Chapter 4

Arrangement of Electrons in Atoms

Section 1 – The Development of a new Atomic Model

Properties of Light Before 1900, scientists thought light behaved

as a wave Changed when it was discovered that light also

had particle-like characteristics

Visible light is a kind of electromagnetic radiation form of energy that exhibits wavelike behavior as it travels through space X-rays, UV, infrared, etc.

Together, all forms of electromagnetic radiation form the electromagnetic spectrum

Properties of EM Radiation All forms of EM radiation travel at a constant

speed (3.0 × 108 meters per second (m/s)) through a vacuum and at slightly slower speeds through matter

It has a repetitive nature, which can be described by the measurable properties wavelength and frequency

Wavelength (λ) the distance between corresponding points on neighboring waves

Frequency (ν) the number of waves that pass a given point in a specific time, usually one second

λ

λ

Frequency and Wavelength

Frequency and wavelength are mathematically related to each other

This relationship is written as follows

c = λν

c is the speed of light λ is the wavelength of the electromagnetic wave ν is the frequency of the electromagnetic wave

Because c is the same for all electromagnetic radiation, the product λν is a constant

The Photoelectric Effect

Early 1900s, scientists conducted two experiments involving relations of light and matter that could not be explained by the wave theory of light

One experiment involved a phenomenon known as the photoelectric effect

Photoelectric effect the emission of electrons from a metal when light shines on the metal

The Mystery

For a given metal, no electrons were emitted if the light’s frequency was below a certain minimum—regardless of how long the light was shone

Light was known to be a form of energy, capable of knocking loose an electron from a metal

Wave theory of light predicted light of any frequency could supply enough energy to eject an electron

Couldn’t explain why light had to be a minimum frequency in order for the photoelectric effect to occur

The Particle Description of Light Explanation 1900, German physicist Max

Planck was studying the emission of light by hot objects

Proposed a hot object does not emit electromagnetic energy continuously, as would be expected if the energy emitted were in the form of waves

Instead, Planck suggested the object emits energy in small, specific amounts called quanta

Quantum the minimum quantity of energy that can be lost or gained by an atom

Planck projected the following relationship between a quantum of energy and the frequency of radiation

E = hν

In the equation, E is the energy, in joules, of a quantum of

radiation ν is the frequency of the radiation emitted h is a constant now known as Planck’s constant

h = 6.626 × 10−34 J• s

1905 Albert Einstein Expanded on Planck’s theory by introducing the

idea that electromagnetic radiation has a dual wave-particle nature

Light displays many wavelike properties, it can also be thought of as a stream of particles

Einstein called these particles photons Photon a particle of electromagnetic

radiation having zero mass and carrying a quantum of energy

The energy of a specific photon depends on the frequency of the radiation

Ephoton = hν

The Hydrogen-Atom Line-Emission Spectrum

When current is passed through a gas at low pressure, the potential 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 potential energy than it has in its ground state is an excited state

Example: Neon Signs

When an excited atom returns to its ground state, it gives off the energy it gained in the form of electromagnetic radiation

Excited neon atoms emit light when falling back to the ground state or to a lower-energy excited state.

Line-Emission Spectrum Scientists passed electric current through a

vacuum tube containing hydrogen gas at low pressure, they observed the emission of a characteristic pinkish glow

Emitted light was shined through a prism, it was separated into a series of specific frequencies of visible light

The bands of light were part of what is known as hydrogen’s line-emission spectrum

Quantum Theory The hydrogen atoms should be excited by

whatever amount of energy was added to them

Scientists expected to see the emission of a continuous range of frequencies of electromagnetic radiation, that is, a continuous spectrum

Why had the hydrogen atoms given off only specific frequencies of light?

Attempts to explain this observation led to an entirely new theory of the atom called quantum theory

Whenever an excited hydrogen atom falls back from an excited state to its ground state or to a lower-energy excited state, it emits a photon of radiation

The energy of this photon (Ephoton = hν) is equal to the difference in energy between the atom’s initial state and its final state

Changes of energy (transition of an electron from one orbit to another) is done in isolated quanta

Quanta are not divisible

There is sudden movement from one specific energy level to another, with no smooth transition

There is no ``in-between‘‘

Hydrogen atoms emit only specific frequencies of light showed that energy differences between the atoms’ energy states were fixed

The electron of a hydrogen atom exists only in very specific energy states

Bohr Model of the Hydrogen Atom

Proposed a model of the hydrogen atom that linked the atom’s electron with photon emission

According to the model, 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

The electron, and therefore the hydrogen atom, is in its lowest energy state when it is in the orbit closest to the nucleus

This orbit is separated from the nucleus by a large empty space where the electron cannot exist

The energy of the electron is higher when it is in orbits farther from the nucleus

The Rungs of a Ladder The electron orbits or atomic energy levels in

Bohr’s model can be compared to the rungs of a ladder

When you are standing on a ladder, your feet are on one rung or another

The amount of potential energy that you possess relates to standing on the first rung, the second rung…

Your energy cannot relate to standing between two rungs because you cannot stand in midair

In the same way, an electron can be in one orbit or another, but not in between

Summary of the Models of the Atom

Section 2 – The Quantum Model of the Atom

1) In 1924, Louis de Broglie proposed that ELECTRONS have a dual wave-particle nature. Other experiments soon demonstrated wave properties of electrons.

The Quantum Mechanical Model of the Atom

The Quantum Mechanical Model of the Atom

2) In 1926 Erwin Schrodinger treated electrons as waves in a model called the quantum mechanical model of the atom.a) Schrodinger’s equation applied

equally well to elements other than hydrogen.

b) Schrodinger’s equations: helps determine probable electron location in an atom

orbital = a three-dimensional region around the nucleus that indicates the probable location of an electron. (fuzzy electron clouds)a) The cloud has no definite boundary, it is

possible that the electron might be found at a considerable distance from the nucleus.

The Quantum Mechanical Model of the Atom

The 4 Quantum Numbers: MAGNETIC

d) Ex. Orbitals around the Nucleus of a Neon Atom

Quantum Numbers Electrons are not locked into fixed orbits

We can only predict the areas where electrons are most likely to be found

Numbers are given to electrons to help with predictions

Quantum NumbersThere are four quantum numbers. The first three quantum numbers result from solutions to Schrodinger’s equation and describe the orbital in which an electron is located.

• Principal quantum number• Angular momentum quantum number• Magnetic quantum number

The fourth quantum number describes an electron’s spin movement within an orbital.

The 4 Quantum Numbers: PRINCIPAL

1) The PRINCIPAL QUANTUM NUMBER indicates the main energy level (shell) of the orbital in which a particular electron is located.

2) The ANGULAR MOMENTUM QUANTUM number indicates the shape (sublevel) of the orbital in which a particular electron is located.

a) The angular momentum quantum number is symbolized by the letter “l”

b) Angular momentum quantum numbers are usually designated with letters s,p,d,f

c) The order of the sublevels can be remembered as follows: “some people don’t forget

The 4 Quantum Numbers: ANGULAR MOMENTUM

The 4 Quantum Numbers: MAGNETIC

3) The MAGNETIC QUANTUM NUMBER indicates the spatial orientation of the orbital in which a particular electron is located.

a) The magnetic quantum number is symbolized by “m”.

b) The orientation of an orbital is designated using a three-dimensional coordinate system with the nucleus at the center.

The 4 Quantum Numbers: MAGNETIC

c) Orientation of orbitals• An “s” orbital has 1 possible orientation (a

sphere centered on the nucleus).• A “p” orbital has 3 possible orientations. (px, py,

pz)• A “d” orbital has 5 possible orientations.• An “f” orbital has 7 possible orientations.

The 4 Quantum Numbers: SPIN

4. The SPIN QUANTUM NUMBER indicates the spin of an electron on its own axis

a) The spin quantum number is symbolized by “s”.b) There are two possible fundamental states

(spins) for an electron in an orbital +1/2 and -1/2 are used to indicate the two possible

states (spins) of an electron in an orbital

s

s

s

s

p

p

p

d

d

f

1

2

3

4

Energy levels can be thought of as floors in an apartment building. The floors that are higher up contain more apartments with different numbers of rooms. The apartments are like the sublevels. The rooms in the apartments are like the number of orbitals in a sublevel.

Summary of the First 4 Energy Levels P r in c ip a l Q u a n tu m N u m b e r :

Main E n e rg y Level (n )

Type(s) o f S u b le v e l

(o r b ita l sh a p es)

# of O rb ita ls

per m a in energy lev e l

Maximum # o f Electrons p e r

su b le v e l

Number o f E lec tr o n s per M a in

E n e rg y Level (2 n 2)

1

s

1

2

2

s

1

2

p

3

6

3

s

1

2

p

3

6

d 5 1 0

4

s

1

2

p

3

6

d

5

1 0

f

7

1 4

Section 3 – Electron Configurations

Quantum model of atom better than Bohr model b/c it describes the arrangements of electrons in atoms other than hydrogen

Electron configuration the arrangement of electrons in an atom

b/c atoms of different elements have different numbers of e-, the e- configuration for each element is unique

Electrons in atoms assume arrangements that have lowest possible energies

Ground-state electron configuration lowest-energy arrangement of electrons for each element

Some rules combined with quantum numbers let us determine the ground-state e- configurations

Rules Governing Electron Configurations To build up electron configurations for the

ground state of any particular atom, first the energy levels of the orbitals are determined

Then electrons are added to the orbitals one by one according to three basic rules

1. Aufbau principle2. Pauli exclusion principle3. Hund’s rule

Aufbau Principle

The first rule shows the order in which electrons occupy orbitals

According to the Aufbau principle, an electron occupies the lowest-energy orbital that can receive it

The orbital with the lowest energy is the 1s orbital

Ground-state hydrogen atom electron in this orbital

The 2s orbital is the next highest in energy, then the 2p orbitals

Beginning with the third main energy level, n = 3, the energies of the sublevels in different main energy levels begin to overlap

The 4s sublevel is lower in energy than the 3d sublevel

Therefore, the 4s orbital is filled before any electrons enter the 3d orbitals

(Less energy is required for two electrons to pair up in the 4s orbital than for a single electron to occupy a 3d orbital)

Pauli Exclusion Principle The second rule

reflects the importance of the spin quantum number

According to the Pauli exclusion principle, no two electrons in the same atom can have the same set of four quantum numbers

Hund’s Rule

The third rule requires placing as many unpaired electrons as possible in separate orbitals in the same sublevel

Electron-electron repulsion is minimized the electron arrangements have the lowest energy possible

Hund’s rule orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron, and all electrons in singly occupied orbitals must have the same spin

Orbital Notation

H He

C

Electron-Configuration Notation

Electron-configuration notation eliminates the lines and arrows of orbital notation

Instead, the number of electrons in a sublevel is shown by adding a superscript to the sublevel designation

The hydrogen configuration is represented by 1s1

The superscript indicates that one electron is present in hydrogen’s 1s orbital

The helium configuration is represented by 1s2

Here the superscript indicates that there are two electrons in helium’s 1s orbital

Sample Problem

The electron configuration of boron is 1s22s22p1. How many electrons are present in an atom of boron? What is the atomic number for boron? Write the orbital notation for boron.

Practice Problems

The electron configuration of nitrogen is 1s22s22p3. How many electrons are present in a nitrogen atom? What is the atomic number of nitrogen? Write the orbital notation for nitrogen.

Practice ProblemsThe electron configuration of fluorine is 1s22s22p5.

What is the atomic number of fluorine? How many of its p orbitals are filled? How many unpaired electrons does a fluorine atom contain?

Answer 9 2 1

Elements of the Second Period According to Aufbau principle, after 1s orbital

is filled, the next electron occupies the s sublevel in the second main energy level

Lithium, Li, has a configuration of 1s22s1

The electron occupying the 2s level of a lithium atom is in the atom’s highest, or outermost, occupied level

The highest occupied level the electron-containing main energy level with the highest principal quantum number

The two electrons in the 1s sublevel of lithium are no longer in the outermost main energy level

They have become inner-shell electrons electrons that are not in the highest occupied energy level

The fourth electron in an atom of beryllium, Be, must complete the pair in the 2s sublevel because this sublevel is of lower energy than the 2p sublevel

With the 2s sublevel filled, the 2p sublevel, which has three vacant orbitals of equal energy, can be occupied

One of the three p orbitals is occupied by a single electron in an atom of boron, B

Two of the three p orbitals are occupied by unpaired electrons in an atom of carbon, C

And all three p orbitals are occupied by unpaired electrons in an atom of nitrogen, N

Elements of Third Period After the outer octet is filled in neon, the next

electron enters the s sublevel in the n = 3 main energy level

Atoms of sodium, Na, have the configuration 1s22s22p63s1

Once past Neon, can use Noble-gas notation

Noble-Gas Notation The Group 18 elements (helium, neon, argon,

krypton, xenon, and radon) are called the noble gases

To simplify sodium’s notation, the symbol for neon, enclosed in square brackets, is used to represent the complete neon configuration:

[Ne] = 1s22s22p6

This allows us to write sodium’s electron configuration as [Ne]3s1, which is called sodium’s noble-gas notation

Elements of the Fourth Period Period begins by filling 4s orbital (empty

orbital of lowest energy)

First element in fourth period is potassium, K E- configuration [Ar]4s1

Next element is calcium, Ca E- configuration [Ar]4s2

With 4s sublevel filled, 4p and 3d sublevels are next available empty orbitals

Diagram shows 3d sublevel is lower energy than 4p sublevel

So 3d is filled next

Total of 10 electrons can fill 3d orbitals

These are filled from element scandium (Sc) to zinc (Zn)

Scandium has e- configuration [Ar]3d14s2

Titanium, Ti, has configuration [Ar]3d24s2

Vanadium, V, has configuration [Ar]3d34s2

Up to this point, 3 e- with same spin added to 3 separate d orbitals (required by Hund’s rule)

Chromium, Cr, has configuration [Ar]3d54s1

We added one electron to 4th 3d orbital We also took a 4s electron and added it to 5th

3d orbital Seems to be against Aufbau principle

In reality, [Ar]3d54s1 is lower energy than [Ar]3d44s2

Having 6 outer orbitals with unpaired electrons in 3d orbital is more stable than having 4 unpaired electrons in 3d orbitals and forcing 2 electrons to pair in 4s

For tungsten, W, (same group as chromium) having 4 e- in 5d orbitals and 2 e- paired in 6s is most stable arrangement

No easy explanantion

Manganese, Mn, has configuration [Ar]3d54s2

Added e- goes to 4s orbital, completely filling it and leaving 3d half-filled

Starting with next element, e- continue to pair in d orbitals

So iron, Fe, has configuration [Ar]3d64s2

Cobalt, Co, has [Ar]3d74s2

Nickel, Ni, has [Ar]3d84s2

With copper, Cu, an electron from 4s moves to pair with e- in 5th 3d orbital

Configuration: [Ar]3d104s1 (most stable)

For zinc, Zn, 4s sublevel filled to give [Ar]3d104s2

For next elements, 1 e- added to 4p orbitals according to Hund’s rule

Elements of Fifth Period In 18 elements of 5th period, sublevels fill in

similar way to 4th period elements BUT they start at 5s level instead of 4s level

Fill 5s, then 4d, and finally 5p

There are exceptions just like in 4th period

Practice ProblemWrite both the complete electron-configuration

notation and the noble-gas notation for iron, Fe.

Write both the complete electron configuration notation and the noble-gas notation for iodine, I. How many inner-shell electrons does an iodine atom contain?

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p5

[Kr] 4d10 5s2 5p5

46

How many electron-containing orbitals are in an atom of iodine? How many of these orbitals are filled? How many unpaired electrons are there in an atom of iodine?

27 26 1

Write the noble-gas notation for tin, Sn. How many unpaired electrons are there in an atom of tin?

[Kr] 5s2 4d10 5p2

2

Without consulting the periodic table or a table in this chapter, write the complete electron configuration for the element with atomic number 25.

1s2 2s2 2p6 3s2 3p6 3d5 4s2

Elements of 6th and 7th periods 6th period has 32 elements To build up e- configurations for elements in

this period, e- first added first to 6s orbital in cesium, Cs, and barium, Ba

Then in lanthanum, La, e- added to 5d orbital

With next element, cerium, Ce, 4f orbitals begin to fill

Ce: [Xe]4f15d16s2

In next 13 elements, 4f orbitals filled

Next 5d orbitals filled

Period finished by filling 6p orbitals

(some exceptions happen)

Practice ProblemWrite both the complete electron-configuration

notation and the noble-gas notation for a rubidium atom.

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s1

[Kr]5s1

Write both the complete electron configuration notation and the noble-gas notation for a barium atom.

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2

[Xe]6s2