--THE QUANTUM MECHANICAL MODEL
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1 --THE QUANTUM MECHANICAL MODEL
2 Bohr s Energy Levels Electrons reside in certain energy levels Each level represents a certain amount of energy Low Energy levels: closer to nucleus High Energy levels: farther from nucleus Ground State: Electron is in the lowest possible energy level
3 Excited Atoms Excited Atom- has absorbed energy Unstable Atoms soon emit the same amount of energy they absorbed Energy seen as visible light (different colors)
4 The Quantum Mechanical Model Energy is quantized (comes in chunks) A quanta is the amount of energy needed to move from one energy level to another Since the energy of an atom is never in between there is a quantum leap in energy Erwin Schrodinger derived an equation that described the energy and position of electrons in an atom
5 Quantum Mechanical Model 1920s Louis de Broglie (electron has wave properties) Werner Heisenberg (Uncertainty Principle) Erwin Schrodinger (mathematical equations using probability, quantum numbers)
6 Louis de Broglie, (France, ) Wave Properties of Matter (1923) Since light waves have a particle behavior (as shown by Einstein in the Photoelectric Effect), then particles could have a wave behavior. Electrons act like waves confined to a certain space around a nucleus de Broglie wavelength E=hv Corresponds to quantized energies of Bohr s orbits
7 Electron Motion Around Atom Shown as a de Broglie Wave
8 Werner Heisenberg: Uncertainty Principle Things that are very small behave differently from things big enough to see The Quantum mechanical model is a mathematical solution Energy levels for electrons Orbits are not circular We can not know both the position and momentum of a particle at a given time. Can only know the probability of finding an electron a certain distance from the nucleus
9 Erwin Schrodinger, 1925 Quantum (wave) Mechanical Model of the Atom The atom is found inside a blurry electron cloud An area where there is a chance of finding an electron Four quantum numbers are required to describe the state of the hydrogen atom.
10 FYI: Schrodinger s Equations!!! y is called the wave function and indicates the probability of where an electron may be found.
11 The Electron Cloud The higher the electron density, the higher the probability that an electron may be found in that region.
12 Atomic Orbital: A region in space in which there is high probability of finding an electron. Within each energy level, Schrodinger s equation describes several shapes Shapes are called atomic orbitals (regions where there is a high probability of finding an electron)
13 Four Quantum Numbers Used to describe an electron in an atom. 1. Principal Quantum Number (n) 2. Orbital Quantum Number (l) 3. Magnetic Quantum Number (m) 4. Spin Quantum Number (s)
14 Principal Quantum Number, n Indicates main energy levels of electrons n = 1, 2, 3, 4 The maximum number of electrons in an energy level is 2n 2 Example: what is the maximum number of electrons that can be in the 5 th main energy level?
15 Orbital Quantum Number, l (Angular Momentum Quantum Number) Indicates shape of the orbital (sublevel) within an energy level l = n-1 lsublevel 0 s 1 p 2 d 3 f 4 g
16 Magnetic Quantum Number, m l Indicates the orientation of the orbital in space. S orbital is spherical and centered around nucleus, so there is only 1 possible orientation (m=0) P orbital can extend along x,y,or z axis so there are 3 p orbitals (m=-1 m= 0 m= 1) There are 5 different d orbitals in each d sublevel (m=-2 m=-1 m=0 m=1 m=2) 7 different f orbitals in each f sublevel
17 Magnetic Quantum Number Values of m l : integers -l to The number of values represents the number of orbitals. Example: for l= 2, m l = -2, -1, 0, +1, +2 Which sublevel does this represent? Answer: d l
18 Electron Spin Quantum Number, (m s or s) Indicates the spin of the electron (clockwise or counterclockwise). Values of m s: +1/2, -1/2
19 Example: List the values of the four quantum numbers for orbitals in the 3d sublevel. Answer: n=3 l = 2 m l = -2,-1, 0, +1, +2 m s = +1/2, -1/2 for each pair of electrons
20 List the values of the four quantum numbers for orbitals in the. 2s 3p 3d 4s 4p 4f
21 Atomic Orbital s 2s
22 The 3 p orbitals
23 The d orbitals
24
25 f orbitals
26 Comparing s, p, d, & f Orbitals
27
28 The Electron Cloud for Hydrogen 90% probability of finding the electron within this space
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