Unit 4 - Electrons in Atoms

Background information:

• Early research focused on the nucleus

• How are the electrons arranged?

• Why weren’t the electrons pulled into the

nucleus?

• Why are there differences in chemical

behavior?

• Certain elements emitted light when heated in

a flame that could be related to the

arrangement of the electrons

Wave Nature of Light

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

• Waves have three primary characteristics:• Wavelength – distance between equivalent

points on a continuous wave (m or cm)• Frequency – number of waves that pass a

point in a given second (s-1)• Amplitude – height of the wave measured

form the origin to the top of a crest

- All electromagnetic waves travel at the same speed, but they have different wavelengths and frequencies.

- This gives the waves different properties.- Visible light is a small portion of the electromagnetic

spectrum.- The electromagnetic spectrum encompasses all forms of

radiation.- The energy of the radiation increases with increasing

frequency and the resultant decreasing wavelength.

Infrared image:

Ultraviolet light images:

X-ray images:

The three characteristics of electromagnetic radiation are related to one another through the equation:

c = λυ

speed of light = wavelength x frequency

= cm ● s-1

c = 3.00 x 1010

c = 3.00 x 108

Determine the wavelength, in cm, of a microwave that has a frequency of 3.44 x 109 s-1.

Use the speed of light equation

c = λν

3.00 x 1010 = λ ∙ 3.44 x 109

λ =

λ = .872 x 101 = 8.72 cm

Determine the frequency of green light. It has a wavelength of 4.90 x 10-7 m.

Use the speed of light equation

c = λν

3.00 x 108 = ν ∙ 4.90 x 10-7

ν = = 6.12244898 x 1014

ν = 6.12 x 1014 s-1

Now solve the following examples on your whiteboard:

• Calculate the wavelength of the red light used in a bar code reader that has a frequency of

4.62 x 1014 s-1.

• A laser used to dazzle the audience in a rock concert emits a blue light with a wavelength of

5.15 x 10-7 m. Calculate the frequency of this light.

SOLUTIONS:• Calculate the wavelength

of the red light used in a bar code reader that has a frequency of

4.62 x 1014 s-1.

c = λν

3.00 x 108 = λ ∙ 4.62 x 1014

λ = = 6.493506494 x 10-7

λ = 6.49 x 10-7 m

• A laser used to dazzle the audience in a rock concert emits a blue light with a wavelength of

5.15 x 10-7 m. Calculate the frequency of this light.

c = λν

3.00 x 108 = ν ∙ 5.15 x 10-7

ν = = 5.825242718 x 1014

ν = 5.83 x 1014 s-1

PARTICLE NATURE OF LIGHT

• Considering light as a wave does not explain much of its everyday behavior.

• It fails to describe some important aspects of light’s interactions with matter.

• The wave model does not explain why heated objects emit only certain frequencies of light at a given temperature.

FLAME TEST:

It cannot explain why some metals emit electrons when colored light of a specific frequency is shined on them.

THE QUANTUM CONCEPT

• Remember that temperature is a measure of the average kinetic energy a substance’s particles. As a metal gets hotter, it possesses a greater amount of kinetic energy and emits different colors of light.

• The colors correspond to different frequencies and wavelengths.

• The wave model could not explain this.

Max Planck

• Max Planck studied this phenomenon and it led him to a startling conclusion: matter can gain or lose energy only in small, specific amounts called quanta.

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

Planck’s Equation:• Planck developed a mathematical relationship between

the energy and frequency of emitted radiation:

E = hνEnergy = Planck’s constant ∙ frequency

Energy is measured in Joules (J)

The unit for frequency is s-1

h = 6.63 x 10-34 J ∙ s

Planck’s Equation – another version:

• Another version of Planck’s equation is:

E =

In this version we use wavelength (λ) and the speed of light instead of frequency.

THE PHOTOELECTRIC EFFECT

• In the photoelectric effect, electrons, called photoelectrons, are emitted from the surface of a metal when light of a certain frequency is shined on the surface.

THE PHOTOELECTRIC EFFECT

• No matter how long it shines, light with a frequency below that required will not cause electrons to be ejected from the surface of the metal.

• Once the correct frequency is reached, even a dim light will cause the electrons to be ejected.

THE PHOTOELECTRIC EFFECT• Einstein proposed that electromagnetic radiation has

both wave-like and particle-like properties.

• While a beam of light has many wave-like characteristics, it can also be thought of as a stream of tiny particles, or bundles of energy, that Einstein called photons.

• A photon is a particle of electromagnetic radiation with no mass that carries a quantum of energy.

• The energy of a photon is: E = hν

Examples:

• Determine the energy of a photon from the violet portion of the rainbow if it has a frequency of

7.23 x 1014 s-1.

E = hν

= (6.63 x 10-34) ∙ (7.23 x 1014)

= 4.79349 x 10-19

= 4.79 x 10-19 J

• The wavelength of red light from the helium-neon laser is

6.328 x 10-7 m. Determine the energy of this light.

E = =

= 3.1431732 x 10-

19

= 3.143 x 10-19 J

Another example:• Calculate the wavelength, in m, of a photon in the red

spectra line of lithium that has an energy of

2.96 x 10-19 J.

E = 2.96 x 10-19 =

λ =

λ = 6.71 x 10-7 m

Now solve the following examples on your whiteboard:

• Calculate the frequency of a photon in yellow light whose energy is

3.37 x 10-19 J.

• A radio station broadcasts on a frequency of 9.83 x 106 s-1 . Determine the energy of the photons traveling through the atmosphere.

Atomic Emission Spectra

• The atomic emission spectra of an element is the set of frequencies of the electromagnetic spectrum emitted by atoms of the element.

• The element’s atomic emission spectrum consists of several individual lines of color, not a continuous range of colors as seen in the visible spectrum.

Atomic Emission Spectra

Atomic Emission Spectra

• Each element’s atomic emission spectrum is unique and can be used to determine if that element is part of an unknown compound.

• The fact that only certain colors appear in an element’s atomic emission spectrum means that only certain specific frequencies of light are emitted. Because those emitted frequencies of light are related to specific energy levels, it can be concluded that only photons having specific energies are emitted.

Atomic Emission Spectra

• Scientists were still confused. They had not expected line spectra. They had expected a continuous series of colors and energies as excited electrons lost energy and spiraled toward the nucleus. But, the electrons weren’t doing this.

QUANTUM THEORY AND THE ATOMThe Bohr Model of the Atom

• Niels Bohr, a Danish physicist, attempted to explain why the emission spectrum of the hydrogen atom was not continuous.

Bohr Model of the Atom• Bohr proposed, using Planck’s and Einstein’s concepts,

that the hydrogen atom has only certain allowable energy states for its electron.

• He suggested that the single electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.

• The smaller the electron’s orbit, the lower the atom’s energy state. The higher the electron’s orbit, the higher the atom’s energy state.

Bohr Model of the Atom

• Bohr assigned a quantum number, n, to each orbit. The higher the value of “n”, the higher the corresponding energy level.

Hydrogen’s Line Spectrum• Bohr suggested that when hydrogen is in the ground

state, the lowest energy state, the electron is in the n = 1 orbit. In this state, the atom does not radiate energy.

• If energy is added (absorbed), the electron moves to a higher energy orbit. The atom is now in an excited state.

• Since nature likes being in the lowest energy state possible, the atom will return to the ground state. This happens when the electron returns to the n = 1 orbit. In the process a photon of energy is emitted.

Hydrogen’s Line Spectrum• According to Bohr’s model, only certain atomic energies

are possible, therefore only certain frequencies of electromagnetic radiation are emitted.

Hydrogen’s Line Spectrum• Bohr’s model explained the hydrogen atom, but failed to

explain the emission spectrum of any other element.

• Bohr’s model did not fully account for the chemical behavior of atoms.

• Also, unlike the models developed to this point, evidence was mounting that the electrons do not move around the nucleus in circular orbits.

THE QUANTUM MECHANICAL MODEL OF THE ATOM: Electrons as Waves

• Louis De Broglie thought that Bohr’s quantized orbits had characteristics similar to those of waves.

ELECTRONS AS WAVES

• His question: if waves can have particle-like behavior, could the opposite also be true? Can particles like electrons behave like waves?

ELECTRONS AS WAVES

• If an electron has a wavelike motion and it’s restricted to a circular orbit of fixed radius, then the electron is allowed only certain possible wavelengths, frequencies, and energies.

ELECTRONS AS WAVES• De Broglie proposed an equation that could be used to

calculate the wavelength of a particle:

λ = λ is the wavelength

h = 6.63 x 10-34 J∙s

m = the mass of the particle

v = the velocity of the particle

Experiments that followed proved that electrons and other moving particles do have wave characteristics.

THE HEISENBERG UNCERTAINTY PRINCIPLE

Werner Heisenberg developed a mathematical system of matrices

that led to the modern version of quantum mechanics. This led to the uncertainty principle:

The more precisely the position of a particle is determined, the less precisely its momentum can be known, and vice versa.

SCHRODINGER WAVE EQUATION

S Erwin Schrodinger through the use of wave mechanics developed a wave equation that treated hydrogen’s electron as a wave.

SCHRODINGER WAVE EQUATION• The wave equation is quite complex and each solution is

known as a wave function.

• The wave function is related to the probability of finding the electron within a particular volume of space around the nucleus.

• The wave function predicts a three-dimensional region around the nucleus called an atomic orbital that describes the electron’s probable location.

SCHRODINGER WAVE EQUATION

• The atomic orbital can be though of as a fuzzy cloud where the density of the cloud at a given point can be thought of as proportional to the probability of finding the electron at that point.

HYDROGEN’S ATOMIC ORBITALS• The boundary of an atomic orbital is fuzzy, so orbitals do

not have a defined size.

• Chemists draw an orbital’s surface to contain 90% of the electron’s total probability distribution.

• Just as the Bohr model assigned a quantum number to the electron’s orbit, the quantum mechanical model does the same.

HYDROGEN’S ATOMIC ORBITALS• The first is the • principal quantum number (n)

• The principal quantum number indicates the relative sizes and energies of the atomic orbitals. As “n” increases, the orbital becomes larger; the electron spends more time farther away from the nucleus; and the atom’s energy level increases.

• Therefore, “n” specifies the atom’s major energy levels, called the

• principal energy levels

LABELING ELECTRONS IN ATOMS• In quantum theory each electron in an atom is assigned

a set of four quantum numbers.• Three of the numbers act like coordinates to describe the

location while the fourth describes the electron’s orientation in the orbital. The first is the

• principal quantum number (n) • This number describes the energy level that the electron

occupies. It is assigned a positive integer, starting with one:

• n= 1, 2, 3, 4, …

LABELING ELECTRONS IN ATOMS• The larger the value of “n”, the further the electron is

from the nucleus and the more energy it will have.• Quantum numbers are used to describe the shapes of

atomic orbitals.• The second quantum number is the• azimuthal or angular quantum number• It is designated by the letter l• “l” has numerical values ranging from:• l = 0, 1, 2, 3, … n-1

LABELING ELECTRONS IN ATOMS• While “l” does have numerical values, the shapes of the

orbitals are often described using letters:

l letter

0 s

1 p

2 d

3 f

LABELING ELECTRONS IN ATOMS• The lowest energy orbital is the “s” orbital. It is the

closest to the nucleus and shaped like a sphere:

There is an “s” orbital in each energy level.

LABELING ELECTRONS IN ATOMS• The next higher orbital is the “p” orbital. There are three

“p” orbital orientations at each energy level above n = 1.

LABELING ELECTRONS IN ATOMS• Orbitals designated “d” and “f” have more complex

shapes and even higher energy.• The “d” orbitals exist at n = 3 and above.

LABELING ELECTRONS IN ATOMS

• The “f” orbitals exist at n = 4 and above

LABELING ELECTRONS IN ATOMS

LABELING ELECTRONS IN ATOMS• A third quantum number, the magnetic quantum number,

is designated

• ml

• The value of ml tells one the electron’s position by designating the spatial orientation of the orbital that the electron occupies.

LABELING ELECTRONS IN ATOMS• So while multiple electrons within an atom may have the

same values of “n” and “l”, they may not necessarily have the same values of “ml”.

• These electrons are said to be in the same sublevel of the atom.

LABELING ELECTRONS IN ATOMS• The relationship between “l”, and “ml” is:

Value of l Letter designation

Range of ml Number of orientations

Maximum number of electrons

0 s 0 1 2

1 p -1, 0, 1 3 6

2 d -2, -1, 0, 1, 2 5 10

3 f -3,-2,-1,0,1,2,3, 7 14

LABELING ELECTRONS IN ATOMS

• The fourth quantum number describes the motion of the electron

• It is the spin quantum number

• ms

• “ms” has values of: + and -

ELECTRON CONFIGURATION• The arrangement of the electrons in an atom is called

the atom’s

• electron configuration

• Since low energy systems are more stable than high energy systems, electrons tend to assume the arrangement that gives them the lowest possible energy.

ELECTRON CONFIGURATION

• Three rules, or principles, define how electrons can be arranged in the orbitals of an atom:

• Aufbau Principle

• Pauli Exclusion Principle

• Hund’s Rule

ELECTRON CONFIGURATION

• The Aufbau Principle states that each electron will occupy the lowest energy orbital available.

• The Pauli Exclusion Principle states that a maximum of two electrons may occupy a single atomic orbital; but only if the electrons have opposite spins.

• Hund’s Rule states that single electrons with the same spin must occupy each equal energy orbital before additional electrons with opposite spins can occupy those same orbitals.

ELECTRON CONFIGURATION

• As stated earlier, an electron configuration is the arrangement of the electrons within an atom. This diagram, known as the diagonal rule will help you sequence the proper filling of the atomic orbitals.

ELECTRON CONFIGURATION

ELECTRON CONFIGURATION• To write an electron configuration, follow these steps:

(1) Locate the element whose electron configuration you wish to write.

(2) Fill in the orbitals in the proper order with electrons. Use the diagonal rule.

(3) Check that the total number of electrons matches the atomic number.

ELECTRON CONFIGURATION• Write the electron configuration for nickel.

Ni = 28 electrons

1s22s22p63s23p64s23d8

or

1s22s22p63s23p63d84s2

ELECTRON CONFIGURATION• You can also create your own guide from a blank

periodic table:

ELECTRON CONFIGURATION• Add in the electron configuration information:

ELECTRON CONFIGURATION• Fill in the details:

ELECTRON CONFIGURATION• There is a shorthand method of writing electron

configurations known as the noble gas electron configuration.

• By using the noble gas just before the element in question and then adding the remaining electron configuration, one can write an abbreviated form of the electron configuration.

ELECTRON CONFIGURATION• Write the noble gas electron configuration for silicon.

Si = 14 electrons

Write the preceding noble gas inside a set of brackets:

[Ne]

Then, add the remaining electrons:

[Ne]3s23p2

ELECTRON CONFIGURATION• On your white board write the complete electron

configuration for the following elements:

rhenium

arsenic

ELECTRON CONFIGURATION• On your white board write the complete electron

configuration for the following elements:

rhenium

1s22s22p63s23p64s23d104p65s24d105p66s24f145d5

1s22s22p63s23p63d104s24p64d104f145s25p65d56s2

arsenic

1s22s22p63s23p64s23d104p6

1s22s22p63s23p63d104s24p6

ORBITAL DIAGRAMS• Orbital diagrams are used to show how electrons are

distributed within sublevels and to show the direction of spin.

• Each orbital is represented by either a box, circle, or line:

_______

The electrons are represented by arrows: ↑↓

The direction of spin is represented by the direction of the arrow.

ORBITAL DIAGRAMS• Construct the orbital diagram for oxygen

• The electron configuration for oxygen is:

• 1s22s22p4

• ↑↓ ↑↓ ↑↓ ↑ ↑

1s2 2s2 2p4

ORBITAL DIAGRAMS

• Electrons are arranged in accordance with Hund’s Rule.

This rule states that orbitals of equal energy are each

occupied by one electron before any pairing occurs by

adding a second electron.

• This way repulsion is minimized.

• All electrons in singly occupied orbitals must have the

same spin.

• When two electrons occupy the same orbital, they must

have opposite spins.

ORBITAL DIAGRAMS• Construct an orbital diagram for aluminum• The electron configuration for aluminum is:

• 1s22s22p63s23p1

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ __ __

1s2 2s2 2p6 3s2 3p1

ORBITAL DIAGRAMS• Construct an orbital diagram for iron.• The electron configuration for iron is:

1s22s22p63s23p64s23d6

First write:

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑ ↑ ↑ ↑1s2 2s2 2p6 3s2 3p6 4s2 3d5

Then add the last electron:

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑ ↑ ↑1s2 2s2 2p6 3s2 3p6 4s2 3d6

ORBITAL DIAGRAMS• On your whiteboard, construct the orbital diagram for

• Arsenic

• Vanadium