Chapter 5Models of the Atom

Atomic ModelsRutherford used existing ideas bout the atom and proposed an atomic model in which the electrons move around the nucleus.

However, Rutherford’s atomic model could not explain the chemical properties of element.

Niels Bohr, a student of Rutherford’s, changed Rutherford’s model to include how the energy of an atom changes when it absorbs or emits light.

The Bohr ModelThe Bohr Model – he proposed that an electron is found only in specific circular paths, or orbits, around the nucleus.

The Bohr ModelEach possible electron orbit in Bohr’s model has a fixed energy. The fixed energies an electron can have are called energy levelsenergy levels.

The fixed energy levels of electrons are somewhat like the rungs of the ladder in which the lowest rung of the ladder corresponds to the lowest energy level.

An electron can jump from one energy level to another.

Electrons in an atom cannot be between energy levels.

The Bohr ModelTo move from one energy level to another, an electron must gain or lose jus the right amount of energy.

In general, the higher an electron is on the energy ladder, the farther it is from the nucleus.

A quantum quantum of energy is the amount of energy required to move and electron from one energy level to another energy level.

The energy of an electron is said to be quantized.

The term quantum leap originates from the ideas found in the Bohr model of the atom.

The Bohr ModelThe amount of energy an electron gains or loses in an atom is not always the same.

The energy levels in an atom are not equally spaced.

The higher energy levels are closer together.

The higher the energy level occupied by an electron, the less energy it takes to move from that energy level to the next energy level.

The Bohr model gave results in agreement with experiments for the hydrogen atom (1e-), but failed to explain the energies absorbed and emitted by atoms with more than one electron.

RefresherEvery atom, except hydrogen, consists of a small dense nucleus composed of protons and neutron that accounts for most of the mass of the atom.

Hydrogen is an exception because it has only one proton in its nucleus.

Negatively charged electrons surround the nucleus and occupy most of its volume. Electrons contribute little to the mass of an atom.

Energy Levels Example

When light shines on a fluorescent material, its electrons absorb the energy and move to a higher energy level.

Almost immediately, the material begins to emit light as the electrons drop back down to their usual energy level.

The Quantum Mechanical Model

The Rutherford planetary model and the Bohr model of the atom are based on describing paths of moving electrons as you would describe the path of a large moving object.

New theoretical calculation and experimental results were inconsistent with describing electron motion this way.

Austrian physicist Erwin Schrodinger used these new results to devise and solve a mathematical equation describing the behavior of the electron in a hydrogen atom.

The Quantum Mechanical Model

The Quantum Mechanical ModelQuantum Mechanical Model is the modern description of the electrons in atoms comes from the mathematical solution to the Schrodinger equation.

Like the Bohr model, the quantum mechanical model restricts the energy of electrons to certain values.

Unlike the Bohr model, the quantum mechanical model does not involve an exact path the electron takes around the nucleus.

The quantum mechanical model determines the allowed energies an electron can have an how likely it is to find the electron in various locations around the nucleus

The Quantum Mechanical ModelHow likely it is to find the electron in a particular location is described by probability.

The quantum mechanical model describes of how the electron moving around the nucleus is similar to the motion of a rotating propeller blade.

The propeller blade has the same probability of being anywhere in the blurry regions it produces, but you cannot tells its precise location at any instant.

The Quantum Mechanical Model

The probability of finding an electron within a certain volume of space surrounding the nucleus can be represented as a fuzzy cloud.

The cloud is more dense where the probability of finding the electron is high. The cloud is less dense where the probability of finding the electron is low.

It is unclear where the cloud ends, there is at least a slight chance of finding the electron at a considerable distance form the nucleus.

The Quantum Mechanical ModelTherefore, attempts to show probabilities as a fuzzy cloud are usually limited to the volume in which the electron is found 90% of the time.

To visualize an electron probability cloud, imagine that you could mold a sack around the cloud so that the electron was inside the sack 90% of the time.

The shape of the sack would then give you a useful picture of the shape of the cloud.

Atomic OrbitalsAtomic orbitalAtomic orbital is often thought of as a region of space in which there is a high probability of finding an electron.

The energy levels of electrons in the quantum mechanical model are labeled by principal quantum numbers (n)

n is assigned the values of 1,2,3,4, …

For each principal energy level, there may be several orbitals with different shapes and at different energy levels.

These energy levels within a principal energy level constitute energy sublevels.

Each energy sublevel corresponds to an orbital of different shape describing where the electron is likely to be found.

Different atomic orbitals are denoted by letters.

s orbitals are spherical and p orbitals are dumbbell-shaped.

Because of the spherical shape of an s orbital, the probability of finding an electron at a given distance from the nucleus in an s orbital does not depend on direction.

The three kinds of p orbitals have different orientations in space.

s orbitalP orbitals

There are five kinds of d orbitals. d orbitals

4 of the five d orbitals have clover leaf shapes but different orientations in space

The shapes of f orbitals are more complicated then for d orbitals.

Energy Level

Energy Sublevel ( # = n)

Number of

Orbitals per

Type

Number of

Orbitals per

Level

Number of e- per Sublevel

Max e- in Sublevel

Maximum e- in

Energy Level (2n2)

n = 1 1s 1 1 2e- 2e- 2 e-

n = 22s2p

13

42e-

2e-

2e-

6e-8 e-

n = 33s3p3d

135

92e-

2e-

2e-

2e-

6e-

10e-

18 e-

n = 4

4s4p4d4f

1357

16

2e-

2e-

2e- 2e-

2e-

6e-

10e-

14e-

32 e-

Questions

Why did Rutherford’s atomic model need to be replaced?

It could not explain why metals or compounds of metals give off characteristic color when heated nor the chemical properties of the elements.

What was the basic new proposal in the Bohr model of the atom.

An electron is found only in specific circular paths or orbits around the nucleus.

QuestionsWhat does the quantum mechanical model determine about electrons in atoms?

It determines the allowed energy levels an electron can have and the likelihood of finding an electron in various locations around the nucleus.

How do two sublevels of the same principal energy level differ from each other?

The sublevels have different shapes.

How can electrons in an atom move from one energy level to another?

By losing or gaining just the right amount of energy – a quantum.

Question

The energies of electrons are said to be quantized. Explain what this means.

In an atom, the electrons can have certain fixed energy levels. To move from one energy level to another requires the emission or absorption of an exact amount of energy, or quantum. Thus the energy of the electron is said to be quantized.

QuestionHow many orbitals are in the following sublevels?

3p3

2s 14p33d54f7

End of Section 5.1

Electron ConfigurationIn most natural phenomena, change proceeds toward the lowest possible energy.

In the atom, electrons and the nucleus interact to make the most stable arrangement possible.

The way in which electrons are arranged into various orbitals around the nuclei of atoms are called electron electron configuration.configuration.

Three rules tell you how to find the electron configurations of atoms.

•The aufbau principle•The Pauli exclusion principle•Hund’s rule

Electron Configuration Rulesaufbau PrincipleElectrons occupy the orbitals of lowest energy first.

Pauli Exclusion Principle • An orbital can hold a maximum of 2 electrons. • 2 electrons in the same orbital must have opposite

spins. • An electron is "paired" if it is sharing an orbital with

another electron with an opposite spin. • An electron is "unpaired" if it is alone in an orbital

Paired unpaired

Electron Configuration Rules

Hund’s Rule•Electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible.•One electron enters each orbital until all the orbitals contain one electron with the same spin direction •For example, three electron would occupy three orbitals of equal energy as follows:•Second electrons then occupy each orbital so that their spins are paired with the first electron in the orbital. Thus each orbital can eventually have two electrons with paired spins.

Electron Configuration PracticeWrite the electron configuration for each atom. How many unpaired electrons does each atom have?Carbon (atomic number 6 so 6 protons = 6 electrons)

1s22s22p2 2 unpaired electronsArgon

1s22s22p63s23p6 no unpaired electronsSilicon

1s22s22p63s23p2 2 unpaired electrons

Exceptional Electron Configurations

Some actual electron configurations differ from those assigned using the aufbau principle because half-filled sublevels are not as stable as filled sublevels.

You can obtain correct electron configurations for the elements up to vanadium (atomic number 23) by following the aufbau diagram for orbital filling.

Cr 1s22s22p63s23p64s23d4 using aufbau

Cr 1s22s22p63s23p64s13d5 correct

Exceptional Electron Configurations

Transition elements are some exceptions to the filling rules.

These exceptions can be explained by the atom’s tendency to keep its energy as low as possible.

These exceptions help explain the unexpected chemical behavior of transition elements.

Shorthand Electron ConfigurationsElectron configurations are often abbreviated by naming the last element with a filled shell (halogens) in brackets and listing only the orbitals after the filled shell.

Na:  1s22s22p63s1

shorthand    Na:  [Ne] 3s1

Al: 1s22s22p63s23p1

shorthand Al: [Ne] 3s23p1

V: 1s22s22p63s23p6 4s23d3

shorthand V: [Ar] 4s23d3

End of Section 5.2

Light

Neon signs are formed from glass tubes bent in various shapes

An electric current passing through the gas in each glass tube makes the gas glow with its own characteristic color.

Each gas glows with a specific color of light.

Light

The quantum mechanical model grew out of the study of light.

Isaac Newton tried to explain what was know about the behavior of light by assuming that light consists of particles.

By 1900, there was enough evidence to conclude that light consisted of waves.

WavesEach complete wave cycle starts at zero, increases to its highest value, passes through zero to reach its lowest value, and returns to zero again.

AmplitudeAmplitude of a wave is the wave’s height from zero to the crest.

WavelengthWavelength (λ) is the distance between the crests.

WavesFrequencyFrequency (ν) is the number of wave cycles to pass a given point per unit of time.

The units of frequency are usually cycles per second. The SI unit of cycles per second is called a hertz (Hz)

A hertz can also be expressed as a reciprocal seconds (s-1)

Hz = sHz = s-1-1

Light

The product of frequency and wavelength always equal a constant (c) = the speed of light(c) = the speed of light

c = λν

The wavelength and frequency of light are inversely proportional to each other. As the wavelength increases, the frequency decreases.

According to the wave model, light consists of electromagnetic waves.

Electromagnetic radiation includes radio waves, microwaves, infrared waves, visible light, ultraviolet waves, X-rays, and gamma rays.

Light

All electromagnetic waves travel in a vacuum at a speed of 2.998 x 102.998 x 1088 m/s m/s

c = 2.998 x 108 m/s

Sunlight consists of light with a continuous range of wavelengths and frequencies. The color of light depends on its frequency.

When sunlight passes through a prism, the different frequencies separate into a spectrumspectrum of color.

A rainbow is an example of this phenomenon.

Each color of the spectrum blends into the next in the order red, orange, yellow green, blue and violet.

In the visible spectrum, red light has the longest wavelength and the lowest frequency.

ElectromagneticSpectrum

Sample ProblemsWhat is the wavelength of radiation with a frequency of 1.50 x 1013 Hz? Does this radiation have a longer or shorter wavelength than red light?

c = λν or λ = c / νλ = (2.998 x 108 m/s) / (1.50 x 1013 s-1)

λ = 2.00 x 10-5 m (longer wavelength than red light)

What frequency is radiation with a wavelength of 5.00 x 10-8m? In what regions of th e electromagnetic spectrum is this radiation?

c = λν or ν = c / λν = (2.998 x 108 m/s) / (5.00 x 10-8 m)

ν = 6.00 x 1015 s-1 (ultraviolet)

Atomic Spectra

Passing an electric current through a gas in a neon tube energizes the electrons of the atoms of the gas, and causes them to emit light.

When atoms absorb energy, electrons move into higher energy levels, and these electrons lose energy by emitting light when they return to lower energy levels.

Ordinary light is made up of a mixture of all the wavelengths of light. However, the light emitted by atoms consists of a mixture of only specific frequencies.

Each specific frequency of visible light emitted corresponds to a particular color.

When light passes through a prism, the frequencies of light emitted by an element separate into discrete lines to give the atomic emission spectrumatomic emission spectrum of the element.

Atomic Spectra

Each discrete line in an emission spectrum corresponds to one exact frequency of light emitted by the atom.

The emission spectrum for each element is like a person’s fingerprint.

No two elements have the same emission spectrum.

Atomic emission spectra are useful for identifying elements. Argon’s

atomic emission spectra

Explanation of Atomic SpectraAtomic line spectra were known before Bohr proposed his model of the H atom. However, Bohr’s model explained why the emission spectrum of H consists of specific frequencies of light.

In the Bohr model, the lone electron in the H atom can have only certain specific energies.

The lowest possible energy of the electron is its ground ground state. state.

In the ground state, the electron’s principal quantum number is 1 (n=1)

Excitation of the electron by absorbing energy raises it from the ground state to an excited state with n = 2,3,4,5…

Explanation of Atomic Spectra

A quantum of energy in the form of light is emitted when the electron drops back to a lower energy level.

The emission occurs in a single abrupt step, called an electronic transition.

Bohr knew from earlier work that the quantum of energy (E) is related to the frequency (ν) of the emitted light by the equation E = h x E = h x νν

h is the fundamental constant of nature, the “Planck constant” and is equal to 6.626 x 10-34 J·s

Explanation of Atomic SpectraThe light emitted by an electron moving from a higher to a lower

energy level has a frequency directly proportional to the energy change of the electrons.

Each transition produces a line of a specific frequency in the spectrum.

Three groups of lines in the hydrogen spectrum correspond to the transition of electrons from higher energy levels to lower energy levels

1.1. Lyman seriesLyman series corresponds to the transition to the n=1 energy level

2.2. Balmer seriesBalmer series corresponds to the transition to the n=2 energy level (smaller change in e- energy than transitions to n=1)

3.3. Paschen seriesPaschen series corresponds to the transition to the n=3 energy level. (smaller change in e- energy than transitions to n=1 and n=2)

Explanation of Atomic Spectra

The light emitted by an electron moving from a higher to a lower energy level has a frequency directly proportional to the energy change of the electrons.

Each transition produces a line of a specific frequency in the spectrum.

(Transition to n = 2 energy levelVisible end of the spectra)

(Transition to the n = 1 energy levelUltraviolet part of the spectra)

(Transition to n = 3 energy level, infrared range of spectra)

Explanation of Atomic Spectra

Spectral lines for the transactions from higher energy levels to n=4 and n=5 also exist.

The spectral lines in each group become more closely spaced at increases values of n because the energy levels become closer together

There is an upper limit to the frequency of emitted light for each set of lines.

The upper limit exists because an electron with enough energy completely escapes the atom.

Explanation of Atomic Spectra

Bohr’s of the atom was only partially satisfactory.

It explained the emission spectrum of hydrogen, but not the emission spectra of atoms with more than one electron.

The quantum mechanical model displaced the Bohr model of the atom.

The quantum mechanical model is based on the description of the motion of material objects as waves.

Questions

Suppose an electron in its ground state at energy level one absorbs enough energy to jump to level two. What type of radiation will it emit when it returns to the ground state?

Ultraviolet radiation

If you observed a hydrogen gas discharge tube through a diffraction grating could you see the line corresponding to this emission?

No, the human eye cannot detect radiation in the UV range.

Which series of lines could you detect?

The Balmer series, which has frequencies in the visible region of the spectrum.

Questions

Compare the energy of the Paschen and Balmer series.

The Paschen series has lower energy.

What do you notice about the spacing of the enrgy levels from n = 1 to n = 7?

The levels are not evenly spaced. The lines get closer as the distance from the nucleus increases.

Quantum MechanicsAlbert Einstein successfully explained experimental data by proposing that light could be described as quanta of energy.

The quanta behave as if they were particles.

Light quanta are called photonsphotons.

Although the wave nature of light was well known, the dual wave-particle behavior of light was difficult for scientists to accept.

Louis de Broglie a French graduate student, asked an important question: Given that light behaves as waves and particles, can particles of matter behave as waves?

The proposal that matter moves in a wavelike way would not be accepted unless experiments confirmed its validity.

Quantum MechanicsTwo scientists, Clinton Davisson and Lester Germer at Bell Labs, had been studying the bombardment of metals with beams of electrons.

They noticed that the electrons reflected from the metal surface produced curious patterns.

The patterns were like those obtained when X-rays (which are electromagnetic waves) reflect from metal surfaces.

The electrons, believed to be particles, were reflected as if they were waves. .

Louis de Broglie was awarded the Nobel Prize for his work on the wave nature of matter. Davisson also received the Nobel Prize for his experiments demonstrating the wave nature of electrons.

Quantum MechanicsToday, the wavelike properties of beams of electrons are useful in magnifying objects.

The electrons in an electron microscope have much smaller wavelengths than visible light.

This allows a much clearer enlarged image of a very small object than is possible with an ordinary microscope.

Dust mite. Yuck!

Quantum MechanicsDe Broglie’s equation predicts that all moving objects have wavelike behavior.

Why can’t we observe the wavelike motion for ordinary objects like baseballs?

The mass of the object must be very small in order for its wavelength to be large enough to observe.

The older theory is called classical mechanicsclassical mechanics and it adequately describes the motions of bodies much larger than atoms.

The newer theory, quantum mechanicsquantum mechanics, describes the motion of subatomic particles and atoms as waves.

Quantum MechanicsGerman physicist Werner Heisenberg examined another feature of quantum mechanics that is absent is classical mechanics.

The Heisenberg uncertainly principleThe Heisenberg uncertainly principle states that it is impossible to know exactly both the velocity and the position of a particle at the same time.

This limitation is critical in dealing with small particles such as electrons.

The Heisenberg uncertainty principle does not matter, however, for ordinary-sized objects such as cars or airplanes.

Quantum Mechanics

To understand the Heisenberg uncertainty principle, consider how you determine the location of an object. .

To locate a set of keys in a dark room, you can use a flashlight. You see the keys when the light bounces off them and strikes your eyes.

To locate an electron, you might strike it with a photon of light. The electron has such a small mass that striking it with a photon affects its motion in a way that cannot be predicted precisely.

Recap

The frequency and wavelength of light waves are inversely related. As the wavelength increases, the frequency decreases. (c = λν)

The electromagnetic spectrum consists of radiation over a broad band of wavelengths. The visible light portion is very small. It is in the 10-7 m wavelength rand 1015 Hz (s-1) frequency range.

When atoms absorb energy, electrons move into higher energy levels, and these electrons lose energy by emitting light when they return to lower energy levels.

RecapA prism separates light into the colors it contains. For white light this produces a rainbow of colors. Light from a helium lamp produces discrete lines.

An electron microscope can produce sharp images of a very small object, because of the small wavelength of a moving electron compared with that of light.

The Heisenberg uncertainty principle states that it is impossible to know exactly both the velocity and the position of a particle at the same time.

QuestionsHow are wavelength and frequency of light related?

They are inversely proportional to each other. c = λν

Describe the cause of atomic emission spectrum of an element.

Electrons in atoms absorb energy as they move to higher energy levels, then lose the energy by emitting it as light as they drop back.

How is the change in electron energy related to the frequency of light emitted in atomic transitions?

The light emitted in an electronic transition from a higher to a lower energy level has a frequency that is directly proportional to the energy change of the electron. E = hλ

QuestionsHow does quantum mechanics differ from classical mechanics?

Quantum mechanics describes the motions of atoms and subatomic particles; classical mechanics describes the motions of larger bodies.

Which electron transitions with an atom are responsible for the Lyman series?

Electron transitions from higher levels to n = 1

Arrange the following in order of decreasing wavelength: infrared radiation from a heat lamp, dental X-rays, signal from a shortwave radio station.

Signal from a shortwave radio station, infrared radiation, dental X-rays

End of Chapter 5