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Penetration & Shielding

    Penetration and shielding are two underlying principles in determining the physical and chemical properties of elements. We can predict basic properties of elements by using shielding and penetration characteristics to assess basic trends.

    1. 1. Penetration
      1. 1.1. Orbital Penetration
    2. 2. Shielding
    3. 3. Radial Distribution Graphs
    4. 4. Periodic Trends Due to Penetration and Shielding
    5. 5. Problem Set
      1. 5.1. Solutions
    6. 6. Outside Links
    7. 7. References
    8. 8. Contributors

    Penetration

    Penetration describes the proximity of electrons in an orbital to the nucleus. Electrons which experience greater penetration experience less shielding and therefore experience a larger Effective Nuclear Charge (Zeff) but shield other electrons more effectively.  Electrons in different orbitals have different wavefunctions and therefore different distributions around the nucleus.

    Orbital Penetration

    Different orbitals have greater nuclear penetration than others.  Penetration refers to how effectively electrons can get close to the nucleus.  The electron probability density for s-orbitals is highest in the center of the orbital, or at the nucleus.  If we imagine a dartboard that represents the circular shape of the s-orbital and if the darts landed in correlation to the probability to where and electron would be found, the geatest dart density would be at the 50 points region but most of the darts would be at the 30 point region.  When considering the 1s-orbital, the spherical shell of 53pm is represented by the 30 point ring. 

    Figure 1.  This figure shows that the s orbital has an electron probabilitydensity at the nucleus and that the p and d orbitals have nodes at the nucleus.

    Shielding

    Shielding describes the amount of screening from nuclear charge that one electron can do with respect to its neighboring electrons. Electrons that have greater penetration can get closer to the nucleus and effectively block out the charge from electrons that have less proximity.  For example, Zeff is calculated by subtracting the magnitude of shielding from the total nuclear charge. The value of Zeff will provide information on how much of a charge an electron actually experiences. 

    Figure 2.  This image shows how inner electrons can shield outer electrons from the nuclear charge.(http://www.grandinetti.org/Teaching/...tielectron.gif

    Because the order of electron penetration from greatest to least is s, p, d, f; the order of the amount of shielding done is also in the order s, p, d, f. 

    Radial Distribution Graphs

    A radial distribution function graph describes the distribution of orbitals with the effects of shielding.

    Figure 3.  Radial Distribution Function: http://physchem.ox.ac.uk/~hill/tutor...tomorb_rdf.png

    The small peak of the 2s orbital shows that the electrons in the 2s orbital are closest to the nucleus. Therefore, it is the electrons in the 2p orbital of Be that are being shielded from the nucleus, by the electrons in the 2s orbital.

    The following is the radial distribution of the 1s and 2s orbitals. Notice the 1s orbital is shifted to the right, while the 2s orbital has a node. The shift is due to the proximity of the electrons to the nucleus in the 1s orbital. Nodes may be determined by the formula: {(n-L-1)=nodes}, where "n" describes the "shell", or energy level the electrons reside, and "L" describes the orbital's angular momentum, or the "shape" of the orbital. Recall that L=0 corresponds to the s-orbital, L=1 to p-orbital, L=2 to d-orbital, and L=4 to f-orbital, and the s-shell consists of 1 atomic orbital, p-shell to 3 atomic orbitals, d-shell to 5, and f-shell to 7.
     

    Periodic Trends Due to Penetration and Shielding

    A) Effective Nuclear Charge (Zeff)

    The effective nuclear charge increases from left to right and increases from top to bottom on the periodic table.

    B) Atomic Radius

    The atomic radius decreases from left to right, and increases from top to bottom.

    C) Ionization Energies

    The ionization energies increase from left to right, and decrease from top to bottom.

    E) Electronegativity

    The electronegativity of the elements is highest near flourine. In general, it increases from left to right and decreases from top to bottom.


    Penetration and shielding are important factors in interpreting trends from the periodic table. Try these problems to test your knowledge of these concepts.

    Problem Set

    Question 1: Which oribtal is more effective in screening?

    1s or 2p?

    Question 2: T/F The greater the penetration of an orbital, the greater the screening capability of that orbital.

    Question 3: Find the Zeff of

    a.Mg

    b. C

    c. F

    d. Ca
    Question 4: Which of these have the smallest electron affinity? B, C, N, O, or F.
     

    Solutions

    1. 1s

    2. T

    3.

    a. 12-2 =10

    b. 6-4=2

    c. 9-7=2

    d. 20-2=18

    4.B

    References

    1. Petrucci, Ralph H., William S. Harwood, F. Geoffrey Herring, and Jeffry D. Madura. General Chemistry: Principles and Modern Applications, Ninth Edition. Pearson Education Inc. Upper Saddle River, New Jersey: 2007.

    Contributors

    • Sidra Ayub (UCD)

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