Quantum Mechanical Theory
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Transcript of Quantum Mechanical Theory
![Page 1: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/1.jpg)
Quantum Mechanical Theory
![Page 2: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/2.jpg)
Bohr
• Bohr proposed that the hydrogen atom has only certain _________________.
• Bohr suggested that the single electron in a hydrogen atom moves around the nucleus in only certain allowed circular orbits.
![Page 3: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/3.jpg)
De Broglie
• Applied wave-particle theory to e-
• __________exhibit wave properties
• Came up with the equation:
![Page 4: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/4.jpg)
The Heisenberg Uncertainty Principle
• The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the __________ and __________ of a particle at the same time.
![Page 5: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/5.jpg)
The Schrödinger wave equation
• The atomic model in which electrons are treated as waves is called the wave mechanical model of the atom or, more commonly, the __________________of the atom.
![Page 6: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/6.jpg)
The Schrödinger wave equation
• A three-dimensional region around the nucleus called an __________ describes the electron’s probable location.
• You can picture an atomic orbital as a fuzzy cloud in which the density of the cloud at a given point is proportional to the probability of finding the electron at that point.
![Page 7: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/7.jpg)
Quantum Numbers(n, l, m)
• n = __________ Quantum Number
• It has whole number values (1, 2, 3, …)
• An n increases, the orbital becomes larger
• n tells you what __________ you are in
• n designates the __________
![Page 8: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/8.jpg)
Size
![Page 9: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/9.jpg)
Quantum Numbers(n, l, m)
• L = __________ Quantum Number or __________Quantum Number
• Can have values from 0 to (n-1) for each value of n
• Defines the __________ of the orbital• L = 0 s• L = 1 p• L = 2 d• L = 3 f• Tells you what __________ you are in
![Page 10: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/10.jpg)
Shapes
s p d f
![Page 11: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/11.jpg)
Quantum Numbers(n, l, m)
• mL = __________ Quantum Number
• Can have whole number values from – L to + L (including zero)
• This describes the orbital’s __________ in space (which axis it is on)
• Tells you what __________ you are in
![Page 12: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/12.jpg)
Orientation
![Page 13: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/13.jpg)
Possible Values for n, l, m
• n (shell) = 1, 2, 3, 4, … (whole numbers)
• L (sub shell) values from 0 (n -1)
• mL (orbital) values from – L to + L (including zero)
![Page 14: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/14.jpg)
Examples
• What are the possible values for L if n =2?
![Page 15: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/15.jpg)
Examples
• What are the possible values of n, L, and m in the 2s sub shell?
![Page 16: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/16.jpg)
Examples
• What are the possible values for n, L, & m in the 3d sub shell?
![Page 17: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/17.jpg)
Example
• What is the designation for the sub shell where n = 2 and L = 1?
![Page 18: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/18.jpg)
Example
• What is the designation for the sub shell where n = 4 and L = 3?
![Page 19: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/19.jpg)
Possible Number of Values(how many answers are there?)
• A shell with Principal Quantum Number (n) has exactly n number of sub shells
• Therefore
• # L’s = n
![Page 20: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/20.jpg)
Example
• If n = 2 how many possible number of values are there for L?
![Page 21: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/21.jpg)
Possible Number of Values(how many answers are there?)
• For a given value of L there are 2L + 1 possible values for m
• Those values as stated before range from –L to +L
![Page 22: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/22.jpg)
Example
• How many values of m are there if L = 0?
![Page 23: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/23.jpg)
Example
• How many possible values are there for m if L = 2?
![Page 24: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/24.jpg)
Example
• What are the values for m if L = 2?
![Page 25: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/25.jpg)
Possible Number of Values(how many answers are there?)
• The number of possible values of m = n2
• Example:• If n = 2, how many values are there for m?
![Page 26: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/26.jpg)
Possible Number of Values(how many answers are there?)
• Since each orbital can hold at most 2 electrons, the number of electrons in a shell is 2n2
• How many electrons are in the n = 3 shell?
![Page 27: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/27.jpg)
Summary
Possible Values L (0 n-1) m (-L +L)
# of Possible Values Orbitals (m)
• #m = 2L +1• #m = n2
Sub shells (L)• # L = n
Electrons• # electrons = 2n2
![Page 28: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/28.jpg)
More examples
• How many sub shells are in n = 4?
![Page 29: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/29.jpg)
More examples
• What designation would n = 5 and L = 1 have?
![Page 30: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/30.jpg)
More examples
• In the 4d sub shell, what are the possible values for n, l, & m?
![Page 31: Quantum Mechanical Theory](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681304a550346895d95f645/html5/thumbnails/31.jpg)
More examples
• In the 3p sub shell, what are the possible values for n, l, & m?