The Wave Behavior of Matter the Wave Behavior of Matter

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The Wave Behavior of The Wave Behavior of Matter Matter The Uncertainty Principle • Knowing that light has a particle nature, it seems • Heisenberg’s Uncertainty Principle: on the mass scale reasonable to ask if matter has a wave nature. of atomic particles, we cannot determine exactly the • Using Einstein’s and Planck’s equations, de Broglie position, direction of motion, and speed simultaneously. h showed: λ = • For electrons: we cannot determine their momentum and mv position simultaneously. • de Broglie summarized the concepts of waves and •If ∆x is the uncertainty in position and ∆mv is the particles, with noticeable effects if the objects are small. uncertainty in momentum, then h • Problem 6.33 ∆x·∆mv ≥ 4π

The Wave Behavior of Matter The Wave Behavior of Matter

• Electron microscopy • Calculating the uncertainty in various objects (Problem • Problem 6.36 6.37)

1 Quantum Mechanics and Quantum Mechanics and Atomic Orbitals Atomic Orbitals Orbitals and Quantum Numbers • Schrödinger proposed an equation that contains both • If we solve the Schrödinger equation, we get wave wave and particle terms. functions and energies for the wave functions. • Solving the equation leads to wave functions. • We call wave functions orbitals. • The wave function gives the shape of the electronic • Schrödinger’s equation requires 3 quantum numbers: orbital (ψ). 1. Principal Quantum Number, n. This is the same as Bohr’s • The square of the wave function, gives the probability of n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. finding the electron (ψ2), • that is, gives the electron density for the atom.

Quantum Mechanics and Quantum Mechanics and Atomic Orbitals Atomic Orbitals Orbitals and Quantum Numbers 2. Azimuthal Quantum Number, l. This quantum number depends on the value of n. 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). Usually we refer to the s, p, d and f- orbitals.

3. Magnetic Quantum Number, ml. This quantum number depends on l. The magnetic quantum number has integral values between -l and +l. Magnetic quantum numbers give the 3D orientation of each orbital.

2 Quantum Mechanics and Quantum Mechanics and Atomic Orbitals Atomic Orbitals Orbitals and Quantum Numbers Orbitals and Quantum Numbers • Orbitals can be ranked in terms of energy to yield an Aufbau diagram. • Note that the following Aufbau diagram is for a single electron system. •As n increases, note that the spacing between energy levels becomes smaller.

Quantum Mechanics and Quantum Atomic Orbitals Quantum Mechanics and • Problems 6.42 and 6.44 Atomic Orbitals Orbitals and Quantum Numbers