Chapter 4 - Arrangement of Electron in Atoms

I: The Development of a New Atomic Model

Rutherford's model of the atom

why electrons not drawn into nucleus

New model based on absorption and emission of light by matter.

A: Properties of Light

Prior to 1900 - light behaved as waves

Light was found to have particle characteristics.

Duality of matter.

Electromagnetic Radiation - definition

Examples

Electromagnetic Spectrum - definition

Figure 4-1 page 92

constant speed of 3 x 10^{8} meters per second - speed
of light through air (c)

Properties of waves:

wavelength - definition

Since it is a length the usual unit is either the meter, centimeter,
or nanometer (10^{-9} m)

frequency (n)- definition

Units are waves/second

Hertz - definition

Figure 4-2 page 92

Relationship between frequency and wavelength:

c = (wavelength)(frequency) or

c = (l)(n)

c is a constant - it is the same for all electromagnetic radiation

(l)(n) equals a constant therefore they are inversely proportional - hyperbolic curve.

Homework: Chapter 4: 4.1

B: The Photoelectric Effect

photoelectric effect - definition

Figure 4-3 page 93

If frequency of light was below a minimum value no electrons were emitted.

Wave theory predicted light of any frequency would be able to supply enough energy to eject an electron.

1. light as Particles

1900 - Max Planck - hot object do not emit electromagnetic energy continuously as would be expected by the wave theory.

Objects emit energy in small specific amounts called quanta.

Quantum - definition

Planck's equation: E = Planck's Constant x frequency or (h)(n)

where E is the quantum of energy in joules; n
is the frequency of the radiation emitted; h is Planck's constant: 6.626 x 10^{-34}
joule second.

1905 Einstein: electromagnetic radiation has a dual wave-particle nature

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

Each particle of light carries a quantum of energy. Einstein called these particles photons.

Photons - definition

The energy of a particular photon depends on the frequency of the radiation:

E_{photon} = (h)(n)

Einstein proposed that electromagnetic radiation is absorbed by matter only in whole numbers of photons.

To have an electron ejected from a metal surface, the electron must be struck by a single photon possessing at least the minimum energy required to knock the electron loose. If the frequency is below the minimum, then the electron remains bound to the metal surface. Different metals require different minimum frequencies to exhibit the photoelectric effect.

Homework: Chapter 4: 4.2

C: The Hydrogen-Atom Line Emission Spectrum

ground state - definition

excited state - definition

ground to excited state: atom absorbs energy in form of electromagnetic radiation

excited state to ground state: atoms emits (gives off) same amount of energy it absorbed to get into the excited state

"neon" signs

When studying hydrogen excitation in cathode ray tube, found typical pink glow. In further studies of this glow through a prism, they found that a line emission spectrum resulted. They expected a continuous spectrum.

Explaining this led to the quantum theory.

When an excited atom (hydrogen in this case) falls from the excited to the ground state, it emits a photon of energy. This photon is equal to the difference between the excited state and the ground state.

Figure 4-6 page 95

The existence of lines as opposed to one line indicates that the differences in the energy states in hydrogen and, thus in all atoms, is fixed.

This led to the conclusion that electrons can only exist in very specific energy states within an atom.

D: Bohr Model of the Hydrogen Atom

1913 - Niels Bohr - solved hydrogen spectrum problem

linked the atom's electron with photon emission

-- electron can circle nucleus in allowed paths or orbits

-- each orbit represents a definite fixed energy

-- the closer to the nucleus the lower the energy of the orbit and visa versa

Orbits are also called energy levels.

Electrons cannot exist between orbitals.

Figure 4-8 page 96

Bohr's model did not explain behavior of electrons in atoms that contain more than one electron and did not fully explain the chemical behavior of atoms.

Homework: Chapter 4: 4.3

II: The Quantum Model of the Atom

Needed to explain why atomic energy states are quantized and thus had to change the way the nature of the electron was viewed.

A: Electrons as Waves

Light could exist as both particles and waves.

What about electrons?

1924 - Louis de Broglie

any wave confined to a space can have only certain frequencies; consider electrons as waves confined to the space around an atomic nucleus; thus the electron would exist only at specific frequencies; and because of E = h (nu) they would have specific energies.

Other scientists showed that electron beams could

-- be diffracted,

-- they could experience interference

B: The Heisenberg Uncertainty Principle

the question of where electrons are in the atom was raised

1927 - Werner Heisenberg

detect electrons by their interaction with photons; any attempt to locate a specific electron with a photon knocks the electron off its course; thus there is an uncertainty in trying to locate an electron

The Heisenberg Uncertainty Principle - statement

It is a fundamental principle of our present understanding of light and matter.

C: The Schrodinger Wave Equation

1926 - Erwin Schrodinger

used duality of matter to develop an equation that treated electrons in atoms as waves

only waves of specific energies and therefore frequencies, provided solutions to the equation

Heisenberg's Principle and Schrodinger's equation laid the foundation for modern quantum theory.

Quantum Theory - definition

Solutions to the wave equation are known as wave functions.

Wave functions give only the probability of finding an electron at a given place around the nucleus.

Electrons do not travel around the nucleus in neat orbits as Bohr had postulated. They exist in regions called orbitals.

Orbitals - definition

Figure 4-11 page 101

D: Atomic Orbitals and Quantum Numbers

Electrons in atomic orbitals have quantized energies.

By solving the Schrodinger equation we can determine the energy level of the electron and other things.

Quantum Numbers are used to indicate orbitals (3 quantum numbers) and electrons (4 quantum numbers).

Quantum Numbers - definition

First three quantum numbers result from solutions to the Schrodinger equation. They indicate a)main energy level; b) the shape of the orbital; c) the orientation of an orbital.

The fourth quantum number describes the fundamental state of the electron that occupies the orbital.

1. Principal Quantum Number

principal quantum number - definition

symbol is n

Values are positive integers only e.g. 1, 2, 3

As n increases the distance from the nucleus increases.

2. Angular Momentum Quantum Number

all orbitals except one can have different shapes; these orbitals are also called sublevels

angular momentum quantum number - definition

symbol is l

For a specific energy level (principal quantum number) the number of orbital shapes is equal to n.

Values are zero and all positive integers up to (n-1).

e.g. if n =1 then l can be 0

if n = 2 then l can be 0 or 1 (n-1 is 2-1 or 1)

if n = 3 then l can be 0 or 1 or 2 (n-1 is 3-1 or 2)

Each value of l is assigned a letter.

table 4-1 page 102

The number of possible values for l indicate how many shapes are in each orbital.

n=1 has one value for l (0 - an s sublevel); therefore the first energy level (n=1) can have only one shape for the orbital.

n=2 has two values for l (0 - an s sublevel and 1 - a p sublevel); therefore the second energy level (n=2) can have two shapes for the orbitals.

s orbitals are spherical (not circular)

p orbitals are dumbbell shaped

d and f orbitals are too complex to describe in words.

Each atomic orbital is designated by the principal quantum number followed by the letter of the sublevel. e.g. 1s or 2s or 1s 2s 2p

3. Magnetic Quantum Number

Atomic orbitals can have the same shape but different orientations around the nucleus.

magnetic quantum number - definition

symbol is m

value can be -l to zero to +l

e.g. If n = 1 then l can be 0 and m can be 0

if n = 2 then l can be 0 or 1 and m can be -1 or 0 or +1

if n = 3 then l can be 0 or 1 or 2 and m can be -2 or -1 or 0 or +1 or +2

if l =0 then m can only be zero indicating an s orbital can have only one orientation around the nucleus -- there is one possible s orbital if l = 0.

if l = 1 then m can be -1 or 0 or +1: indicating that a p orbital can have three orientations around the nucleus -- there are three possible p orbitals if l = 1.

if l = 2 then m can be -2 or -1 or 0 or +1 or +2: indicating that d orbital can have five orientations around the nucleus -- there are five possible d orbitals if l = 2.

figure 4-15 page 103

table 4-2 page 104

the number of orbitals in each main energy level equals n^{2}

4. Spin Quantum Number

An electron can be considered to be spinning around an axis very much like the earth spins around an axis.

As such it has one of two possible spins -- clockwise and counterclockwise -- around the axis.

This spin creates a magnetic field.

spin quantum number - definition

two possible values +1/2 and -1/2

A single orbital can hold a maximum of two electrons, which must have opposite spins.

Homework: Chapter 4: 4.4

III: Electron Configurations

electron configuration - definition

atoms of different elements have different atomic numbers and therefore have different number of electrons; each element has a characteristic electron configuration

The ground state is the lowest energy state of an atom and it is this electron configuration in which we are interested.

A: Rules Governing Electron Configuration

1. Aufbau Principle - definition

figure 4-16 page 105

Rather than memorize the exceptions we use the diagonal rule chart.

2. Pauli Exclusion Principle - definition

The principal, angular momentum, and magnetic quantum numbers specify the energy, shape, and orientation of an orbital (first three quantum numbers describe an orbital).

The two values of the spin quantum number allow two electrons of opposite spin to occupy the orbital (all four quantum numbers describe an electron).

See figure 4-17 page 106

3. Hund's Rule (of Maximum Multiplicity) - definition

figure 4-18 page 106

B: Representing Electron Configurations

Skip author's orbital notation.

Use electron configuration notation.

1. Electron Configuration Notation

use a superscript to indicate the number of electrons in a sublevel

for hydrogen (atomic number 1) 1s^{1}

for helium (atomic number 2) 1s^{2}

for lithium (Z = 3)

for aluminum (Z = 13)

for selenium (Z = 34)

C: Elements of the Second Period

Valence electrons are all the electrons in the highest occupied energy level.

Inner shell electrons are all the electrons not in the highest occupied energy level.

Use principal quantum number in the electron configuration to determine the highest occupied energy level.

In the second period, the electrons from three to ten enter the second energy level.

Use diagonal rule chart to do the following electron notations.

Lithium (atomic number 3): 1s^{2} 2s^{1}

Beryllium (atomic number 4): 1s^{2}
2s^{2}

Boron (atomic number 5): 1s^{2} 2s^{2}
2p^{1}

Carbon (atomic number 6): 1s^{2} 2s^{2}
2p^{2}

Nitrogen (atomic number 7): 1s^{2} 2s^{2}
2p^{3}

Oxygen (atomic number 8): 1s^{2} 2s^{2}
2p^{4}

Fluorine (atomic number 9): 1s^{2} 2s^{2}
2p^{5}

Neon (atomic number 10): 1s^{2} 2s^{2}
2p^{6}

Orbital notation for each of the above.

Check Hund's Rule for each when doing orbital notation.

An octet is a filled s and p sublevel of the
outermost energy level.

Both s and p must be in the same energy level, it must be the outermost energy
level (highest principal quantum number) e.g. Neon

D: Elements of the Third Period

1. Noble Gas Notation

Will show both the electron configuration and the nobel gas configuration:

Sodium (Z=11): 1s^{2} 2s^{2}
2p^{6} 3s^{1} or [Ne] 3s^{1}

Magnesium (Z=12) 1s^{2} 2s^{2}
2p^{6} 3s^{2} or [Ne] 3s^{2}

Aluminum (Z=13): 1s^{2} 2s^{2}
2p^{6} 3s^{2} 3p^{1} or [Ne] 3s^{2}
3p^{1}

Silicon (Z=14): 1s^{2} 2s^{2}
2p^{6} 3s^{2} 3p^{2} or [Ne] 3s^{2}
3p^{2}

Phosphorus (Z=15): 1s^{2} 2s^{2}
2p^{6} 3s^{2} 3p^{3} or [Ne] 3s^{2}
3p^{3}

Sulfur (Z=16): 1s^{2} 2s^{2}
2p^{6} 3s^{2} 3p^{4} or [Ne] 3s2
3p^{4}

Chlorine (Z=17): 1s^{2} 2s^{2}
2p^{6} 3s^{2} 3p^{5} or [Ne] 3s^{2}
3p^{5}

Argon (Z=18): 1s^{2} 2s^{2}
2p^{6} 3s^{2} 3p^{6} or [Ne] 3s^{2}
3p^{6}

E: Elements of the Fourth Period

18 elements (2 electrons in s, 10 electrons in d, 8 electrons in p)

18 elements ns, (n-1)d, np where n is equal to the series number -- in this case 4.

s holds 2 + d holds 10 + p holds 6 = 18 electrons for the 18 elements

Exceptions: chromium and copper

stability of orbitals: filled > half filled > partially filled

partially filled orbital is one that has electrons in it but is not filled or half filled

F: Elements of the Fifth Period

18 elements: (2 electrons in s, 10 electrons in d, 8 electrons in p)

18 elements: Ns, (n-1)d, NP where n is equal to the series number -- in this case 5.

Some exceptions here but not as important as in series 4.

G: Elements of the Sixth and Seventh Periods

Period 6: 32 elements

Period 6: Ns, (n-2)f, (n-1)d, NP

s holds 2 + f holds 14 + d holds 10 + p holds 6 = 32 electrons

Period 7 incomplete and we rarely use these elements in normal chemical reactions.

Homework: Chapter 4: 4.5

end of notes

Electromagnetic radiation
is a form of energy that exhibits wavelike behavior as it travels through space.

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The Electromagnetic
Spectrum is all forms of electromagnetic radiation.

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Wavelength is the distance between
corresponding points on adjacent waves.

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Frequency is the number of waves
that pass a given point in a specific time, usually one second.

Back

A hertz is a unit defined as one wave
per second.

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The photoelectric effect
refers to the emission of electrons from a metal when light shines on the metal.

Back

A photon is a particle of electromagnetic
radiation having a zero rest mass and carrying a quantum of energy.

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A quantum is the minimum quantity of
energy that can be lost or gained by an atom.

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The ground state is the lowest
energy state of an atom.

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The excited state is a state in
which an atom has a higher potential energy than it has in its ground state.

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Heisenberg's Uncertainty Principle:
It is impossible to determine simultaneously both the position and velocity
of an electron or any other particle.

Back

Quantum theory describes mathematically
the wave properties of electrons and other very small particles.

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An orbital is a three dimensional region around the nucleus
that indicates the probable location of an electron.

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Quantum numbers specify the
properties of atomic orbitals and the properties of electrons in orbitals.

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The principal quantum
number indicates the main energy level occupied by the electron.

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The angular momentum quantum
number indicates the shape of the orbital.

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The magnetic quantum number indicates
the orientation of an orbital around the nucleus.

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The spin quantum number indicates the
two fundamental spin states of an electron in an orbital.

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