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10.7 The Hydrogen Orbitals

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10.7 The Hydrogen Orbitals

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  1. 10.7 The Hydrogen Orbitals • In the Wave Mechanical model of the atom an orbital represents the space around the nucleus occupied by an electron. • An orbital is the probability distribution for an electron where it can be found 90% of the time (see fig 10.20, 10.24, 10.25).

  2. Hydrogen orbitals • The discrete energy levels of hydrogen are called principal energy levels and are labeled with an integer (1, 2, 3, 4 …) • The principal levels have sublevels which contain spaces (orbitals) for electrons (fig 10.22). Ex: 1s, 2s, 2p, 3s, 3d, etc • 1 = energy level, s = shape (sphere) • 2 = energy level, s = shape (sphere) • 2 = energy level, p = shape (lobed) • 3 = energy level, d = shape (fig 10.28)

  3. energy level 1 has one sublevel: • 1s has one orbital • energy level 2 has two sublevels: • 2s has one orbital • 2p has three orbitals (2px, 2py, 2pz) • energy level 3 has three sublevels: • 3s has one orbital • 3p has three orbitals (3px, 3py, 3pz) • 3d has five orbitals (fig 10.28) • energy level 4 has four sublevels: • 4s has one orbital • 4p has three orbitals (4px, 4py, 4pz) • 4d has five orbitals • 4f has 7 orbitals

  4. hydrogen also has energy levels above level 4 • an orbital is potential space for an electron • energy can excite the electron in the 1s orbital (ground state) and move it to a higher energy level (2s, 2p, 3s, etc.) further from the nucleus • when the excited electron returns to its lower energy orbital it gives off a photon of light with equal energy to the amount of energy it absorbed

  5. 10.8 The Wave-Mechanical Model: Further Development • Wave mechanics: Matter as waves • Light (photons) can be demonstrated to behave as either waves or particles. • Similarly, matter can behave as waves. • In 1923 Louis de Broglie proposed that a particle of mass can have wavelike properties. This meant that electrons can have a wave-particle duality, much like light does. • In 1926 Erwin Schroedinger worked out the mathematics of depicting electrons as waves: • An electron could only exist in different regions around a nucleus, meaning its energy was quantized. • The regions of stability were a complex interplay of the electrostatic field generated by charged electrons and atomic nuclei.

  6. The wave mechanical model applies to all atoms, not just hydrogen. • Electrons (in ground states, i.e., unexcited) are arranged in an atom’s orbitals following specific rules. • The Pauli exclusion principle: no more than two electrons of opposite spin (designated by ↑ ↓ ) can occupy an atomic orbital. • The Aufbau principle: electrons fill orbitals at the lowest possible energy level before filling higher levels (e.g., 1s before 2s, 2p before 3s, etc.)

  7. Order of filling orbitals • Hund’s Rule: electrons of the same spin are added to each orbital in a sublevel before a second electron of opposite spin is added

  8. Principal Components of the Wave Mechanical Model (see pg 293) • Atoms have a series of principal energy levels, n; which can equal 1, 2, 3, 4, . . . 2. The energy of the level increases as n increases. 3. Each principal energy level contains one or more types of orbitals, called sublevels.

  9. 4. The number of sublevels in a given principal energy level equals n. level 1 contains 1 sublevel level 2 contains 2 sublevels level 3 contains 3 sublevels and so on . . . 5. The n value is always followed with a letter indicating the shape of the orbital (s, p, d, f ). • An orbital can be empty or contain one or two electrons with opposite spin. • The shape of the orbital is a probability distribution for an electron in that orbital.

  10. 10.9 Electron Arrangements in First Eighteen Elements • Electrons are placed in various orbitals starting with n = 1, and continuing with n = 2, n = 3, and so on. • The orbital closest to the nucleus is the 1s. As n increases, the orbital becomes larger and the electron occupies space further from the nucleus. • Electron configurations show the electrons occupying orbitals in each energy level. • Orbital diagrams (box diagrams) show orbitals as boxes grouped by sublevels with arrows showing electrons.

  11. Valence electrons are the electrons in the outermost (highest) principal energy level of the atom. • These electrons are involved in forming chemical bonds • For main group (representative group) elements, those in groups 1A to 8A, the valence electrons are those in the outermost s and p sublevels of the atom. • The group number corresponds to the number of valence electrons. • Metals (groups 1A, 2A, 3A) lose their valance electrons to form cations. • Nonmetals (groups 5A, 6A, 7A) gain valence electrons to form anions. • In either case, an atom gains or loses electrons to form a more stable electron configuration – one with a full outer duet or octet of electrons. • Example:

  12. For the transition metals, the valence electrons come from the (n-1)d sublevel orbitals as well as the outermost principal energy level electrons. • Example: • Core electrons are the electrons not involved in bonding atoms to each other. • Example

  13. 10.10 Electron Configurations and the Periodic Table • The electron configuration of any element can be determined by understanding its position in the periodic table. See fig 10.31 • Some transition metals, however, do not follow the general pattern for placing electrons in orbitals. See fig 10.34. • Copper, for example, has the e-configuration [Ar]4s13d10 instead of the more logical [Ar]4s23d9 Why? • Stable electron configurations are preferred over less stable. Copper is more stable when it has10 electrons in its d sublevel, thereby filling it, rather than having a filled 4s sublevel and an unfilled 3d sublevel. • There are other unusual transition metal configurations, for the same reason, such as Cr, Ag, Pt, Au and others.

  14. In the case of chromium, 4s13d5 is more stable than 4s23d4 because both sublevels are half-filled rather than having a filled 4s and less than half-filled 3d. • Note that the ns and (n-1)d sublevels have very similar energy (e.g., 4s and 3d, 5s and 4d) • Is it now apparent why the 4s sublevel is filled before the 3d, or the 5s before the 4d?

  15. Summary of Wave-Mechanical Model and Valence-Electron Configurations. • The W-M model pictures electrons in an atom arranged in orbitals, with each orbital holding two electrons. • The same type of orbitals recur in going from one principal energy level to another. • This means valence electron configurations recur periodically. See fig 10.34 • Elements in particular groups (such as the alkali metals, halogens, etc.) have the same valence electron arrangement and, therefore, share similar chemical properties