## A Quantum Picture of the Atom, cont.

Let's review where we were last time, keeping in mind all of the calculations and models are actually for hydrogen, but they model larger atoms as has been confirmed with approximate calculations for other atoms.

### Electronic Energy Levels:

• We will designate the primary energy level, corresponding to the average radial distance of the electron from the nucleus as a shell, and give it the symbol n. The lowest possible energy level is then the ground state with n = 1.
• The value of n also gives the number of nodes in each of the orbitals in that shell, with each shell having one node at infinity, where:
• A node is a region of zero probability of finding an electron.
• Nodes can have two general geometries:
• radial (or spherical, since they describe a spherical shell at a specific radial distance from the nucleus), with each atom having at least one radial (spherical) node at infinity;
• angular (either planar, e.g. as in the planar p-node and diagonal d-nodes, or cone shaped, e.g. as in the cone-shaped nodes of the dz2 orbitals which results in the donut shaped orbitals).
• Shells with n > 1 may have subshells which are different geometrical patterns of electron distribution. Thus:
• The lowest energy pattern is spherical and given the designation s.
• The next lowest energy distribution is bi-lobed with a planar symmetry. It is given the designation p.
• The third lowest energy distribution has diagonal planes of symmetry and is designated d.
• The fourth lowest energy distribution is designated f. This is the highest subshell type occupied by ground state electrons in any atom, so we will not look any further (an infinite number of subshells exist in theory for excited states, but they are not important to our understanding).
• The average energies of the different subshells are the energy of the shell, thus when subshells are present the energy of the shell is split. For example, in the n=2 shell the 2s orbital becomes lower in energy than the shell, while the 2p orbitals become higher in energy.
• The regions of electron occupancy in subshells are called orbitals.
• For each shell there is one s orbital.

Atomic Orbitals Supplement More orbitals and some additional explanations.

# Quantum Numbers

This is an alternate way of designating the electrons in an atom. Each electron will have a unique set of quantum numbers.

• Pauli Exclusion Principle: No two electrons in the same atom can have the same value for all quantum numbers. (i.e. no two electrons can occupy the same state).
 Quantum Number Symbol Characteristic specified Information provided Possible values Principle quantum number n Shell Average distance from nucleus (r) 1, 2, 3, 4, ... Angular momentum (Azimuthal) quantum number l Subshell Shape of orbital 0, 1, 2, 3, ...n - 1 Magnetic quantum number ml Orbital Orientation of orbital - l ... 0 ... +l Spin quantum number ms Electron spin Spin direction ± 1/2

Note that the Pauli exclusion principle and electron spin mean that a maximum of two electrons may occupy a single orbital.

# The Periodic Table

Look at the Periodic Chart. The pattern arises due to a repetition or periodicity of chemical properties. The vertical columns of the charts are called groups, while the rows are referred to as periods.

 IA IIA IIIA IVA VA VIA VIIA VIIIA H He Li Be B C N O F Ne Na Mg IIIB IVB VB VI VIIB VIIIB IB IIB Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn

Note the numbering of the groups. The numbers from 1 - 18 are the internationally accepted numbers. We will also use the I - VIII "American" numbering system. Note that the "tallest" columns comprise what are referred to as the "representative elements" (IA - VIIIA).

Terms:

• Period: the rows of elements showing a repeating pattern of properties (e.g. Na - Ar).
• Group: a vertical column of elements on the table sharing a family resemblance of properties (e.g. Li - Fr).
• Representative elements: the elements of the s-block and p-block (blue and green on the table above).
• Transition metal elements: the elements of the d-block (yellow in the table above).
• Inner-transition metal elements: The f-block or Lanthanides and Actinides (not shown on the table above)
• Groups:
• IA = alkali metals;
• IIA = Alkaline earth metals;
• VIIA = Halogens (note the generic symbol of X standing for any halogen);
• VIIIA = Noble gases (older = inert gases).

You should know the terminology above.

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