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Transcript
Chapter 8 (Lecture 11) Atomic Orbitals The energy depends on the principal quantum number alone while wave function depend on the quantum numbers Thus, the energy level has a degenaracy of s-Orbitals The orbital spherically symmetric and and they have radial nodes Table shows real Hydrogenic orbitals in atomic units. p and d Orbitals The lowest energy solution deviating from spherical symmmetry is 2p orbitals. Consider functions: And The function The function is real and contains in chemical application this is designated as orbital are complex. Making use of equle Formula We obtain The orbital Periodic Table is like are real function it is known in chemistry orbital and can be expressed as . A block of the periodic table of elements is a set of adjacent groups. The term appears to have been first used (in French) by Charles Janet. The respective highest-energy electrons in each element in a block belong to the same atomic orbital type. Each block is named after its characteristic orbital; thus, the blocks are: s-block p-block d-block f-block g-block (hypotetical) The block names (s, p, d, f and g) are derived from the quality of the spectroscopic lines of the associated atomic orbitals: sharp, principal, diffuse and fundamental The following is the order for filling the "subshell" orbitals, according to the Aufbau principle, which also gives the linear order of the "blocks" (as atomic number increases) in the periodic table: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, ... The "periodic" nature of the filling of orbitals, as well as emergence of the s, p, d and f "blocks" is more obvious, if this order of filling is given in matrix form, with increasing principal quantum numbers starting the new rows ("periods") in the matrix. Then, each subshell (composed of the first two quantum numbers) is repeated as many times as required for each pair of electrons it may contain. The result is a compressed periodic table, with each entry representing two successive elements: (http://en.wikipedia.org/wiki/Block_%28periodic_table%29) 1s 2s 2p 2p 2p 3s 3p 3p 3p 4s 3d 3d 3d 3d 3d 4p 4p 4p 5s 4d 4d 4d 4d 4d 5p 5p 5p 6s 4f 4f 4f 4f 4f 4f 4f 5d 5d 5d 5d 5d 6p 6p 6p 7s 5f 5f 5f 5f 5f 5f 5f 6d 6d 6d 6d 6d 7p 7p 7p The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on farther and farther from the nucleus. The shells correspond with the principal quantum numbers (1, 2, 3, 4 ...) or are labeled alphabetically with letters used in the X-ray notation (K, L, M, …). Each shell can contain only a fixed number of electrons: The 1st shell can hold up to two electrons, the 2nd shell can hold up to eight (2 + 6) electrons, the 3rd shell can hold up to 18 (2 + 6 + 10), and the 4th shell can hold up to 32 (2 + 6 + 10 + 14) and so on. Since electrons are electrically attracted to the nucleus, an atom's electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a strict requirement: Atoms may have two or even three incomplete outer shells. (See Madelung rule for more details.) The electrons in the outermost occupied shell (or shells) determine the chemical properties of the atom; it is called the valence shell. Each shell consists of one or more subshells, and each subshell consists of one or more atomic orbitals. Subshells Each shell is composed of one or more subshells, which are themselves composed of atomic orbitals. For example, the first (K) shell has one subshell, called "1s"; the second (L) shell has two subshells, called "2s" and "2p"; the third shell has "3s", "3p", and "3d"; the fourth shell has "4s", "4p", "4d" and "4f"; the fifth shell has "5s", "5p", "5d", and "5f" and can theoretically hold more but the "5f" subshell, although occupied in actinides, is not filled in any element occurring naturally. The various possible subshells are shown in the following table: Subshell label l Max electrons 2(2l+1) Shells containing it Historical name s 0 2 Every shell sharp p 1 6 2nd shell and higher principal d 2 10 3rd shell and higher diffuse f 3 14 4th shell and higher fundamental g 4 18 5th shell and higher (theoretically) (next in alphabet after f)[3] An atom's electron shells are filled according to the following theoretical constraints: Subshell Shell Shell Subshell max max name name electrons electrons K 1s 2 2s 2 L M N 2 2+6=8 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 2 + 6 + 10 = 18 2+6+ + 10 + 14 = 32 4f 14 Magnetic Effects on Atomic Spectra—The Normal Zeeman Effect The Dutch physicist Pieter Zeeman showed the spectral lines emitted by atoms in a magnetic field split into multiple energy levels. It is called the Zeeman effect. Consider the atom to behave like a small magnet. Think of an electron as an orbiting circular current loop of I = dq / dt around the nucleus. The current loop has a magnetic moment μ = IA and the period T = 2πr / v. where L = mvr is the magnitude of the orbital angular momentum. The dipole has a potential energy: The angular momentum causes a precession of Where is aligned with the magnetic moment, and the torque between and is called a Bohr magneton. The potential energy is quantized due to the magnetic quantum number mℓ. When a magnetic field is applied, the 2p level of atomic hydrogen is split into three different energy states with energy difference of ΔE = μBB Δmℓ. mℓ Energy 1 E + μBB 0 E −1 E− μBB A transition from 2p to 1s