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Unit 2-6 Quantum Mechanical model

Unit 2-6 Quantum Mechanical model. h 4 . (  x ) (  mv ) . The Uncertainty Principle. Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known:

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Unit 2-6 Quantum Mechanical model

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  1. Unit 2-6 Quantum Mechanical model

  2. h 4 (x) (mv)  The Uncertainty Principle • Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known: • In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!

  3. Quantum Mechanics • Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. • It is known as quantum mechanics.

  4. Schrodinger Wave Equation- no need to remember! • The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.

  5. Quantum Numbers • Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. • Each orbital describes a spatial distribution of electron density. • An orbital is described by a set of quantum numbers. You do NOT need to know the name and how to calculate the quantum numbers.

  6. An orbital is a region within an energy level where there is a probability of finding an electron. This is a probability diagram for the s orbital in the first energy level… Orbital shapes are defined as the surface that contains 90% of the total electron probability.

  7. Principal Quantum Number, n • The principal quantum number, n, describes the energy level (shell) on which the orbital resides. it denotes the probable distance of the electron from the nucleus. • The values of n are integers ≥ 0. • Number of electrons that can fit in a shell: 2n2

  8. Azimuthal Quantum Number, l • l defines the shape of the orbital. It describes the sublevel/subshell. • Allowed values of l are integers ranging from 0 to n − 1. • The maximum amount of subshells on each shell = n. • n=1 , s • n = 2, s and p • n= 3, s, p and d • We use letter designations to communicate the different values of l and, therefore, the shapes and types of sublevel/subshell.

  9. Azimuthal Quantum Number, l Silly professor dance funny

  10. Magnetic Quantum Number, ml • Describes the three-dimensional orientation of the orbital. • Therefore, on any given energy level, there can be up to one s orbital, three p orbitals, five d orbitals, seven f orbitals, etc.

  11. Magnetic Quantum Number, ml • Orbitals with the same value of n form a shell. • Different orbital types with the same shape, within a shell, are grouped into subshells.

  12. sOrbitals • Value of l = 0. • Only one orbital in each s subshell. • Spherical in shape. • Radius of sphere increases with increasing value of n.

  13. Sizes of sorbitals Orbitals of the same shape (s, for instance) grow larger as n increases… Nodes are regions of low probability within an orbital.

  14. pOrbitals • Value of l = 1. • Have two lobes with a node between them.

  15. dOrbitals • Value of l is 2. • Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.

  16. Energies of Orbitals • For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. • That is, they are degenerate.

  17. Energies of Orbitals • As the number of electrons increases, though, so does the repulsion between them. • Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate. But they are on the same subshell. • Beginning in the 3rd energy level, the energies of the sublevels begin to overlap.

  18. Spin Quantum Number, ms • The spin quantum number has only 2 allowed values. • Therefore, each orbital can only accomendate 2 e- maximum.

  19. Homework • Page 222 6.59.

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