11.6 The Wave Mechanical Model of the Atom Objective: · PDF file · 2013-03-2011.6...

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11.6 The Wave Mechanical Model of the Atom

• Objective: To understand how the electron’s position is represented in the wave mechanical model.

• In the mid-1920’s, an Austrian and French scientist found Bohr’s model to be insufficient in locating electrons and came up with a new model.

Erwin Schrödinger

Louis Victor de Broglie

http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/Broglie.html

http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/Schrodinger.html


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Electrons as Waves

• Schrödinger and de Broglie noticed that electrons and light behaved not only as particles, but also as waves.

• Schrödinger began working with a mathematical model to understand the behavior of electrons.

• He came up with the following:

[(-h2/8π2m) 2 +Ep] = EΨ

In simpler form:

ĤΨ=E Ψ

• This mathematical model worked not only for hydrogen, but all atoms.


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Firefly Experiment

Figure 11.18: A representation of the photo of the firefly experiment.

• Suppose a male firefly is in a dark room with an open vial of female sex-attractant hormones. If we set up a camera to take pictures every time the firefly flashes and records the firefly’s location in the room we will find that most of it’s time is around the female, however, sometimes he flies farther away and around the room.

• If we plot the firefly’s location we would see a picture like the one here• The area most often occupied is darkest in the picture and is the center where the

hormones are found.• Now suppose you see the firefly flash in the center of the room, where will you see

it flash next? Is there any way to know? Is the path of the firefly predictable? • NO, we cannot predict the location, but we can find the probability of its location.

Thus the picture on the right is a sort of probability map.


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Bohr Model vs Wave Mechanical Model

• Both models allow electrons to only be at particular energy levels. (ladder model)

• The wave mechanical model is different in that it does NOT define an exact path the electron takes (No more ring model)

• Wave mechanical model uses probability to estimate the probability of finding an electron in a certain position.

Figure 11.19:The orbital that

describes the hydrogen electron

in its lowest possible energy state.


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Some Important Quantum Terms

• An energy level of an electron is a region around the nucleus where the electron is likely to be moving.

• A quantum of energy is the amount of energy required to move an electron from it’s present energy level to the next one.

• A quantum leap is a change in energy levels.


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Energy Levels

• Energy levels are not evenly spaced.

• The farther away from the nucleus an energy level is, the closer together they are.

• Imagine an escalator, as you get close to the top, the steps are smaller and smaller, it’s easier to step off at the top of the escalator.

• Similarly it’s easier for an electron to escape the atom at the outer energy levels


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Quantum Numbers

• Bohr had already come up with principle quantum numbers (n) with his rings

• Each principle quantum number refers to a principle energy level in an atom assigned in values of increasing energy. n=1,2,3…

Ground State

Excited States

43

2

1

n

Principle Energy Levels

• There are 7 energy levels which corresponds to the rows or periods on the periodic table. 1-7

• Each energy level

(aka energy shells) are

designated by the #’s.

1, 2, 3, …… 7.

• Within each level, there

are sublevels designated

by letters: s, p, d, f

• Within each sublevel (aka orbital), there are specific locations of electrons; each orbital can hold a maximum of 2 electrons


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Orbital Shapes

• First there are principle energy levels.

• These are divided into sublevels. The number of the energy level determines how many sublevels.

• The sublevels are then divided further into orbitals-regions where electrons are likely to be found.

• Some sublevels have multiple orbitals.


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Figure 11.22: How principal levels can be divided into sublevels.


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Types of Orbitals

s-orbitals - sphere shaped, exist as a single orbital

p-orbitals – sort of pear shaped, come in 3’s.

Figure 11.24: The relative sizes of the 1s

and 2s orbitals of hydrogen.

Figure 11.25: The three 2p orbitals.


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More Orbitals

d-orbitals – much more complex shape, come in sets of 5.

f-orbitals – even more complex than d-orbitals, come in sets of 7.

Figure 11.28: The shapes and labels of the five 3d orbitals.


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Figure 11.26: Diagram of principal energy levels 1 and 2.


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How to Label Orbitals

• 1. The number tells the principal energy level.

• 2. The letter tells the shape.

– S means a spherical orbital.

– P means a 2 lobed orbital, the x, y, or z subscript on the p-orbital label tells along which of the coordinate axes the two lobes lie

Remember, these are all regions where electrons are likely to be found.

One electron can only occupy 1 orbital at a time, but the other orbitals will still exist, because if the electron gets excited it may change energy levels or orbitals.


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If Hydrogen has 1 electron, how can it have multiple energy levels???

Figure 11.27: Relative sizes of the spherical 1s, 2s, and 3s orbitals of hydrogen.

•Which of these orbitals represents the ground state?

•Which of these orbitals has the highest probability of finding the electron during the ground state?

•Which would you find the electron in an excited state?

• Why is 3s larger than 1s?

• It’s like a circular theater, the farther you are from the center, the more seats, or more space for orbitals.


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Electron Spin

• Electrons have a property called spin.

• Just as tops spin only 2 directions, electrons can only spin 2 directions.

• We represent the 2 opposite directions an electron spins with arrows, or .

• It is important to recognize that two electrons must have opposite spin to fill an orbital.

• Two electrons with the same spin cannot occupy the same orbital.

• All orbitals can hold a maximum of 2 electrons with opposite spin.


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3 Rules for Filling orbitals

We must first determine how many electrons is in an atom, then we apply these 3 rules to determine the filling of the orbitals.

Aufbau Principle – Electrons enter orbitals of lowest energy first.

Pauli Exclusion Principle – The most electrons any orbital can hold is 2 electrons of opposite spins. We recognize the spins as arrows. One’s spin and the other is .

Hund’s Rule – Electrons occupy orbitals of equal energy. One electron enters each orbital until all are filled, then the second enters each orbital.

• So let’s look at Helium, how many electrons does it have?

What will the first orbital that is used be?

How many electrons will be in that orbital?

How will we write this configuration?

• Carbon.

How many electrons in Carbon?

Start filling the orbitals with 2 electrons each.

Draw opposite spin arrows to show which orbitals are filled.

1s___ 2s____ 2p____ ____ ____

Rewrite the above without arrows.

1s2 2s2 2p2

Write the electron configurations for the following:

Li, F, Ne, Na, Mg, Ar


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11.9 Electron Configuration for the First 18 Atoms on the Periodic Table

• Let’s look at Hydrogen’s electron configuration. We would write it as 1s1

• The first 1 represents the principle energy level.

• The electron is an s-orbital.

• The little one represents the number of electrons in the orbital.


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Figure 11.31: Orbitals being filled for elements in various parts of the periodic table.

• Using this version of the periodic table, write the electron configuration for these elements:

• Ca, Fe, As, Kr


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Figure 11.34:Periodic table with atomic

symbols, atomic numbers,

and partial electron

configurations.Look at this on p. 347 in your book.

Do you see any patterns?


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11.11 Atomic Properties and the Periodic Table

• Electron configurations can give us a lot of information about trends in the periodic table.

• Recall that valence electrons are the electrons on the outer most part of the atom.

• To determine the number of valence electrons, we can look at the group number as we did in the past, or we can look at the electron configuration.


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Valence Electrons• The number of valence electrons determines an

elements properties. • The number of valence electrons is determined by the

number of electrons in the outermost energy level.• Example: Write the electron configuration for oxygen.• 1s22s22p4

• How many electrons in the 2nd energy level? How many more electrons are needed to fill the p-orbital?

• There are 6 electrons in the 2nd energy level, and only 2 more electrons are needed to fill the p-orbital…if oxygen gains these 2 electrons this would give oxygen ion a 2-charge.


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Practice

• Using the electron configuration, how many valence electrons do each of the following have? How many would they gain or lose as an ion?

• Cl

• Mg

• C

• F

• Ar


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Figure 11.36: Relative atomic sizes for selected atoms.

Electronegativity: For an element, the tendency for atoms of the element to attract electrons when

combined with another element.


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Trends in Electronegativity

• As you move down a group, electronegativity decreases.

• As you move across a period left to right, electronegativity increases.

• Where do you find the most electronegative element on the periodic table?

• What is the most electronegative element?

• What is the least electronegative element?What does this mean in terms of bonding with other elements?

• Ionization Energy: The amount of energy required to overcome the attraction of the nuclear charge and remove an electron from a atom.


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Trends in Ionization Energy• Group Trends: As you move down a group, 1st

ionization energy decreases.

• This means it gets easier to remove the 1st

electron.

• Period Trend: As you move across a period from left to right the 1st ionization energy generally increases.

• Which would have a higher 1st ionization energy, alkali metals or noble gases? Why?


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Electronegativity and Atom Size

• Compare the atom sizes and electronegativies.

• Where is the largest atom? Where is the smallest?

• How do these relate to electronegatitivies?

• Which element is more electronegative?

• Be or Ba

• O or I

• Ca or As

11.6 The Wave Mechanical Model of the Atom Objective: · PDF file · 2013-03-2011.6...

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