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Topic 3: Electromagnetic Spectrum &

Quantum Theory

Arrangement of Electrons in Atoms (Chapter 4 in Modern Chemistry)

Introduction

There were two light theories in the early 1900. Sir Isaac Newton subscribed to the particle

theory of light. Christian Huygens subscribe to the wave theory of light. There was data to

support both theories. Einstein developed the idea of a photon, Bohr proposed a quantized

model of the atom, and eventually, Louis deBroglie, came up with the Wave-Particle Duality

of Nature. He said that sometimes waves act like particles and sometimes particles act like

waves. This was true of very small particles. Eventually, the Quantum theory was developed

and so were electron configurations.

Newton Huygens Einstein Bohr deBroglie

Properties of Light

Visible light is a kind of electromagnetic radiation, which exhibits wavelike behavior as it travels

through space. There are other types of light that make up the electromagnetic spectrum. All

forms of electromagnetic radiation move at a constant speed. We call this the speed of light (c);

c = 3.00 x 108 m/s.

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Wave motion is repetitive. It is characterized by wavelength and frequency. Wavelength () is

the distance between corresponding points on adjacent waves. Wavelength is a length unit so it

is expressed in meters, centimeters, or nanometers.

Frequency (is defined as the number of waves that pass a given point in a specific time,

usually one second. Frequency is expressed in waves/second, s-1

,or hertz (Hz).

Wavelength & frequency are inversely proportional, meaning longer wavelengths have lower

frequencies and vice versa. Mathematically, they are related to each other in the following

relationship.

c =

The Photoelectric Effect

The photoelectric effect refers to the emission of electrons from a metal

when light shines on the metal. It was found that only light above certain

minimum frequencies could cause these electrons to be released no matter

how intense the light. This could not be explained by the wave theory.

Max Planck suggested that energy is emitted or absorbed not as

continuous waves, but as small, specific packets of energy called quanta. A

quantum of energy is the minimum quantity of energy that can be lost or

gained by an atom.

E = h

E is the energy, in joules

is the frequency in s-1

or Hz Max Planck

h is Planck’s constant; h = 6.63 x 10-34

Js or J/Hz

By combining the equations, c = and E = h, another useful equation can be derived.

E = hc

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Task 3a

1. Characterize each of the following as absorption or emission:

a. an electron moves from E2 to E1

b. an electron moves from E1 to E3

c. an electron moves from E6 to E3

2. Which energy-level change above emits or absorbs the highest energy? The lowest

energy?

3. Solve the following problems using the equations in this section.

a. Determine the frequency of light whose wavelength is 4.257 x 10-7

cm.

b. Determining the energy in joules of a photon whose frequency is 3.55 x 1017

Hz.

c. When sodium is heated; a yellow spectral line whose energy is 3.37 x 10-19

J per

photon is produced. What is the wavelength of this light?

d. The laser in an audio compact disc player uses light with a wavelength of 7.80 x

102 nm. Calculate the frequency of this light. Calculate the energy of a single

photon of this light.

Rydberg Equation

You can also determine the amount of energy absorbed or emitted as electrons move from one

energy level to another using a form of the Rydberg equation.

E = Ef – Ei = Ephoton

E = the energy associated with a particular quantum number, n. By calculating the energies

associated with two different quantum levels and finding the difference, one can calculate the

energy required to promote an electron from one level to another, or calculate the energy

released when an electron falls back from a higher level to a lower level. Energy emitted is

exothermic and is given a negative charge. Energy absorbed is endothermic and is given a

positive charge.

Task 3b

1. What is the energy difference when an electron moves from E3 to E5? Is the energy

emitted or absorbed. Use the appropriate sign.

E = - 2.178 x 10-18

n2

E = ( -2.18 x 10-18

J

) ( 1

- 1

) nf

2 ni

2

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The Hydrogen-Atom Line-Emission Spectrum

When electricity is passes through a gas at low pressure, the energy of some of the gas atoms

increases. The lowest energy state of an atom is its ground state. A state in which an atom has

a higher energy than it has in its ground state is an excited state. For an electron to move from

its ground state to an excited state, energy must be absorbed. When an electron falls from an

excited state to a lower excited state, or to its ground state, energy will be released. This energy

is released in the form of light called a photon. The production of colored light in neon lights is

an example of this process.

When electricity was passed through hydrogen gas at low pressure, a pinkish glow was given

off. When a narrow beam of the emitted light was shined through a prism, it was separated into

four specific colors of the visible spectrum. The four bands (lines) of light were part of what is

known as hydrogen’s line-emission spectrum.

These distinct bands at specific wavelength & frequencies indicated that the energy differences

between the atoms’ energy states were fixed. This led to the Bohr model of the atom. In this

model, Niels Bohr linked the atom’s electron to photon emission. The electron can circle the

nucleus only in allowed paths, or orbits. When the electron is in one of these orbits, the atom has

a definite, fixed energy.

Here are two animations that will help you visualize what happens to electrons as they absorb or

emit energy.

http://science.sbcc.edu/physics/solar/sciencesegment/bohratom.swf

http://physics.gac.edu/~chuck/PRENHALL/Chapter%2031/AABXTEJ0.html?I1.x=40&I1.y=17

The Quantum Model of the Atom

So, after the photoelectric effect and hydrogen’s line-emission spectrum

revealed that light could behave as particles and waves, Louis de Broglie

proposed the wave-particle duality of nature. Then Werner Heisenberg tried to

determine where the electrons were in the atom. Because you need a photon to

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detect an electron, and a photon causes an electron to be knocked off course, there is always an

uncertainty about the location of an electron. This is called the Heisenberg uncertainly

principle. It states that it is impossible to determine simultaneously both the position and

velocity of an electron or any other particle. There are only probable positions of electrons.

Max Planck founded the Quantum theory, which describes

mathematically the wave properties of electron and other very small

particles. This theory states that electrons do not travel around the

nucleus in neat orbits, as Bohr postulated, but exist in certain

regions or volumes, called orbitals. An orbital is a three-

dimensional region around the nucleus that indicates the probable

location of an electron.

s orbital

Atomic Orbitals and Quantum Numbers

In order to completely describe orbitals, scientists use quantum numbers. Quantum numbers

specify the properties of atomic orbitals and the properties of electron in those orbitals. There

are four quantum numbers. The first three indicate the main energy level, the shape, and the

orientation of an orbital. The fourth, describes the spin on an electron in the orbital.

Quantum number notes

There are 4 Quantum Numbers: n, , m, s

1. n = Principal Quantum Number (n = 1, 2, 3…)

Represents the main energy level, if n = 1, 1st energy level, n = 2, 2

nd energy level,

etc.

This also represents the size of the electron cloud.

n = 1 is the energy level closest to the nucleus, the larger n, the farther away from

the nucleus

2n2 – determines maximum number of electrons that can occupy an energy level

2. = sublevel ( = 0 to n-1)

Refers to different energy states in each energy level

Determines the shape of the orbital(s)

Number of sublevels = n

o n = 1, has 1 sublevel s ( = 0)

o n = 2, has 2 sublevels s ( = 0), p ( = 1)

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o n = 3, has 3 sublevels s ( = 0), p ( = 1), d ( = 2)

o n = 4, has 4 sublevels s ( = 0), p ( = 1), d ( = 2), f ( = 3)

3. m = orbital (m = - to +)

Space occupied by a pair of electrons

Determines orientation in space

Each orbital can be represented by a box

Each orbital can hold a maximum of two electrons

s = 1 orbital, 1 box, a maximum of 2 electrons (0)

p = 3 orbitals, 3 boxes, a maximum of 6 electrons (-1,0,1)

d = 5 orbitals, 5 boxes, a maximum of 10 electrons (-2, -1, 0, 1, 2)

f = 7 orbitals, 7 boxes, a maximum of 14 electrons (-3, -2, -1, 0, 1, 2, 3)

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4. s = spin

in order for 2 electrons to occupy the same orbital, they must have opposite spins

the box represents the orbital, the arrows represent electrons spinning in opposite

directions, there cannot be arrows pointing in the same direction in the same box

Each arrow represents an electron (+ ½, -½)

Task 3c

Answer the following questions based on quantum numbers.

1. How many quantum numbers are there?

2. What is the maximum number of electrons in an orbital?

3. What is the maximum number of electrons in n = 2?

4. Which quantum number represents the shape of the electron cloud?

5. Which quantum number represents the volume of the electron cloud?

6. How many orbitals are in the p sublevel?

7. How many electrons can be in the d sublevel?

8. Which energy level has the lowest energy?

9. Which sublevel has the lowest energy?

10. How many sublevels are in n = 4? What are they?

Rules for placing electrons in orbitals

Pauli’s Exclusion Principle

No two electrons in an element can have the same set of quantum numbers.

Aufbau Principle

Electrons occupy orbitals of lowest energy first – 1s

Hund’s Rule

Within a sublevel, orbitals are half-filled with electrons before they become filled

p sublevel with 3 electrons

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n m s Honors (ex.)

1 s 1

1,0,0,+ ½

1,0,0,- ½

2 s, p 1, 3

2,0,0,+ ½

2,0,0,- ½

2,1,-1, + ½

2,1,-1, - ½

2,1,0, + ½

2,1,0, - ½

2,1,1, + ½

2,1,1, - ½

3 s, p, d 1, 3, 5

4 s, p, d, f 1, 3, 5, 7

Look up the atomic number of the element for which you are drawing the orbital filling diagram. Since

these are atoms, this not only tells you the number of protons but also the number of electrons. The

electrons are represented by arrows. For example, K has atomic number of 19, so its atoms have 19

electrons, therefore, 19 arrows.

For example the orbital filling diagrams for

for H is: For He:

1s1 1s

2

For Li: For Be:

1s2 2s

1 1s

2 2s

2

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For B: For N:

1s2 2s

2 2p

1 1s

2 2s

2 2p

3

For F:

1s2 2s

2 2p

5

For Si:

1s2 2s

2 2p

6 3s

2 3p

2

Note that you always start with 1s. Always start with an “up” arrow. When you are starting to

fill up the orbitals (boxes) you placed “up” arrows in all the boxes until there is at least one

arrow in the orbital, then you go back and finish filling that orbital. Only two arrows can go in a

box. You can also write the electron configurations for the same elements. You just write the

numbers below without drawing the boxes.

For H: 1s1 (read as: one s one)

For He: 1s2

For Li: 1s2 2s

2

For Be: 1s2 2s

2

For B: 1s2 2s

2 2p

1

For N: 1s2 2s

2 2p

3

For F: 1s2 2s

2 2p

5

For Si: 1s2 2s

2 2p

6 3s

2 3p

2

It is very important that you write the electron configuration in order of lowest energy to highest

energy. You can use the diagonal rule or the periodic table.

The diagonal rule shows the order of electron filling. Follow

the arrows.

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Task 3d

1. Draw the orbital filling diagram for the following.

a. P

b. V

c. Na

2. Write the electron configuration for the following.

a. W

b. Zn

c. Ca

d. Tl

e. Br

3. What are the quantum numbers for the last electron in each of the following?

a. As

b. Nb

c. Ba

4. Four electrons in an atom have the four sets of quantum numbers given below. Which

electrons are in the same orbital? Explain your answer.

a. 1, 0,0, -___

b. 1, 0, 0, +___

c. 2, 1, 1, +___

d. 2, 1, 0, +___

5. Which of the sets of quantum; numbers below are possible? Which are impossible?

Explain your choices.

a. 2, 2, 1, +___

b. 2, 0, 0, -___

c. 2, 0, 1, -___

You also need to be able to write the quantum numbers for electrons. In the notes above there

were numbers in parentheses. These are the quantum numbers. For example: Li has an electron

configuration of the quantum numbers for the last electron would be 2, 0, 0, +½.

1s2 2s

1

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The 2 represents the 2 level, the first 0 represents the s sublevel, the second 0 represents the box,

and the + ½ represents the clockwise spin. (We actually do not know if it is clockwise or

counterclockwise, by convention we use + ½ for the up arrow.)

Another example: Nitrogen’s orbital filling diagram is

1s2 2s

2 2p

3

The quantum numbers for the last electron would be 2, 1, -1, +½.

Electron Configuration & the Periodic Table (Chapter 5 in Modern Chemistry)

You can also write electron configurations using the periodic table. Below is a periodic table

labeled with the appropriate blocks. This is the method I use, and the method taught in most

college classes.

1

2

3

4

5

6

7

The rows on the periodic table represent the outer energy level or principle quantum number.

The first two columns are the s blocks plus He. The middle section (transition metals) is the d

block elements. Notice that the principle quantum number decreases by one in this section. In

other words a d block element on row 5, has a 4d sublevel. The last 6 columns of the periodic

table are the p block elements. Notice that the principle quantum number for these elements is

the same as the row number. The f section of the periodic table is located on the bottom two

rows of the table.

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When using the periodic table to write electron configurations, follow the chart, counting the

elements in each block until you reach the element you are writing the configuration for.

Alternately, you can write the noble gas configuration, by writing the noble gas immediately

before the specified element in brackets [ ].

Here are some examples using the periodic table above.

Electron Configuration Noble gas configuration

For Sr: 1s2 2s

2 2p

6 3s

2 3p

6 4s

2 3d

10 4p

6 5s

2 [Kr] 5s

2

For Al: 1s2 2s

2 2p

6 3s

2 3p

1 [Ne] 3s

2 3p

1

For Pb: 1s2 2s

2 2p

6 3s

2 3p

6 4s

2 3d

10 4p

6 5s

2 4d

10 5p

6 6s

2 4f

14 5d

10 6p

2 [Xe] 6s

2 4f

14 5d

10 6p

2

Now you try some.

Task 3e

1. Write the quantum numbers for the last filling electron in the following.

a. K

b. Co

c. Sn

2. Write the electron configuration for the following using the periodic table.

a. O

b. Mo

c. Cs

3. Write the noble gas configuration for the following.

a. Mg

b. Fe

c. Cl

d. Au

e. Fr

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4. Write the symbol of the element that is represented below by the electron configuration

or noble gas configuration.

a. 1s2 2s

2 2p

6 3s

2 3p

6 4s

2 3d

8

b. [Kr] 5s2 4d

10 5p

3

c. 1s2 2s

2 2p

6 3s

2 3p

4

Exceptions to the electron configuration

There are some elements that do not follow the general rules for writing electron configuration,

for example, Cr and Cu. The anomalies of Cr and Cu are easy to explain once you know that a

half-filled or completely filled d shell is considered to have extra stability. Hence configurations

ending 4s1 3d

5 and 4s

1 3d

10 rather than 4s

2 3d

4 and 4s

2 3d

9 are considered to be preferable. In

each case one of the s electrons is promoted to the d shell to create a more stable configuration.

Valence Electrons

Valence electrons are the electrons that are located on the outside energy level. You can tell

which electrons are valence by the main energy level. For example, in the electron

configuration, 1s2 2s

2 2p

6 3s

2 3p

4, the highest energy level is 3. There are 6 electrons in level

three, two in the s sublevel, and 4 in the p sublevel.

Electron Dot Diagrams

Electron Dot Diagrams are visual representations of the valence electrons in an atom. For

example: Al has a noble gas configuration of [Ne] 3s2 3p

1. If I were to draw the orbitals for the

valence electrons only they would be

.

3s 3p

There are two electrons in the 3s and 1 electron in the first orbital of the 3p. I could draw the

valence electrons around the symbol.

Al

The electron dot diagram for Al would be : Al . It doesn’t matter where you put the electrons

only that you put the correct number of electrons in each box. It is called electron dot because

you use dots instead of arrows. In the electron dot diagram, the symbol represent the nucleus

and all the inner electrons. The dots represent the valence electrons.

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Here’s another example: Te [Kr] 5s2 4d

10 5p

4 (Remember 4d is not valence)

5s 5p

The electron dot would be

Task 3f

1. Using the periodic table, how many valence electrons are in the following elements?

a. Br

b. Sr

c. Ar

d. Fr

2. Draw the electron dot diagram for each atom in (1).

Electron Configurations of Ions

You can also write the electron configurations of ions. The positive ions have lost electrons.

Electrons can only be removed from the outside energy level. For example, Na has an electron

configuration of [Ne] 3s1. Na

+ has an electron configuration of [Ne] or preferably [He] 2s

2 2p

6.

Fe has an electron configuration of [Ar] 4s2 3d

6. Fe

2+ has an electron configuration of [Ar] 3d

6.

Fe3+

has an electron configuration of [Ar] 3d5. Negative ions have gained electrons. Electrons

should be placed in the next available orbital. For example: S has and electron configuration of

[Ne] 3s2 3p

5. Cl

- has an electron configuration of [Ne] 3s

2 3p

6.

Isoelectronic Species

Species that have the same electron configuration are called isoelectronic. These usually come

in a series. For example: Ne is isoelectronic with O2-

, F-, Na

+, and Mg

2+.

Predicting Oxidation Numbers

An oxidation number is the tendency of an atom to gain or lose electrons. According to the

octet rule atoms are more stable whenever they have 8 valence electrons (except for things in

period 1). To determine the oxidation number, you need to know how many electrons are gained

or lost, or how many are likely to be gained or lost.

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For example: Ca has a configuration of [Ar] 4s2. It is easier to lose those 2 valence electrons

than to gain 6 to make 8. Losing electrons cause the charge to be positive, so the oxidation

number of Ca that is most likely is 2+. The calcium ion is usually written as Ca

2+.

P has a configuration of [Ne] 3s2 3p

3. It has 5 valence electrons. It is easier to gain three

electrons to make a total of eight than to lose the 5 it has. So it will gain 3 electrons, making it a

negative three charge. This is written as P3-

.

Task 3g

1. Without looking at the periodic table, identify the group, period, and block in which the

element that has the electron configuration [Xe] 6s2 is located.

2. Without looking at the periodic table, write the electron configuration for the Group 1

element in the third period. Is this element likely to be more reactive or less reactive than

the element described in (1)?

3. Write the electron configurations for the following ions.

a. Cl-

b. K+

c. Fe2+

d. Fe3+

e. P3-

4. Which of the ions in (3) are isoelectronic with each other?

5. Which of the following does not have the same configuration as a noble gas: Na+, Rb

+,

O2-

, Br-, Ca

+, Al

3+, S

2-?

6. What is the probable oxidation number for the following elements?

a. Mg

b. K

c. S

d. I

e. P

7. What is the electron configuration of silver? It only has one oxidation number, what is

it?