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- 1. Chapter 1 Atoms, Molecules & Chemical bonding Introduction Quantum Theory Atomic Orbitals Electronic Configuration Prepared by: Mrs Faraziehan Senusi PA-A11-7C Molecular Orbitals Bonding and Intermolecular Compounds David P. White Prentice Hall © 2003
- 2. Quantum Theory Hydrogenic Orbitals Atomic Orbitals Wave functions Shells and subshells David P. White Prentice Hall © 2003
- 3. Lesson Plan At the end of this topic, the students will be able: To describe atomic orbitals. To write electronic configurations To explain the bonding between different atoms To explain the interactions between molecules David P. White Prentice Hall © 2003
- 4. Quantum Mechanics and Atomic Orbitals • Schrödinger proposed an equation that contains both wave and particle terms. • The important point is that each solution of the Schrödinger wave equation () describes a possible energy state for the electrons in a hydrogen atom. • Each solution is described by a set of quantum numbers. • Solutions of the Schrödinger equation also tell us about the shapes and orientations of the probability distributions of the electrons. David P. White Prentice Hall © 2003
- 5. Quantum Mechanics and Atomic Orbitals • The square of the wave function, gives the probability of finding the electron, that is, gives the electron density for the atom. • Each solution to the equation (that is, each energy state of the atom) is associated with a given wave function, also called an atomic orbital. • Atomic orbital can be thought as the wave function of an electron in an atom. • An orbit is an electron’s path around the nucleus whereas, an orbital is a mathematical function with no direct physical meaning. David P. White Prentice Hall © 2003
- 6. Quantum Mechanics and Atomic Orbitals An atomic orbital is specified by 3 quantum 1. 2. 3. numbers to describe the distribution of : electrons in hydrogen and other atoms. Principal Quantum Number, n, related to the size of the orbital. This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. The higher the value of n, the higher the energy level. Orbital Angular Momentum (or, Azimuthal) Quantum Number, l. (related to shape of orbital). This quantum number depends on the value of n. The number of l value = the number of n value. The values of l begin at 0 and increase to (n - 1). We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3, respectively). Usually we refer to the s, p, d and f-orbitals. Magnetic Quantum Number, ml related to orientation in space. This quantum number depends on l. The magnetic quantum number has integral values between -l and +l. The number of possible ml values equals the number of orbitals, which is 2l+1 for a given l value. David P. White Prentice Hall © 2003
- 7. Quantum Mechanics and Atomic Orbitals Summarizes the hierarchy among the three quantum numbers: David P. White Prentice Hall © 2003
- 8. Quantum Mechanics and Atomic Orbitals Example What values of the angular momentum (l) and magnetic (ml) quantum numbers are allowed for a principal quantum number (n) of 3? How many orbitals exist for n = 3? Determining l values for n = 3, l = 0,1,2 Determining ml for each l value: • For l = 0, ml = 0 • For l = 1, ml = -1, 0, +1 • For l = 2, ml = -2,-1,0,+1,+2 There are nine ml values, so there are nine orbitals with n = 3. The total number of orbitals for a given n value is n2, and for n = 3, n2 = 9. David P. White Prentice Hall © 2003
- 9. Quantum Mechanics and Atomic Orbitals The energy states and orbitals of the atom are described with specific terms and associated with one or more quantum numbers: Shell/Level - The atom's energy levels, or shells, given by the n value: the smaller the n value, lower the energy level and the greater probability of the electron being closer to nucleus. David P. White Prentice Hall © 2003 are the the the
- 10. Quantum Mechanics and Atomic Orbitals Subshell/Sublevel - The atom's levels contain sublevels, or subshells, which designate the orbital shape. Each sublevel has a letter designation: l = 0 is an s subshell l = 1 is a p subshell l = 2 is a d subshell l = 3 is an f subshell The letters derived from the names of spectroscopic lines: sharp, principal, diffuse and fundamental Subshells are named by joining the n value and the letter designation. For example, n=2 and l=0 is called 2s subshell. David P. White Prentice Hall © 2003
- 11. Quantum Mechanics and Atomic Orbitals Orbital – Each allowed combination of n, l and ml values specifies one of the atom’s orbitals to describe the shape, size and the spatial orientation. The value of n = the number of possible l values (an integer from 0 to n-1). So, when n = 2, l will have only two values, 0 and 1. The number of orbitals in each subshell is 2l+1 for a given l value. One s orbital (l=0), 3p orbitals (l=1) and 5d orbitals (l=2) and 7f orbitals (l=3). David P. White Prentice Hall © 2003
- 12. Shapes of Atomic Orbitals • Each sublevel of the H atom consists of a set of orbitals with characteristic shapes. The s Orbital • An orbital with l = 0 has a spherical shape with the nucleus at its center and is called an s orbital. • The H atom's ground state, for example, has the electron in the 1s orbital, and the electron probability density is highest at the nucleus. • An s orbital has a spherical shape, so it can have only one orientation and, thus, only one value for the magnetic quantum number: for any s orbital, ml = 0. David P. White Prentice Hall © 2003
- 13. Shapes of Atomic Orbitals The s-Orbitals David P. White Prentice Hall © 2003
- 14. Shapes of Atomic Orbitals The p Orbital • • • • • An orbital with l = 1, called a p orbital, has two regions of high probability, one on either side of the nucleus. The orbitals are dumbbell shaped. There are three p-orbitals px, py, and pz. The three p-orbitals lie along the x-, y- and z- axes. The letters correspond to allowed values of ml of -1, 0, and +1. David P. White Prentice Hall © 2003
- 15. Shapes of Atomic Orbitals The p - Orbitals David P. White Prentice Hall © 2003
- 16. Shapes of Atomic Orbitals The d Orbital • An orbital with l = 2 is called a d orbital. • There are five possible ml values for the l = 2 value: -2, -1, 0, + 1, and +2. Orbitals with Higher l Values • There are seven f orbitals (2l+1=7), each with a complex, multilobed shape. David P. White Prentice Hall © 2003
- 17. Quantum Mechanics and Atomic Orbitals • Thus, the three quantum numbers that describe an orbital express its size (energy), shape, and spatial orientation. David P. White Prentice Hall © 2003
- 18. Quantum Mechanics and Atomic Orbitals Example • The 2s sublevel has only one orbital, and its quantum numbers are n = 2, l = 0, and ml = 0. • The 3p sublevel has three orbitals: n = 3, l = 1, and ml = -1; n = 3, l = 1, and ml = 0; n = 3, l = 1, and ml = +1. David P. White Prentice Hall © 2003
- 19. Quantum Mechanics and Atomic Orbitals Example How many orbitals exist for n = 3? For n = 3, l will have 3 values, i.e., 0, 1 and 2. For l = 0, ml will have 0 value (0) For l = 1, ml will have 3 values (-1, 0 and +1) For l = 2, ml will have 5 values, -2 through 0 to +2. (-2, -1, 0 ,+1 and +2). There are 9 ml values which means 9 orbitals. In other words, n2=32=9. David P. White Prentice Hall © 2003
- 20. Quantum Mechanics and Atomic Orbitals • A fourth quantum number – the spin quantum number. • The spin quantum number, ms, refers to the spin of an electron and the orientation of the magnetic field produced by this spin. • For every set of n, l, and ml values, ms can take the value + ½ or –½ : ms = ½ • Each atomic orbital can accommodate no more than two electrons, one with ms= + ½ and another with ms= –½ . David P. White Prentice Hall © 2003
- 21. Quantum Mechanics and Atomic Orbitals • Thus, each electron in an atom is described completely by a set of four quantum numbers: the first three describe its orbital, and the fourth describes its spin. David P. White Prentice Hall © 2003
- 22. Quantum Mechanics and Atomic Orbitals • Spin is an intrinsic property of an electron and this is another quantum number besides the other three. This is not a property of the orbitals. • A beam of atoms was passed through a slit and into a magnetic field and the atoms were then detected. • Two spots were found: one with the electrons spinning in one direction and one with the electrons spinning in the opposite direction. David P. White Prentice Hall © 2003
- 23. Quantum Mechanics and Atomic Orbitals David P. White Prentice Hall © 2003

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