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Quantum Mechanical Theory. 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. De Broglie. Applied wave-particle theory to e -

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Presentation Transcript
slide2
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.
de broglie
De Broglie
  • Applied wave-particle theory to e-
  • __________exhibit wave properties
  • Came up with the equation:
the heisenberg uncertainty principle
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.
the schr dinger wave equation
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.
the schr dinger wave equation1
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.
quantum numbers n l m
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 __________
quantum numbers n l m1
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
quantum numbers n l m2
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
possible values for n l m
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)
examples
Examples
  • What are the possible values for L if n =2?
examples1
Examples
  • What are the possible values of n, L, and m in the 2s sub shell?
examples2
Examples
  • What are the possible values for n, L, & m in the 3d sub shell?
example
Example
  • What is the designation for the sub shell where n = 2 and L = 1?
example1
Example
  • What is the designation for the sub shell where n = 4 and L = 3?
possible number of values how many answers are there
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
example2
Example
  • If n = 2 how many possible number of values are there for L?
possible number of values how many answers are there1
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
example3
Example
  • How many values of m are there if L = 0?
example4
Example
  • How many possible values are there for m if L = 2?
example5
Example
  • What are the values for m if L = 2?
possible number of values how many answers are there2
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?
possible number of values how many answers are there3
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?
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

Summary
more examples
More examples
  • How many sub shells are in n = 4?
more examples1
More examples
  • What designation would n = 5 and L = 1 have?
more examples2
More examples
  • In the 4d sub shell, what are the possible values for n, l, & m?
more examples3
More examples
  • In the 3p sub shell, what are the possible values for n, l, & m?
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