited state”

    e

    Ground State

    nucleus


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    n = 6

    n = 5

    n = 4

    n = 3

    n = 2

    n = 1

    Chapter 6: Electronic Structure of Atoms

    Bohr’s Model of the Hydrogen Atom

    Energy

    e

    Ground State

    nucleus


    Slide31 l.jpg

    n = 6

    n = 5

    n = 4

    n = 3

    n = 2

    n = 1

    Chapter 6: Electronic Structure of Atoms

    Bohr’s Model of the Hydrogen Atom

    Energy

    e

    Ground State

    emission of a photon

    nucleus


    Slide32 l.jpg

    n = 6

    n = 5

    n = 4

    n = 3

    n = 2

    n = 1

    Chapter 6: Electronic Structure of Atoms

    Which of these transitions represents

    an absorption process?

    (a)

    (b)

    (c)

    Energy

    Which of these transitions involves the

    largest change in energy?

    Which of these transitions leads to the

    emission of the longest wavelength photon?

    Ground State

    Does this wavelength correspond to a high or low frequency?

    nucleus


    Slide33 l.jpg

    Transitions corresponding to

    the Balmer series

    Chapter 6: Electronic Structure of Atoms


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    Energy of electron in a given orbit:

    n = 6

    n = 5

    n = 4

    n = 3

    n = 2

    n = 1

    Chapter 6: Electronic Structure of Atoms

    n = Principal Quantum Number (main energy levels)

    h=Planck’s constant, c=speed of light, RH = Rydberg constant


    Slide35 l.jpg

    n = 6

    n = 5

    n = 4

    n = 3

    n = 2

    n = 1

    Chapter 6: Electronic Structure of Atoms

    For an electron moving from n = 4 to n = 2:


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    n = 6

    n = 5

    n = 4

    n = 3

    n = 2

    n = 1

    Chapter 6: Electronic Structure of Atoms

    For an electron moving from n = 4 to n = 2:

    DE = - 4.09 x 10-19 J


    Slide37 l.jpg

    n = 6

    n = 5

    n = 4

    n = 3

    n = 2

    n = 1

    Chapter 6: Electronic Structure of Atoms

    The energy of the photon emitted is:

    E = 4.09 x 10-19 J

    What wavelength (in nm) does this

    energy correspond to?

    l = 486 x 10-9 m

    = 486 nm


    Slide38 l.jpg

    n=3 → n=2

    n=4 → n=2

    n=6 → n=2

    n=5 → n=2

    Chapter 6: Electronic Structure of Atoms

    Balmer Series

    l = 486 nm


    Slide39 l.jpg

    Chapter 6: Electronic Structure of Atoms

    The Wave Behavior of Matter

    If light can behave like a stream of particles (photons)…

    … then (small) particles should be able to behave like waves, too

    For a particle of mass m, moving at a velocity v:

    De Broglie Wavelength

    e.g electrons have a wavelength (electron microscope!)


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    Chapter 6: Electronic Structure of Atoms

    The Uncertainty Principle

    Werner Heisenberg (1901-1976)

    and Niels Bohr


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    Chapter 6: Electronic Structure of Atoms

    The Uncertainty Principle

    It is impossible to know both the exact position and the exact

    momentum of a subatomic particle

    uncertainty in momentum, mv

    uncertainty in position, x


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    Chapter 6: Electronic Structure of Atoms

    Quantum Mechanics and Atomic Orbitals

    Erwin Schrödinger (1887-1961)


    Slide43 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Quantum Mechanics and Atomic Orbitals

    • Schrödinger proposed wave mechanical model of the atom

    • Electrons are described by a wave function, ψ

    • The square of the wave function, ψ2, provides information on

    • the location of an electron (probability density or electron density)


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    Chapter 6: Electronic Structure of Atoms

    Quantum Mechanics and Atomic Orbitals

    • the denser the stippling, the

    • higher the probability of finding

    • the electron

    • shape of electron density

    • regions depends on energy of

    • electron


    Slide45 l.jpg

    z

    y

    x

    Chapter 6: Electronic Structure of Atoms

    Bohr’s model:

    n = 1

    orbit

    electron circles around nucleus

    Schrödinger’s model:

    orbital

    n = 1

    or

    electron is somewhere

    within that spherical region


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    Chapter 6: Electronic Structure of Atoms

    Bohr’s model:

    • requires only a single quantum number (n) to describe an orbit

    Schrödinger’s model:

    • requires three quantum numbers (n, l, and m) to describe an orbital

    n: principal quantum number

    l : second or azimuthal quantum number

    ml: magnetic quantum number


    Slide47 l.jpg

    - energy of electron in a given orbital:

    Chapter 6: Electronic Structure of Atoms

    Schrödinger’s model:

    (1) n = principal quantum number (analogous to Bohr model)

    - the higher n, the higher the energy of the electron

    - is always a positive integer: 1, 2, 3, 4 ….


    Slide48 l.jpg

    - lis normally listed as a letter:

    Value of l: 0 1 2 3

    letter: spdf

    Chapter 6: Electronic Structure of Atoms

    Schrödinger’s model:

    (2)l = azimuthal quantum number

    - takes integral values from 0 to n-1

    e.g.

    n = 3

    - ldefines the shape of an electron orbital


    Slide49 l.jpg

    p-orbital

    (1 of 3)

    d-orbital

    (1 of 5)

    f-orbital

    (1 of 7)

    Chapter 6: Electronic Structure of Atoms

    Schrödinger’s model:

    z

    y

    x

    s-orbital


    Slide50 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Schrödinger’s model:

    (3) ml = magnetic quantum number

    - takes integral values from -lto +l, including 0

    e.g.

    l = 2

    - mldescribes the orientation of an electron orbital in space


    Slide51 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Shells:

    • are sets of orbitals with the same quantum number, n

    • a shell of quantum number n has n subshells

    Subshells:

    • are orbitals of one type within the same shell

    • total number of orbitals in a shell is n2


    Slide52 l.jpg

    n=3 shell

    4f subshell

    Chapter 6: Electronic Structure of Atoms

    3

    n =

    1

    2

    4

    l =

    0

    0, 1

    0, 1, 2

    0, 1, 2, 3

    1s

    2s, 2p

    3s, 3p, 3d

    4s, 4p, 4d, 4f

    ml =

    0

    0, -1,0,1

    0; -1,0,1; -2,-1,0,1,2

    0; -1,0,1; -2,-1,0,1,2; -3,-2,-1,0,1,2,3

    # orbitals

    in subshell

    1

    1

    3

    3

    5

    1

    3

    5

    1

    7

    Total # of

    orbitals

    in shell

    1

    4

    9

    16


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    Chapter 6: Electronic Structure of Atoms

    3s-room

    3p-room

    3deluxe-room

    3rd floor

    2s-room

    2promotion-room

    2nd floor

    standard-room

    1st floor


    Slide54 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Orbital energy levels

    in the Hydrogen Atom


    Slide55 l.jpg

    Chapter 6: Electronic Structure of Atoms

    What is the designation for the n=3, l=2 subshell ?

    How many orbitals are in this subshell ?

    What are the possible values for ml for each of these orbitals ?


    Slide56 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Which of the following combinations of quantum numbers

    is possible?

    n=1, l=1, ml= -1

    n=3, l=0, ml= -1

    n=3, l=2, ml= 1

    n=2, l=1, ml= -2


    Slide57 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Representation of Orbitals

    1s

    2s

    3s


    Slide58 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Representation of Orbitals

    2p orbitals


    Slide59 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Representation of Orbitals

    all three p orbitals


    Slide60 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Representation of Orbitals

    3d orbitals


    Slide61 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Which combination of quantum numbers is possible for the

    orbital shown below?

    (a) n=1, l=0, ml= 0

    (c) n=3, l=3, ml= -2

    (d) n=3, l=2, ml= -1

    (b) n=2, l=-1, ml= 1


    Slide62 l.jpg

    Chapter 6: Electronic Structure of Atoms

    There is a fourth quantum number that characterizes electrons:

    spin magnetic quantum number, ms

    ms can only take two values, +1/2 or -1/2


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    Chapter 6: Electronic Structure of Atoms

    Wolfgang Pauli (1900-1958)

    A. Einstein & W. Pauli


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    Chapter 6: Electronic Structure of Atoms

    Pauli’s Exclusion Principle:

    No two electrons in an atom can have the same set of 4 quantum numbers, n, l, ml, and ms

    For a given orbital, e.g. 2s, n, l, ml are fixed:

    n=2, l=0, ml =0

    => an orbital can only contain two electron if they differ in ms


    Slide65 l.jpg

    Chapter 6: Electronic Structure of Atoms

    A maximum of 2 electron can occupy one orbital, IF these two electrons have opposite spin:

    n=2, l=0, ml =0, ms = +1/2

    n=2, l=0, ml =0, ms = -1/2

    2s

    2p

    arrows pointing up/down indicate electron spin


    Slide66 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Energy levels in the hydrogen atom:

    all subshells of a given shell

    have the same energy


    Slide67 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Energy levels in many-electron atoms:

    • In many-electron atoms, the energy of an orbital increases with l, for a given n

    • In many-electron atoms, the lower energy orbitals get filled first

    • orbitals with the same energy are said to be degenerate


    Slide68 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Electron Configurations:

    Line Notation:

    1H

    1s1

    2He

    1s2

    1s22s1

    3Li

    1s22s2

    4Be

    1s22s22p2

    6C

    1s22s22p3

    7N

    10Ne

    1s22s22p6

    1s22s22p63s1

    11Na


    Slide69 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Electron Configurations:

    Hund’s Rule:

    For degenerate orbitals, the energy is minimized when the number of electrons with the same spin is maximized

    => degenerate orbitals (p, d, etc)

    get filled with one electron each first (same spin).

    1s22s22p3

    7N


    Slide70 l.jpg

    Chapter 6: Electronic Structure of Atoms

    the Aufbau Principle helps you to remember the order in which orbitals get filled:

    1s

    2s 2p

    3s 3p 3d

    4s 4p 4d 4f

    5s 5p 5d 5f

    6s 6p 6d 6f

    7s 7p 7d 7f


    Slide71 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Line notation

    1s22s22p63s23p2

    14Si

    [Ne]

    3s23p2

    Condensed line notation

    orbital diagram

    (no energy info)

    3

    d

    2

    p

    1

    “coreelectrons”

    s


    Slide72 l.jpg

    valence (outer shell) electrons”

    Chapter 6: Electronic Structure of Atoms

    Line notation

    1s22s22p63s23p2

    14Si

    [Ne]

    3s23p2

    Condensed line notation

    orbital diagram

    (no energy info)

    3

    d

    2

    p

    1

    s

    Valence electrons take part in bonding


    Slide73 l.jpg

    Chapter 6: Electronic Structure of Atoms

    What is the electronic structure of Cl?

    3s23p5

    [Ne]

    17Cl :

    valence electrons (7)

    3

    d

    2

    p

    1

    coreelectrons

    =

    electron configuration

    of the preceding noble gas

    s


    Slide74 l.jpg

    valence electrons (2)

    coreelectrons

    =

    electron configuration

    of the preceding noble gas

    Chapter 6: Electronic Structure of Atoms

    What is the electronic structure of Ca?

    [Ar]

    4s2

    20Cl :

    (4s orbital is filled before 3d !)

    4

    f

    3

    d

    2

    p

    1

    s


    Slide75 l.jpg

    coreelectrons

    =

    electron configuration

    of the preceding noble gas

    Chapter 6: Electronic Structure of Atoms

    What is the electronic structure of Br?

    [Ar]

    3d104s24p5

    35Br :

    (4s orbital is filled before 3d !)

    valence electrons (7)

    4

    f

    3

    For main group elements,

    electrons in a filled d-shell

    (or f-shell) are not valence

    electrons

    d

    2

    p

    1

    s


    Slide76 l.jpg

    Chapter 6: Electronic Structure of Atoms

    Does it matter in which order the electron configuration is written ?

    1s22s22p63s23p63d104s24p5

    ordered by orbital number

    35Br :

    or:

    1s22s22p63s23p64s23d104p5

    ordered by energy

    4

    f

    3

    d

    2

    p

    1

    NO, both are correct!

    s


    Slide77 l.jpg

    Chapter 6: Electronic Structure of Atoms

    What is the electron configuration of vanadium (V)?

    [Ar]

    3d34s2

    23V:

    (4s orbital is filled before 3d !)

    4

    f

    3

    d

    2

    valence electrons (5)

    p

    1

    coreelectrons

    =

    electron configuration

    of the preceding noble gas

    s


    Slide78 l.jpg

    [Ar]

    3d44s2

    is less stable than

    [Ar]

    3d54s1

    Chapter 6: Electronic Structure of Atoms

    What is the electron configuration of chromium (Cr)?

    [Ar]

    3d54s1

    24Cr:

    4

    f

    3

    d

    2

    p

    1

    s

    A half-filled or completely filled d-shell is a preferred configuration


    Slide79 l.jpg

    1s

    2p

    2s

    3p

    3d

    3s

    4p

    4s

    4f

    Chapter 6: Electronic Structure of Atoms


    Slide80 l.jpg

    Chapter 6: Electronic Structure of Atoms

    What is the electronic structure of the Ca ion?

    [Ar]

    4s2

    20Ca :

    [Ar]

    20Ca2+ :

    4

    f

    3

    d

    2

    p

    1

    s


    Slide81 l.jpg

    Chapter 6: Electronic Structure of Atoms

    • Metals tend to lose electrons to form cations

    • Nonmetals tend to gain electrons to form anions

    • Atoms tend to gain or lose the number of electrons

      needed to achieve the

      electron configuration of the closest noble gas


    Slide82 l.jpg

    Chapter 6: Electronic Structure of Atoms

    What is the electronic structure of the ion formed by Se?

    [Ar]

    3d104s24p4

    34Se :

    [Ar]

    3d104s24p6

    = [Kr]

    34Se2- :

    4

    f

    3

    d

    2

    p

    1

    s


    Slide83 l.jpg

    Chapter 6: Electronic Structure of Atoms

    What is the electronic structure of the ion formed by Br?

    [Ar]

    3d104s24p5

    35Br :

    [Ar]

    3d104s24p6

    = [Kr]

    35Br- :

    4

    f

    3

    d

    2

    p

    1

    s


    Slide84 l.jpg

    Chapter 6: Electronic Structure of Atoms

    What is the electronic structure of the ion formed by Rb?

    [Kr]

    5s1

    37Rb :

    [Kr]

    37Rb+ :

    5

    4

    f

    3

    d

    2

    p

    1

    s


    Slide85 l.jpg

    have the same electron configuration:

    37Rb+

    ,

    35Br-

    ,

    34Se2-

    , and 36Kr

    Chapter 6: Electronic Structure of Atoms

    37Rb+ :

    [Ar]

    3d104s24p6

    = [Kr]

    35Br- :

    [Ar]

    3d104s24p6

    = [Kr]

    34Se2- :

    [Ar]

    3d104s24p6

    = [Kr]

    they are isoelectronic


    Slide86 l.jpg

    a.

    b.

    c.

    d.

    Chapter 6: Electronic Structure of Atoms

    Which of the four orbital diagrams written below for nitrogen violates the Pauli Exclusion Principle?

    violates Hund’s rule

    (all spins must point in the same direction)

    violates Hund’s rule

    (degenerate orbitals get one electron each, first)

    doesn’t violate anything

    violates Pauli’s Exclusion Principle

    there are two same spin electrons in one orbital, i.e. all 4 quantum numbers are the same – which is impossible

    1s

    2s

    2p


    Slide87 l.jpg

    Chapter 6: Electronic Structure of Atoms

    What is the total number of orbitals in the fourth shell (n=4) ?

    a. 16 b. 12 c. 4 d. 3

    what is the total number of different s,p, d and f orbitals?

    n=4

    l = 0 1 2 3

    s p d f

    0

    -1,0,1

    -3,-2,-1,0,1,2,3

    ml =

    -2,-1,0,1,2

    one s + three p + five d + 7 f orbitals

    =

    16 orbitals

    (n2)


    Slide88 l.jpg

    Chapter 6: Electronic Structure of Atoms

    What is the number of subshells in the third shell (n=3) ?

    a. 18 b. 9 c. 3 d. 1

    How many different types of orbitals are there?

    n=3

    l = 0 1 2

    s p d


    Slide89 l.jpg

    Chapter 6: Electronic Structure of Atoms

    What is the electron configuration of the sodium cation, Na+ ?

    a. 1s22s22p63s1 b. 1s22s22p6

    c. 1s22s22p63s2 d. 1s22s22p7

    11Na+

    = 11 electrons -1 = 10 electrons

    1s2

    2s2

    2p6


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