Quantum model of an atom chapter 17
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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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Quantum model of an Atom Chapter 17

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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

  • 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.


Newton’s Laws ok

Perspective

largesmall

fast

slow

Relativity

Wave-Particle Duality


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.


Standing Waves


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

  • These are patterns of vibration.


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

  • 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.


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

  • 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 Patterns

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

One orbital

s

p

d


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


D Orbitals

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


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.


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


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 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

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Helium

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Lithium

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Beryllium

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Boron

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Carbon

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Nitrogen

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


Oxygen

free electron

3d

3p

3s

Level 3

2p

Level 2

2s

Level 1

1s


250

0

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

  • 1

  • 2

  • 3

  • 6


250

0

10

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

  • 3

  • 5

  • 9

  • 16


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

  • 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

  • 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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