Quantum mechanical theory
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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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Quantum Mechanical Theory

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Quantum mechanical theory

Quantum Mechanical Theory


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

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 mechanical theory

Size


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


Shapes

s

p

d

f

Shapes


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


Orientation

Orientation


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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