1 Chapter 5: Electrons in Atoms Objectives: the student will be able to: compare the wave and particle models of light; define a quantum of energy and.

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Chapter 5: Electrons in Atoms

Objectives: the student will be able to:

compare the wave and particle models of light; define a quantum of energy and explain how it is related to an energy change in matter;contrast continuous electromagnetic spectra and atomic emission spectra; compare and contrast the Bohr and quantum mechanical model of the atom.explain the impact of de Broglie’s wave-particle duality and the Hisenburg uncertainty principle on the modern view of electrons in atoms; identify the relationships among a hydrogen atom’s energy levels, sublevels and atomic orbitals.apply the Pauli exclusion principle, the aufbau principle, and Hund’s rule to write electron configurations; define valence electrons and draw electron-dot structures representing an atom’s valence electrons.make connections between changes in historical models of the atom and the application of the scientific method

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Model of the Atom (So Far): Rutherford’s Nuclear Atom

Nucleus contains protons and neutrons and the electrons are outside of the nucleus but their location is not well understood

In order to create a better model of the atom, scientists needed to learn more about the electron.

As scientists studied the atom, they discovered that electrons shared some of their properties with light.

The physics of light became an important part of learning about electrons in atoms. Therefore our discussion of atomic theory continues with a discussion of some of the properties of light.

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is lambda

is nulower frequency

higher frequency

longer wavelength

shorter wavelength

Units:

Wavelength m or nm

Frequency 1/s or s-1 or Hz

Properties of Light (Wavelength () and Frequency ())

What is the relationship between wavelength and frequency?

Inverse Relationship!As one increases, the other decreases.

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Rainbow: sunlight is white light (contains all colors of light)

Water droplets act like prisms and separates the light into the different colors.

Early experiments with light taught us that the color of light we see is linked to the wavelength and frequency of the light.

Further experiments showed that there are many other forms of “light” that we can not see with our eyes. We call all forms of light “Electromagnetic Radiation”

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Electromagnetic Spectrum: all types of “light”-colored light is only a small portion of the spectrum.

High FrequencyShort WavelengthHigh Energy

Low FrequencyLong WavelengthLow Energy

Blue Green Yellow RedOrange

What does ROY G BIV mean?

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Converting from Wavelength to Frequency

c =

c is the speed of light c = 3.00X108 m/s

What is the frequency () of light that has a wavelength () of 7.32X106 m?

What is the wavelength of light that has a frequency of 7.32X105 1/s?

Start with: c = then divide both sides by to get by itself.

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Demonstration: Atomic Emission

Balmer Series: n6 → n2 n5 → n2 n4 → n2 n3 → n2

Highest Energy (violet)

Lowest Energy (red)

When atoms are “excited”, have extra energy, they can lose some of the energy in the form of light, but only very specific wavelengths of light are given off from a particular element-not all wavelengths are given off. If electrons can be anywhere in the atom, then all wavelengths of light should be seen-since only certain wavelengths are seen, electrons must be restricted to certain energies.

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Highest

Lowest

Relative Energy

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Lyman Series: n7 → n1 n6 → n1 n5 → n1 n4 → n1 n3 → n1 n2 → n1

Highest Energy (ultraviolet)

Lowest Energy (ultraviolet)

Higher energy than visible light(longer drop)

Paschen Series: n7 → n3 n6 → n3 n5 → n3 n4 → n3

Highest Energy (infrared)

Lowest Energy (infrared)

Lower energy than visible light(shorter drop)

The larger the “drop”, the higher the energy of the light emitted.

Visible light (Balmer Series) is in between Lyman and Paschen

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Energy of Light: Units of energy are joules (J)

E = h

h = Plank’s Constant = 6.626X1034 J·s

What is the energy of light that has a frequency of 3.92X107 1/s?

What is the energy of light that has a wavelength of 3.92X106 m?

What is the wavelength of light having an energy of 8.93X1020 J?

c =

c = speed of light = 3.00X108 m/s

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Extra Practice Work (Optional)

What is the frequency of light that has a wavelength of 8.31X1011 m?

What is the wavelength of light that has a frequency of 1.93X108 1/s?

What is the energy of light that has a frequency of 4.70X104 1/s?

What is the energy of light that has a wavelength of 8.21X102 m?

What is the wavelength of light having an energy of 1.300X1018 J?

What is the frequency of light that has a wavelength of 3.02X10 m?

What is the wavelength of light that has a frequency of 6.31X102 1/s?

What is the frequency of light having an energy of 1.300X1018 J?

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Photoelectric Effect

Light hitting a metal surface can cause electrons to be ejected from the surface of the metal.

Number of electrons being ejected depends upon the “amount” of light hitting the surface (not on the energy of the light).

The energy of the ejected electron depends upon the energy of the light hitting the surface.

Light below a certain energy does not cause any electrons to be ejected no matter how much of the light hits the surface.

Conclusion: light behaves like a particle or package of energy-we now call these packages of light energy photons.

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Light is Electromagnetic Radiation and exhibits wave properties and particle properties

During the study of light and electrons, our understanding of both changed.Light can now be thought of as both a wave and a particle and eventually electrons will be thought of as both a particle and a wave.

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After all of these discoveries: Bohr Model of the Atom-explains atomic emission of Hydrogen atom (n is the energy level of an orbit in the Balmer, Lyman, and Paschen series).

Electrons must have only certain energy values available to them. The energy depends upon the distance from the nucleus-Bohr called these locations “orbits”.

The lowest energy state possible for an atom is called the “Ground State”-all electrons are in their lowest possible orbits.

An “Excited State” is when one or more electrons is in a higher energy orbit than it should be.

Atomic Emission occurs when electrons in an excited state “drops” to a lower energy orbit. The “length” of the drop determines the amount of energy in the emitted photon. We measure the energy by looking at wavelength or frequency.

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Problems with the new model:

Bohr model does not actually work for any atom larger than hydrogen (one electron atom).

Physics says that objects in an orbit will decay (crash into the surface) over time. According to the Bohr model, electrons should fall into the nucleus rather quickly because of the physics involved. Electrons do not generally fall into the nucleus!

Properties of waves can be used to avoid the

problem with the decay in orbits.

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Standing Waves have different energies.

Low Energy

High Energy

0 nodes

1 node

2 nodes

Energy can be transmitted through the wave without ever being at the node!

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If an electron can be thought of as a wave instead of as a particle, a standing wave would not decay like an orbit.

n is the energy level (like Bohr’s orbit)

When n = 1, there are 0 nodes.

When n = 2, there is one node.

When n = 3, there are 2 nodes.

More nodes means a higher energy wave!

If the ends of the wave do not align, then that wavelength is not an allowed energy.

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Wave nature of electrons-particles that move have wave characteristics. Massive objects will have undetectable wave characteristics because their size. Electrons are very small, so their wave characteristics can be measured.

de Broglie equation: = h/(mv)

Wavelength () of a moving object equals Plank’s constant (h) divided by mass (m) divided by velocity (v).

Notice that if mass is very large, the wavelength will be very small or undetectable.

m = massv = velocity

Only atomic scale objects have detectable wavelengths.

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Heisenberg Uncertainty Principle

On the atomic scale, we can not know an object’s location and momentum (velocity and direction) at the same time.

The impact of this is that we really can not know exactly where an electron is located. Instead we talk about the probability that an electron is within a certain distance of the nucleus.

The reason being that electrons are so small that anything we use to “look at” an electron will give or take energy from the electron and cause it to change its momentum.

Momentum is a combination of mass, velocity, and direction.

An orbital is the volume of space where we have a 90% probability of finding the electron.

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Quantum Mechanical Model of the Atom

Model is based on Schrödinger’s wave equation-treats electrons as wave and describes the electron’s possible location as a wave function.

Solutions to the wave equation are called wave functions and represent the three-dimensional space around a nucleus where the electron may be located. These 3-dimensional spaces are called atomic orbitals (these are not the same as Bohr’s orbits).

For hydrogen, the lowest energy solution to the wave function is called the 1s orbital.

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a) The Probability Distribution for the Hydrogen 1s orbital in three-dimensional space

(b) The Probability of finding the electron at different distances from the Nucleus for the Hydrogen 1s Orbital

Notice that the probability of finding the electron close to the nucleus is much greater than finding it farther away.

More intense color indicates greater probability.

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Imagine that electrons live in a fancy hotel with the following rules.

1) Electrons must go the lowest energy bedroom available. Lower floors are lower in energy.

3) Smaller suites are lower in energy than larger suites on the same floor. There are four types of suites: 1 bedroom, 3 bedrooms, 5 bedrooms, and 7 bedrooms.

5) Electrons can not move into higher energy suites until the lower energy suites are full.

4) Electrons will not share a bedroom until each bedroom in that suite has one electron in it.

2) The maximum number of electrons in a bedroom is 2.

6) The 5 bedroom suites are so much higher in energy than the 3 bedroom suites, that they appear one floor above their real floor number. The 7 bedroom suites appear 2 floors above their real floor number for the same reason.

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1st floor

2nd floor

3rd floor

4th floor

5th floor

6th floor

A diagram of our electron “hotel”

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Electron Configuration Practice

Example: Sulfur S 1s2, 2s2, 2p6, 3s2, 3p4

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Quantum Numbers:

n is the principle quantum number and is related to the major energy levels of the electron. n must be a positive integer!As n increases, the size of the orbital increases and the electron spends

more time farther from the nucleus. Farther from the nucleus is higher energy.(a) The Electron probability distribution (cut away view) where n = 1, n = 2, and n = 3 respectively.

(b) The surface represents a 90% probability that the electron is inside that space

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Quantum Numbers

l is the angular momentum quantum number and is related to shape of the atomic orbital. l must be a whole number which can range from 0 to (n-1)!

For example: when n = 1, l must be 0 when n = 2, l is either 0 or 1 when n = 3, l is either 0, 1, or 2 when n = 4, l is either 0, 1, 2, or 3

When l = 0, the shape is a sphere (s orbital).

When l = 1, the shape is a dumbbell with 2 lobes (p orbital).

When l = 2, the shape is a dumbbell with 4 lobes (d orbital).

When l = 3, the shape is a dumbbell with 8 lobes (f orbital).

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Drawings of the three 2p orbitals (n = 2, l = 1)

These three orbitals are equal in energy but are oriented in different directions in space.

px py pz

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Drawings of the five 3d orbitals (n = 3, l = 2)

These five orbitals are equal in energy but are oriented in different directions in space.

dxz dyz dxy dx2 – y2 dz2

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Drawings of the seven 4f orbitals (n = 4, l = 3)

These seven orbitals are equal in energy but are oriented in different directions in space.

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Quantum Numbers

ml is the magnetic quantum number and is related to the

orientation in space of the atomic orbital. ml must be an

integer which can range from -l through 0 to +l

For example, when l = 0, ml = 0

when l = 1, ml = -1, 0, 1

when l = 2, ml = -2, -1, 0, 1, 2

when l = 3, ml = -3, -2, -1, 0, 1, 2, 3

1 value (only one s orbital)

3 values (three p orbitals)

5 values (five d orbitals)

7 values (seven f orbitals)

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Quantum Numbers

ms is the spin quantum number and is related to the direction

of “spin” of the electron. ms must be either + ½ or ½

Two values for each set of three other quantum numbers. This means that 2 electrons can only occupy an orbital if they have opposite “spin”.

Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers. Another way of saying this is that two electrons can only occupy the same orbital if they have opposite spin. Two electrons in the same orbital must have the same first three quantum numbers and ms

must be + ½ for one and ½ for the other.

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One way of thinking about “spin”

The gold arrows represent magnetic fields created by the “spinning” electrical charge. Notice that the arrows point in opposite directions-therefore the electrons are spinning in opposite directions (one clockwise and one counterclockwise).

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Quantum Numbers

First electron in an atom

General Rule: electrons must have lowest possible energy

n = 1l = 0ml = 0

ms = +½

Quantum Numbers are like addresses for the electrons in an atom. Each electron needs to have its own unique address.

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Quantum Numbers

1st electron in an atom

General Rule: electrons must have lowest possible energy

n = 1l = 0ml = 0

ms = +½

2nd electron in an atom

n = 1l = 0ml = 0

ms = ½

Only Electron in H (1s1)

First Electron in He (1s1)

Second Electron in He (1s2)

Helium has 2 electrons and each electron must have a different set of quantum numbers. This is an expression of the Pauli Exclusion Principle.

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n = 2l = 0ml = 0

ms = +½

n = 2l = 0ml = 0

ms = ½

3rd 4th

5th

n = 2l = 1ml = 1ms = +½

6th

n = 2l = 1ml = 0

ms = +½

7th

n = 2l = 1ml = 1

ms = +½

8th

n = 2l = 1ml = 1ms = ½

9th

n = 2l = 1ml = 0

ms = ½

10th

n = 2l = 1ml = 1

ms = ½

since l = 0, “s” orbital being filled

No 2 electrons have the same set of quantum numbers!

since l = 1, “p” orbitals being filled

2s1 then 2s2

2p1, then 2p2, and so on … 2p3, 2p4, 2p5, 2p6

If we keep adding electrons to an atom:

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Summary of Quantum Number meanings.

Each orbital can contain up to two electrons One will be spin (+½) and one will be spin (½)

# e when full

2

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26

10

26

1014

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Electron Configurations: like a bookkeeping system for where electrons will be located in an atom in its ground state.

Electrons fill into the lowest possible energy orbitals using rules much like those we used for the electron “hotel”.

The pattern can easily be remembered by using the periodic table to full effect.

Start at element 1 and follow the atomic numbers. Fill in all electrons according to the Period Number (principle quantum number “n”) and the number of electrons in the orbital type (s, p, d, and f are the orbital types-from the angular quantum number (l)).

The technical name for this is called the aufbau principle

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(n-1)

(n-2)

(n)

sblock

dblock

p block

f block

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Designation for last electron of each of the first 18 elements.

Notice: Elements in the same group have the same type of electron as the last electron (except He).

s1 s2 p1 p2 p3 p4 p5 p6

He is in the last group because it has a full outer shell!

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Practice:

See Table 5-3 on page 137 for the electron configurations for the first 10 elements. Notice the orbital diagrams (also called box diagrams) as well.

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Notice the two exceptions to normal electron configurations.

Designation for last electron of each of elements 19 through 36.

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Orbital Diagrams:

In the first energy level ( n = 1), l can only be 0 and ml must also be 0. Therefore, there is only an “s” orbital

in the first energy level.

In the second energy level ( n = 2), l can be 0 or 1 and ml can be 1, 0, or 1. When l is 0, an “s” orbital is present, and when l is 1, three “p” orbitals are present.

In the third energy level ( n = 3), l can be 0, 1, or 2 and ml can be 2, 1, 0, 1, or 2. When l is 0, an “s” orbital is

present, when l is 1, three “p” orbitals are present, and when l is 2,five “d” orbitals are present.

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Why only one “s” orbital in any energy level?

When l = 0, ml must also = 0 (only value), so one “s” orbital.

Why three “p” orbitals in any energy level above 1?

When l = 1, ml can be 1, 0, or 1 (three values), so three “p” orbitals.

Why five “d” orbitals in any energy level above 2?

When l = 2, ml can be –2, 1, 0, 1, or 2 (five values), so five “d” orbitals.

Why seven “f” orbitals in any energy level above 3?

When l = 3, ml can be –3, –2, 1, 0, 1, 2, or 3 (seven values), so seven “f”

orbitals.

s p d f

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Why two columns of elements in the “s” block?

Each orbital can contain up to two electrons (ms can only be +½

or ½) and there is only one “s” orbital in any energy level.

Why six columns of elements in the “p” block?

Each orbital can contain up to two electrons (ms can only be

+½ or ½) and there are three “p” orbitals in any energy level.

Why ten columns of elements in the “d” block?

Each orbital can contain up to two electrons (ms can only be

+½ or ½) and there are five “d” orbitals in any energy level.

Why fourteen columns of elements in the “f” block?

Each orbital can contain up to two electrons (ms can only be

+½ or ½) and there are seven “f” orbitals in any energy level.

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Valence Electrons:

Electrons in the outermost orbitals-highest energy electrons in the atom.

The valence electrons are the electrons that are taking part in chemical reactions of an element.

Electron Dot Structures:

Diagrams showing the number of electrons in the valence shell using an element symbol and “dots” to represent electrons. Note: electrons in “d” or “f” orbitals are not shown in dot structures.

See Table 5-5 on page 140 for dot structures of 2nd period elements.

Examples:

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3d

Fill in the orbital diagram for the valence shell of sulfur.

S is 1s2, 2s2, 2p6, 3s2, 3p4 3s 3p

outershell

Fill in the orbital diagram for the valence shell of bromine.

Br is 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p5

4s 4p

outershell

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Noble-Gas Configurations:

Noble-Gases: He, Ne, Ar, Kr, Xe, Rn

Each of these elements has an entirely full outer shell of electrons. This makes them very stable-unreactive.

To shorten electron configurations of other elements, we can replace part of the electron configuration with a noble-gas symbol in brackets and then show just the outer shell electrons.

Br: 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p5

For example:

Br: [Ar] 4s2, 3d10, 4p5

electrons in Ar

Therefore:

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Orbital energies in single electron

system.Bohr Model

Orbital energies in multi electron

systems.Quantum Model

Bohr’s theory did not predict different energies within the same principle energy level for multi electron systems. Quantum mechanics does!