ATOMIC STRUCTURE PART 2

• ·        Bohr Planetary Model
  

In 1913, Niels Bohr proposed a theory for the electronic structure of the hydrogen atom that explained the line spectrum of this element. The hydrogen atom contains one electron and a nucleus that consists a single proton. Bohr’s theory includes the following points:

1.      The electron of the hydrogen atom can exist only in certain circular orbits (which are also called energy levels or shells). These shells are arranged concentrically around the nucleus. Each shell is designated by a letter (K, L, M, N, O…..) or a value of n (1, 2, 3, 4, 5…..).

2.      The electron has a definite energy characteristic of the orbit in which it is moving. The K level (n-1), the shell closest to the nucleus, has the smallest radius. An electron in the K level has the lowest possible energy since it is as close to the positive charge of the nucleus as is possible. With increasing distance from the nucleus (K, L, M, N, O; n- 1, 2, 3, 4, 5), the radius of the shell and the energy of an electron in the shell increase. Energy would have to be supplied to move the electron (which bears a negative charge) farther and farther away from the positive charge of the nucleus. No electron can have an energy that would place it between the permissible shells.

3.      When the electrons of an atom are as close to the nucleus as possible (for hydrogen, one electron in the K shell), they are in the condition of lowest possible energy, called the ground state. When the atoms are heated in an electric arc or Bunsen Flame, electrons absorb energy and jump to outer levels, which are higher energy states. The atoms are said to be in excited state.

4.      When an electrons falls back to a lower level, it emits a definite amount of energy. The energy difference between the high-energy state and the low-energy state is emitted in the form of a quantum of light. The light quantum has a characteristic frequency (and wavelength) and produces a characteristic spectral line.

• ·        The Quantum Mechanical Model of the Atom

Quantum mechanical model replaced the Bohr model of the atom.

§  Bohr model depicted electrons as particles in circular orbits of fixed radius.

§  Quantum mechanical model depicts electrons as waves spread through a region of space (delocalized) called an orbital.

§  The energy of the orbitals is quantized like the Bohr model.

§  Electrons exhibit wave-like behavior. The first evidence of the wave nature of electrons came through diffraction of electrons shown in 1927.

Orbitals

§  An orbital is the quantum mechanical equivalent of the location of an electron. This location is actually a region of space rather than a particular point.

§  Names of orbitals:

1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, etc.

 

Quantum Numbers

            Quantum numbers – used to name atomic orbitals.

• ·        Three quantum numbers used:

§  Principal quantum number, n (n= 1, 2, 3, 4, 5, …)

§  Secondary quantum number, l

§  Magnetic quantum number, m₁

• ·        The principal quantum number, n, defines the shell in which a particular orbital is found.

§  n must be a positive integer

§  n = 1 is the first shell, n = 2is the second shell, etc.

§  Each shell has different energies

§  The larger the value of n, the greater the average distance of an electron in the orbital from the nucleus and therefore the larger the orbital.

• The secondary quantum number, l, indexes energy differences between orbitals in the same shell in an atom.

• ·        l has integral values from 0 to n-1.

§  l specifies subshell

§  each shell contains as many l values as its value of n.

Table 6.1

Letter designations for the secondary quantum number
e-value Letter Designation	0 s	1 p	2 d	3 f	4 g

 

• ·        The third quantum number is the magnetic quantum number, m₁.

§  m₁ has integer values

§  m₁ maybe either positive or negative

§  m₁’s absolute value must be less than or equal to l

§  for l = 1, m₁ = -1, 0, +1

Table 6.2

Relationships among values of the different quantum numbers are illustrated. This table allows us to make another observation about quantum numbers. If we count the total number of orbitals in each shell, it is equal to the square of the principal quantum number, n2. Value of n                  values for l                            values for ml                         number of                               (Letter designation)                                                                  orbitals

1                                   0 (s)                                             0                                     1 2                                      0 (s)                                          0                                     1                                      1 (p)                                       -1, 0, 1                                 3 3                                   0 (s)                                             0                                     1                                      1 (p)                                       -1, 0, 1                                 3                                      2 (d)                                  -2, -1, 0, 1, 2                             5 4                                   0 (s)                                             0                                     1                                      1 (p)                                       -1, 0, 1                                 3                                      2 (d)                                  -2, -1, 0, 1, 2                             5                                      3 (f)                             -3, -2, -1, 0, 1, 2, 3                         7

Example Problem 6.5

            Write all the allowed sets of quantum numbers (n, l, and m_l) for a 3p orbital

Practice Problem

1. An orbital has a quantum numbers of n = 4, l = 2, m_l = -1. Which type of orbital (1s, etc.) is this?

          2. Write all of the allowed sets of quantum numbers (n, l, and m_l) for a 3d orbital.

3         3. An orbital has a quantum numbers of n = 3, l = 0. What must this orbital be?

4         4. Which of the following represent valid sets of quantum numbers?

                 (a) n=3, l=3, m_l=0

                 (b) n=2, l=1, m_l=0

                 (c) n=6, l=5, m_l= -1

                 (d) n=4, l=3, m_l= -4

Visualizing Orbitals 

•   S orbitals are spherical shape
•   P orbitals have two lobes separated by a nodal plane. (dumbbell shape)
•   D orbitals have more complicated shapes due to the presence of two nodal planes. (with 4 lobed)

•  Uncertainty Principle (Werner Heisenberg)

        §  States that it is impossible to determine both the position and momentum of an electron simultaneously and with complete accuracy.

 

The Pauli Exclusion Principle and Electron Configurations

• §  The spin quantum number, m_s, determines the number of electrons that can occupy an orbital.
• §  m_{s =} +½
• §  There are 2 values for m_s + ½ and -1/2

↑↓                          ↑

                          -1/2 (paired)              +1/2 (unpaired)

• §  Electrons described as “spin up” or “spin down”.

    Pauli Exclusion Principle – no two electrons in ana tom may have the same set of four quantum number.

• Two electrons can have the same values of n, l, and m_l, but different values of m_s.
• Two electrons maximum per orbital.
• Two electrons occupying the same orbital are spin paired. 
• 
  
  Orbital Energies and Electron Configurations
  
  
  
   Electrons in smaller orbitals are held more tightly and have lower energies
   Orbital size increases as the value of n increases
  As nuclear charge increases, orbital size decreases. Larger nuclear charges exert stronger attractive forces on the electrons, so the size of the orbitals will tend to decrease for higher atomic numbers.
  
  
  Electrons interact with other electrons as well as the positively charged nucleus.
  
  
  For electrons in larger orbitals, the charge “felt” is a combination of the actual nuclear charge and the offsetting charge of electrons in lower orbitals.
  ·        The masking of the nuclear charge is called shielding.
  ·        Shielding results in a reduced, effective nuclear charge.
  The energy ordering for atomic orbitals is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, and 7p.
   Electronic configurations – the distribution of electrons in the different shells and subshells or orbitals within the atom. The number of electrons of an atom can be taken from the atomic number of the elements.
  
  
  Maximum number of electrons for each sublevel;
  s = 2
  p = 6
  d = 10
  f = 14
  
  
  Hund’s Rule and the Aufbau Principle
  
  
  Aufbau principle – when filling orbitals, start with the lowest energy and proceed to the next highest energy level.
  Hund’s rule – within a subshell, electrons occupy the maximum number of orbitals possible.
  Electron configurations are sometimes depicted using boxes to represent orbitals. This depiction shows paired and unpaired electrons explicitly.
   
  1s                 2s                               2p
  ↑↓            ↑↓            ↑         ↑
  
  
   Example Problem 6.6
              What is the electron configuration of a sulfur atom?
  
  
  Practice Problem 6.6
              What is the electron configuration of a silicon atom?
  
  
  Practice Problem
              Write the electron configuration of the following then identify the four quantum numbers (n, l, m_l, and m_s).
  1.      Be (Z = 4)
  
  
  2.      B (Z = 5)
  
  
  3.      C (z = 6)
  
  
  4.      N (Z = 7)
• 
  
  
  
  Hund’s Rule and the Aufbau Principle
  §  A simplified depiction uses superscripts to indicate the number of electrons in an orbital set.
  ·       1s², 2s², 2p² is the electronic configuration for carbon.
  ·    Noble gas electronic configuration are used as a shorthand for writing electronic configuration.
  ·        Relates electronic structure to chemical bonding.
  ·       Electrons in outermost occupied orbitals give rise to chemical reactivity of the element.
  ·        [He] 2s² 2p² is the shorthand for carbon
  
  
  §  The inner electrons, which lie closer to the nucleus, are referred to as core electrons.
  ·        Core electrons can be represented by the noble gas with the same electronic configuration.
  ·        The outer electrons are usually referred to as valence electrons.
  ·        Valence electrons are shown explicitly when a noble gas shorthand is used to write electronic configurations.
    

Example Problem 6.7

            Rewrite the electron configuration for sulfur using the shorthand notation.

Practice Problem

            1. Use the shorthand notation to write the electron configuration for gallium.

 

The Periodic Table and Electronic Configurations

§  The periodic table and the electronic configurations predicted by quantum mechanics are related.

·        The periodic table is broken into s, p, d, and f blocks.

·        Elements in each block have the same subshell for the highest electron.

·        Structure of periodic table can be used to predict electronic configurations.

§  The shape of the periodic table can be broken down into blocks according to the type of orbital occupied by the highest energy electron in the ground state.

§  Then we determine the valence electrons by noting where the element sits within its own period in the table.

Representative element (main groups – s and p block):

            n = period

Transition elements (d-block):

            n = period – 1

Lanthanides and actinides (f-block):

            n = period – 2 

 

Example Problem 6.8

            Use the periodic table to determine the electron configuration of tungsten (W), which is used in the filament of most incandescent lights.

Practice Problem

            Use the periodic table to determine the valence configuration of the following:

a.      Cl

b.      Ca

c.      V

d.      La

Periodic Trends in Atomic Properties

§  Using the understanding of orbitals and atomic structure, it is possible to explain some periodic properties.

·        Atomic size

·        Ionization energy

·        Electron affinity

Atomic Size

§  The shell in which the valence electrons are found affects atomic size.

·        The size of the valence orbitals increases with n, so size must increase from top to bottom for a group.

·        As we go down a group, we observe an increase in atomic size.

·        As we go across a period, we observe a decrease in atomic size.

§  The strength of the interaction between the nucleus and the valence electrons affects atomic size.

·        The effective nuclear charge increases from left to right across a period, so the interaction between the electrons and the nucleus increases in strength.

·        As interaction strength increases, valence electrons are drawn closer to the nucleus, decreasing atomic size.

Example Problem 6.9

            Using only the periodic table, rank the following elements in order of increasing size: Fe, K, Rb, S, and Se.

Practice Problem 6

            Using only the periodic table, rank the following elements in order of increasing size: Cr, Cs, F, Si, and Sr. 

Ionization Energy

§  Ionization energy – the energy required to remove an electron from a gaseous atom, forming a cation.

·        Formation of X⁺ is the first ionization energy, X²⁺ would be the second ionization energy, etc.

X (g) → X^-(g) + e^-

·        Effective nuclear charge increases left to right across a period. So, ionization energy increases across a period

·        As valence electrons move further from the nucleus, they become easier to remove. So, ionization energy decreases as we move down a column in the periodic table.

Example Problem 6.10

            Using only the periodic table, rank the following elements in order of increasing ionization energy: Br, F, Ga, K, and Se.

Practice Problem

            Using only the periodic table, rank the following elements in order of increasing ionization energy: He, Mg, N, Rb and Si.

Electron Affinity

§  Electron Affinity – energy required to place an electron on a gaseous atom, forming an anion.

X (g) + e^- → X^- (g)

§  Electron affinities may have positive or negative values.

·        Negative values – energy released

·        Positive values – energy absorbed

§  Electron affinities increase (numerical value becomes more negative) from left to right for a period and bottom to top for a group.

§  The greater (more negative) the electron affinity, the more stable the anion will be.

·        Going across a period, electron affinity increases.

·        Going down a group, electron affinity decreases.


RECORDED LECTURES

The Periodic Table: Atomic Radius, Ionization Energy, and Electronegativity

https://www.youtube.com/watch?v=hePb00CqvP0&t=58s

Quantum Numbers, Atomic Orbitals, and Electron Configurations

https://www.youtube.com/watch?v=Aoi4j8es4gQ&t=21s

ONLINE PUBLISHED RESEARCH

An electrospray mass spectrometric and voltammetric study of horse heart cytochrome c in the presence of metal ions
http://www.sciencedirect.com/science/article/pii/S0020169397057757