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I. Indeterminacy and Probability Distribution Maps

I. Indeterminacy and Probability Distribution Maps. A. Newton’s classical mechanics laws for particle behavior are deterministic We can predict exactly where a macroscopic particle is going to go if we know where it’s been

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I. Indeterminacy and Probability Distribution Maps

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  1. I. Indeterminacy and Probability Distribution Maps • A. Newton’s classical mechanics laws for particle behavior are deterministic • We can predict exactly where a macroscopic particle is going to go if we know where it’s been • This behavior correlates with what we see in everyday behavior of objects • B. Quantum Mechanics is based on Uncertainty and Probability: Indeterminate • We can’t predict exactly where an electron is going, or even where it is right now • This behavior does not correlate to everyday objects, but correctly predicts small particle behavior

  2. Solutions to the Schrodinger Equation • There are many, quantized solutions • These solutions are related through Quantum Numbers that are the results of how the solutions are arrived at. • These Quantum Numbers will eventually help us explain the shapes of orbitals, as well as the format of the Periodic Table • Preview:

  3. II. Quantum Numbers (QN) • Principal QN(n = 1, 2, 3, . . .) • Related to size of the atomic orbital (distance from the nucleus). • Larger n value indicates higher energy • Larger n value means electrons are less strongly bound to nucleus • Angular Momentum QN(l = 0 to n 1) • Relates to shape of the atomic orbital. • Each l number is assigned a letter • n = 3, l= 0, 1, 2 (s, p, and d orbitals in the third shell) • Magnetic QN(ml = l to  l) • Relates to orientation of the orbital in space relative to other orbitals. • 2. For l = 2, ml = -2, -1, 0, 1, 2 (Five d-orbitals)

  4. Electron Spin QN(ms= +1/2, 1/2) • Relates to the spin statesof the electrons. • Electrons are –1 charged and are spinning • Spinning charge creates a magnetic field • You can tell the direction of the spin by which way the magnetic moment lines up in an external magnetic field • The two possible spin directions are called +½ and –½

  5. Pauli Exclusion Principle • In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml, ms). • 2. Therefore, an orbital can hold only two electrons, and they must have opposite spins. • 3. Electrons can have the same n, l, and ml values • a) n = 3, l = 2 (d-orbital), ml= -2 (a single d-orbital) • b) That single d-orbital can only hold 2 e-, one with • ms = +1/2, and one with ms = 1/2

  6. III. Orbital Shapes and Energies • Atomic orbital shapes are surfaces that surround 90% of the total probability of where its electrons are • Look at l = 0, the s-orbitals • Basic shape of an s-orbital is spherical • centered on the nucleus • Basic shape is same for same l values • Nodes = areas of zero probability • Number of nodes changes for larger n • We will usually just use outer surface • to describe the shape of an orbital

  7. p-orbitals • There are no 1p orbitals (n = 1, l = 0 only) • 2p orbitals (n = 2, l = 1) have 2 lobes with a node at the nucleus • There are three different p-orbitals (l = 1, ml = -1, 0, 1) • 2px lies along the x-axis • 2py lies along the y-axis • 2pz lies along the z-axis • All three 2p orbitals have the same energy = degenerate • 3p, 4p, 5p, etc… have the same shape and number, just larger, internal lobes

  8. d-orbitals • There are no 1d or 2d orbitals (d needs l = 2, so n = 3) • 5 degenerate d-orbitals (ml = -2, -1, 0, 1, 2) • 4 of the d-orbitals have 4 lobes which lie in planes on or between the xyz axes: 3dxy, 3dxz, 3dyz, 3dx2-y2 • 1 is composed of 2 lobes and a torus-shaped area: 3dz2 • The 4d orbitals etc…are the same shape, only larger

  9. f-orbitals • n = 4, l = 3, ml = -3, -2, -1, 0, 1, 2, 3 • 7 f-orbitals in the fourth shell are degenerate • The f-orbital are only used for the lanthanides and actinides and are complex shapes. We won’t use them.

  10. Orbital Energies • Orbital energies are largely determined by • the n value: 3 > 2 > 1 for H atom (s = p) • But, for polyelectron atoms, the different • l values are not all degenerate (s ≠ p) • a. 2s is larger than 2p orbital • b. 2s “penetrates” the 2p, so is lower energy • c. Penetration effects help explain energy ordering

  11. The Phase of Orbitals • Waves can have + and – areas above and below the origin • The area above zero is called Positive Amplitude • The area below zero is call Negative Amplitude • The +/- have nothing to do with the electrical charge, it is just a way to mathematically differentiate between parts of orbitals • Spherical Nature of Atoms: • All the orbitals taken together = sphere

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