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Quantum model of an Atom Chapter 17. 0 of 250. 10. I read Chapter 15 before coming to class. Yes, the whole thing. Nope, essentially none. Well some, more than ½. A little only. 250. 0. The wave nature of moving particles is interpreted as being.

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I read chapter 15 before coming to class

0

of

250

10

I read Chapter 15 before coming to class

  • Yes, the whole thing.

  • Nope, essentially none.

  • Well some, more than ½.

  • A little only.


The wave nature of moving particles is interpreted as being

250

0

The wave nature of moving particles is interpreted as being

  • An up and down path that the particle travels in as it moves.

  • A back and forth path that the particle travels in as it moves.

  • Not a traditional wave at all but instead is a function that tells us the probability of detecting the particle.


Perspective

Newton’s Laws ok

Perspective

large small

fast

slow

Relativity

Wave-Particle Duality


Standing waves are created when

250

0

10

Standing waves are created when

  • Waves reflect and bounce back to where they started from.

  • Waves wrap around and come back to where they started from.

  • Both 1 and 2 are ways standing waves can be created.



2 dimensions
2 Dimensions

  • It is easy to create standing waves in 2 dimensions as well.

Two waves on a drum head

A single wave on a drum head

Three waves on a drum head


Wrap standing waves around a point
Wrap standing waves around a point

  • These are patterns of vibration.


Bohr model explained
Bohr Model Explained!

  • Take de Broglie’s waves and wrap them in a standing wave pattern around the nucleus.

  • Put one wave , then two waves, then three waves, etc and you exactly predict the location of the Bohr radii!

A CRUDE representation!


The quantum model of the atom
The Quantum Model of the Atom

  • Electrons are found in 3-D electron probability waves.

  • They do not orbit. Instead they exist in the locations given by standing wave clouds.

  • We call these wave clouds orbitals to reflect the fact that the electrons do not orbit like a planet.


Three dimensional atomic orbitals

The shape and energies of the actual orbitals depend on the number of standing waves in the pattern. They are found from solving the Shrödinger Wave equation:

h2 d2Y(x)

8 p2m dx2

+ V(x) Y(x) = EY(x)

Three Dimensional Atomic Orbitals

Kinetic Energy + Potential Energy = Total Energy


Orbital patterns
Orbital Patterns

  • One wave:

    • Electrons will resonate in one pattern, called an “s” orbital.

  • Two waves:

    • Electrons will resonate in two patterns, “s” and “p” orbitals

s

s

p


Orbital patterns1
Orbital Patterns

  • Three waves: Electrons will resonate in “s”, “p” and “d” orbitals.

One orbital

s

p

d


S orbitals
S Orbitals

  • All numbers of standing waves have “s” orbitals.

  • They are all round but their interiors are different.

  • Still, in each case there is just one orbital.


P orbital
P Orbital

  • P orbitals come in sets of 3, whether there are 2 waves or 3 waves or more.


D orbitals
D Orbitals

  • D orbitals come in sets of 5, whether there are 3 waves or 4 waves or more.


Orbital patterns2
Orbital Patterns

  • The pattern continues on as s, p, d, f, g, h, i, j, etc. Each new orbital set has two more orbitals than the previous one.


The pauli exclusion principle

e

-

e

-

The Pauli Exclusion Principle

  • At most two electrons can occupy the same orbital. If two electrons are in the same orbital, they must have different spins.

Spin Down Spin Up


Understanding atoms

High energy

Low energy

1

2

3

Understanding Atoms

  • How do electrons fill the orbitals as we move along the periodic table?

  • Electrons fill the lowest energy levels first. For the lighter atoms, fewer standing waves and simpler orbitals usually means lower energies.

  • From here on I’ll refer to number of standing waves (physics lingo) as energy levels or shells (chemistry lingo).


Electrons in an atom energy wells fill the lowest energy orbitals first
Electrons in an Atom: Energy WellsFill the lowest energy orbitals first

free electron

Zero Energy

3d

3p

3s

Level 3

2p

Level 2

2s

Energy

It is negative for a bound electron

Level 1

1s


Hydrogen
Hydrogen

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Helium
Helium

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Lithium
Lithium

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Beryllium
Beryllium

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Boron
Boron

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Carbon
Carbon

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Nitrogen
Nitrogen

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Oxygen
Oxygen

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


What is the maximum number of electrons in the entire set of p orbitals of any given shell

250

0

What is the maximum number of electrons in the entire set of p orbitals of any given shell?

  • 1

  • 2

  • 3

  • 6


How many orbitals all together are in the third shell by itself

250

0

10

How many orbitals all together are in the third shell by itself?

  • 3

  • 5

  • 9

  • 16


How many electrons total are in an atom that has the first and second shells completely filled

250

0

10

How many electrons total are in an atom that has the first and second shells completely filled?

  • 4

  • 6

  • 10

  • 12


Absorption line spectra revisited
Absorption line spectra revisited

  • The outer electron of any atom can jump up to higher orbitals creating a unique absorption spectrum for that element

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Emission line spectra revisited
Emission line spectra revisited

  • It can then fall down creating the emission spectrum for that element.

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


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