Electrons/bonding and quantum numbers

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Bennett Holland
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Electrons/bonding and quantum numbers Electrons, Atomic Orbitals, and Energy Levels In an atom, the number if electrons equals the number if protons in the nucleus.

1 Electrons/bonding and quantum numbers Electrons, Atomic Orbitals, and Energy Levels In an atom, the number if electrons equals the number if protons in the nucleus. Thus an electrically neutral carbon atom has six electrons, and an oxygen atom has eight electrons. The negatively charged electrons are very much smaller than are protons and neutrons and add very little to the mass if an atom. In addition, electrons are in constant motion. Because each electron's negative charge is equal to the positive charge of each proton an isolated atom of any element is said to be electrically balanced, or neutral. Electrons are so small that if we could collect and weigh then just 1.0 gram (g) of electrons would contain 10 x electrons. Although the mass of an atom is concentrated in the protons and neutrons, in the nucleus, the atom's properties are based on the electrons. These tiny negatively charged particles occupy a "volume" as they move around the nucleus. Electrons "move" around the nucleus of the atom, but why don't they fly off into space? And what path do they follow? It is the electrical attraction of the positively charged protons in the nucleus and the negatively charge electrons that prevents them from flying off. At the same time electrons are repelled by one another. According to the accepted model of atomic structure, electrons are confined in "atomic orbitals" specific to dimensional zones around the nucleus. The path of an electron cannot be precisely defined; in other words we can never say exactly where an electron will be or how fast it is moving. An atomic orbital is best defined as a cloud-like region in which there is a 90% probability of finding the electron in motion around the nucleus. An orbital that contains two electrons - the maximum number possible is said to be filled. The orbital that is closest to the nucleus is filled first. This orbital, the one at the lowest energy level, is spherical and is called the "1s" orbital. At the next higher energy level are four orbitals, capable of holding a total of eight electrons. The "2s orbital is like the "1s" orbital, spherical. The other three second-level orbitals, each shaped like a "dumbbell" are termed "2p" orbitals. Only two electrons can occupy an orbital at any one time. Therefore, the more electrons an atom has the more orbitals it posses. Atoms with more than two electrons have a series of orbitals at increasing distances from the nucleus. Each atomic

2 orbital and the electrons in it are associated with a specific amount of energy, and the farther an electron is from the nucleus the greater its energy (very important). The third energy level has a capacity to accommodate eighteen electrons and still higher energy levels can hold increasing numbers of electrons in greater numbers of orbitals. The distribution of electrons among orbitals is governed by four basic rules. 1) An electron will occupy the lowest available energy level. 2) Lower energy level orbitals are filled completely before higher energy level orbitals are occupied. 3) In any one energy level, a simpler orbital will be filled before an orbital of more complex shape is occupied. 4) Orbitals of similar shape at the same energy level must have one electron each before any of them can be filled. Quantum Numbers to Orbitals Chemists recognize s, p, d and f-orbitals. The shape, phase & electron occupancy of these orbitals are described by four quantum numbers: n The principal quantum number l The subsidiary or azimuthal or angular momentum or orbital shape quantum number ml The magnetic quantum number ms The electron spin quantum number Electrons enter and fill orbitals according to four rules: Pauli Exclusion Principal Aufbau or Build-up Principle Hund's Rule Madelung's Rule Orbitals can contain a maximum of two electrons which must be of opposite spin Electrons enter and fill lower energy orbitals before higher energy orbitals. When there are degenerate (equal energy) orbitals available, electrons will enter the orbitals one-at-a-time to maximize degeneracy, and only when all the orbitals are half filled will pairing-up occur. This is the rule of maximum multiplicity. Orbitals fill with electrons as n + l, where n is the principal quantum number and l is the subsidiary quantum number. This rule 'explains' why the 4s orbital has a lower energy than the 3d orbital, and it gives the periodic table its characteristic appearance.

3 Certain 'magic' numbers of electrons exhibit energetic stability: 2, 10, 18, 36, 54, 86 and, one assumes, 118, are associated with the Group 18 (8A) the noble gases: He, Ne, Ar, Kr, Xe, Rn & Uuo. The 'magic' numbers inevitably arise from the underlying quantum mechanics, but as Richard Feynman told us (here): "I think I can safely say that nobody understands quantum mechanics." We can predict quantum mechanical patterns, but we don't know why we can predict the patterns. We do not understand QM in terms of a deeper theory. Quantum Patterns The pattern of orbital structure can be mapped onto the two dimensions of paper in many different ways. Some mappings emphasize how the orbitals are ordered and filled with electrons, others stress how the chemical elements and their orbitals are ordered with respect to atomic number Z. Each tells us something different about atomic orbital structure and/or elemental periodicity. Orbital Filling The sequence of orbital filling is, from the bottom of this diagram, upwards:

4 Electron Shells Another way to order electron shell filling is shown below. As electrons are added, the quantum numbers build up the orbitals. Read this diagram, from the top downwards: Quantum Number n n=1 n=2 n=3 n=4 n=5 n=6 n=7 Elements by Orbital, And Some Subtleties... The electronic structure can be illustrated adding electrons to boxes (to represent orbitals). This representation shows the Pauli Exclusion Principle, the Aufbau principle and Hund's rule in action. [note: There are some subtle effects with the d block elements chromium, Cr, and copper, Cu. Hund's rule of maximum multiplicity lowers the energy of the 3d orbital below that of the 4s orbital, due to the stabilization achieved with a complete and spherically symmetric set of five 3d orbitals containing five or ten electrons. Thus, Chromium has the formulation: [Ar] 3d 5 4s 1 and not: [Ar] 3d 4 4s 2 Copper has the formulation: [Ar] 3d 10 4s 1 and not: [Ar] 3d 9 4s 2 ]

LABELING ELECTRONS IN ATOMS

Date: Name: LABELING ELECTRONS IN ATOMS The location of each electron in an atom is determined by a few different factors. Each factor is represented by a QUANTUM NUMBER. Prediction: What do you think