6.3 Development of Quantum Theory

Bohr's model of the hydrogen atom doesn't account for electron-electron interactions in atoms with more than one electron.

Several important features of all models used to describe the distribution of electrons in an atom are introduced.

Increasing distance from the nucleus increases the electron's energy.

The lines in the elements are the result of quantized electronic energies.

The most important feature is the postulate of quantized energy levels for an electron in an atom.

The foundation for the quantum mechanical model of the atom was laid by the model.
His contributions to our understanding of the structure of atoms and how that is related to line spectrum emissions earned him a prize.

By the end of this section, you will be able to understand the concept of wave-particle duality and the general idea of the quantum mechanical description of electrons in an atom.

Scientists needed to completely revise how they thought about matter.

The objects that are large enough to be seen by the naked eye follow the rules of classical physics.

A billiard ball moving on a table will behave like a particle, unless it collides with another ball or the table cushion, or is acted on by some other force.
The ball is moving in a way that is classical.
The typical behavior of a classical object is this.

When waves interact with each other, they show interference patterns that are not displayed by particles.

Waves and particles are very different phenomena on the scale, and this is a case of wave behavior.

Waves interact on the water surface to form an interference pattern.

Waves are caused by the reflection of water.

By the 1920s, it became clear that small pieces of matter follow a different set of rules than large objects.

The separation of waves and particles was not the same as it used to be.

The first person to pay attention to the behavior of the tiny world was Louis de Broglie.

The wave-particle duality of light was extended by de Broglie in his 1925 thesis.

The two symbols are very different.

If the electron is not a particle but a circular standing wave, then the assumption of quantization made by Bohr can be explained.

If an electron is seen as a wave circling around the nucleus, a number of wavelengths must fit into the circle for this to be possible.

The diagram shows the direction of motion.

Two scientists at Bell Laboratories, C. J. Davisson and L. H. Germer, demonstrated that electrons can exhibit wavelike behavior by showing an interference pattern for electrons travelling through a regular atomic pattern in a crystal.

The atomic layers were used in interference experiments.
Since the spacing between the layers serving as slits needs to be similar in size to the wavelength of the tested wave for an interference pattern to form, Davisson and Germer used a crystalline nickel target for their "slits."
When only a few electrons have been recorded, they show clear particle-like behavior, having arrived in small packets that appear to be random.
The hallmark of wavelike behavior emerged as more and more electrons arrived and were recorded.
electrons are small particles that do not follow the equations of motion implied by classical mechanics, but they are governed by a wave equation that governs a probability distribution even for a single electron's motion The wave-particle duality is a fundamental behavior of all quantum particles.

Increasing numbers of electrons are being recorded from the left image to the right as the electrons pass through a very closely spacing slit.

It is clear that the electrons arrive as individual particles, but in a seemingly random pattern.
A wavelike interference pattern begins to emerge as more electrons arrive.
The probability of the final electron location is still governed by the wave-type distribution, even for a single electron, but it can be observed more easily if many electron collisions have been recorded.

There are associated experiments in the Dr. Quantum - Double Slit Experiment.

We can use de Broglie's equation to solve the problem, but first we have to convert the constant into a unit.

You know that 1 J is 1 kg m2/s2.

This is a small value, but it is larger than an electron in the classical view.

The size is the same as the size of an atom.

electron wavelike behavior is going to be visible in an atom.

Assume that a softball with a mass of 100 g can be modeled as a single particle.

Since the wavelength of a thrown softball is so small, it's impossible for our senses to detect it, and a real baseball has the same wavelength.

For matter that has a very small mass and/or a very high speed, the de Broglie wavelength is only useful.

The limits of how accurately we can measure the properties of particles was considered by Heisenberg.

There is a limit to how accurately one can measure both a particle's position and its momentum at the same time.
The more accurately we measure the momentum of a particle, the more accurate we can determine its position at that time.

The limit to how precisely we can know the simultaneous position of an object and its momentum is calculated by this equation.

Uncertainty can be large and significant if the mass of the object is small.

Heisenberg's uncertainty principle is not limited to uncertainties in position and momentum, but it also links other variables.

As will be discussed later, the components of the momentum can't all be specified at the same time.

The limits of what is knowable in science are imposed by Heisenberg's principle.

The uncertainty principle can be shown to be a consequence of wave-particle duality, which is what distinguishes modern quantum theory from classical mechanics.
Classical mechanics shows that the equations of motion can be determined at any given moment in time.
Heisenberg's uncertainty principle implies that there are fundamental limitations to the motion of quantum particles.
This doesn't mean that particles don't move, it's just that they aren't as precise as they could be.
Changes in the system that is being observed are introduced by measurement.

There is an article about a recent demonstration of the uncertainty principle applied to objects.

After de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as a circular standing wave instead of a particle moving in quantized circular orbits, a new work was done by the same man.

When he applied his equation to hydrogen-like atoms, he was able to reproduce Bohr's expression for the energy and, thus, the Rydberg formula governing hydrogen spectrum.
There is a chance that a quantum particle is present near a location in space.
Waves can be used to determine the distribution of the electron's density with respect to the nucleus in an atom.

You might have heard of his famous thought experiment.

The goal of this section is to understand the properties of electrons in atoms.

The use of quantum theory gives the best understanding.
Chemical bonding is a result of this knowledge.

electrons in atoms can only exist on a single energy level but not between them It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain values and can jump from one energy level to another but not transition smoothly or stay between these levels.

The shell number is a name for the principal quantum number.

The electrons are most likely to be found in the circular area.
The higher the shell number, the higher the energy level and so on.
The more energy the electron has, the closer it is to the nucleus.

Different shells are numbered.

The model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another.

The energy change has a positive value if the transition is to a higher energy level.
A photon is absorbed by the atom to get the amount of energy needed.
A negative energy change is associated with a transition to a lower energy level.
Emission of a photon by the atom is a part of this process.

One of the three quantum numbers is the principal quantum number.

The probability of finding an electron in the three-dimensional space around the nucleus is specified by the quantum mechanical model.
The energy of an electron in a hydrogen or hydrogen-like atom or an ion is determined by the principal quantum number and the general region in which the electrons are located.

The size and energy of the orbital are determined by the principal quantum number.

The greater the quantum number, the greater the electron's momentum.

There are certain distances from the nucleus where the probability of finding an electron is zero.

This can point in different directions.

The electronic structure and periodic properties of elements are caused by interacting with the field.

The general value of the electronic energy is defined by the principal quantum number.
The shape of the orbital is determined by the quantum number.
The chart shows the electron orbitals in an atom.

The figures show the energy levels for various orbitals.

The three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, but some experiments showed that they were not enough to explain all observed results.

In the 1920s, it was shown that some lines are not single peaks but pairs of closely spacing lines.
The fine structure of the spectrum implies that there are additional small differences in the energies of electrons even when they are located in the same orbital.
The observations led to the idea that electrons have a fourth quantum number.

The equation for electrons in atoms is called the Schrodinger equation.

The electron spin is a different type of property.
There is no analogues in the classical realm.
Even though the rotation cannot be observed in terms of the coordinates, the electron acts as a tiny magnet.

An electron can only spin in one of two quantized states, and the magnitude of the spin can only have one value.

Any electron can only have one of the two values of the spin quantum number if it is located in the atomic orbital.
If an external magnetic field is applied, they are different.

The electron has a spin value in the magnetic field.

This phenomenon is shown in Figure 6.24.

There is a slightly higher energy in the field.
This is true for an electron in an atom.
The line in the spectrum will show a fine structure splitting if there is a transition for electrons from the same orbital but with different spin quantum numbers.

The orbital is defined by the first three quantum numbers and the fourth number describes the spin property.

Wolfgang Pauli formulated a general principle that gives the last piece of information we need to understand the behavior of electrons in atoms.

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

Any atomic orbital can only have zero, one, or two electrons.

The meaning of the quantum numbers of electrons in atoms is summarized in Table 6.1.

The four orbitals can hold eight electrons.

50 electrons can fit in this shell if each orbital holds two electrons.

We can use our understanding of quantum numbers to determine how atomic orbitals relate to one another after introducing the basics of atomic structure and quantum mechanics.

We can determine which orbitals are occupied by electrons.

This pattern doesn't work for larger atoms.

As we move up the chart, such overlaps occur frequently.

An energy-level diagram for atomic orbitals in an atom with two or more electrons.

Low-energy orbitals are usually filled first by the electrons in successive atoms on the periodic table.

The filling order has been confirmed by theoretical calculations.
The attraction to the nucleus is weaker and the energy associated with the orbital is less stable.
We have to take other effects into account.

Shielding is a phenomenon that will be discussed in more detail in the next section.

Electrons that experience more shielding are more energy efficient.
Methods for remembering the order will be discussed.

There is an electron configuration with a symbol that contains three pieces of information.

The number of electrons in the subshell is determined by a superscript number.

We can "build" the structures in the order of atomic numbers to determine the electron configuration.

We add one electron and one protons to the nucleus at a time until we have described the electron configurations of all the elements.

After lower-energy subshells have been filled to capacity, higher-energy subshells can enter.

An alternative method for determining the electron configuration can be found in Figure 6.28.

The arrow leads through each shell.

This chart is easy to make.

Draw diagonal lines from top to bottom.

The table shows the electron configuration.

The table can be used to determine the electron configuration for any atom on the periodic table.

The ground-state electron configuration and orbital diagram will be constructed for a selection of atoms in the first and second periods of the periodic table.

We start with a single hydrogen atom, which has one electron and one protons.
Usually the value is filled first.

The noble gas helium has an atomic number of 2.

There are two protons and two electrons in the atom.
The Pauli exclusion principle states that no two electrons in the same atom can have the same set of four quantum numbers.

The electronic structure and periodic properties of elements must point in opposite directions.

A shell is filled with a helium atom.

The atomic number of the next atom is 3.

Four protons and four electrons are present in an atom of the alkaline earth metal, with an atomic number of 4.

Five electrons are contained in an atom of boron.

We include empty boxes to depict empty orbitals in the same subshell that we are filling.

Carbon has six electrons.

There are three electrons with unpaired spins.

2 shells are filled.

The neon atom has one less electron than the alkali metal.

Since the core electron shells correspond to noble gas electron configurations, we can shorten them by writing the noble gas that matches the core electron configuration along with the valence electrons in a condensed format.

A core-abbreviated electron configuration replaces the core electrons with the noble gas symbol.

The configuration of the helium atom is the same as that of the filled inner shell of lithium.

This way of writing the configurations emphasizes their similarity.

The outer-shell electron configuration of each element is shown in this version of the periodic table.

The configuration is often similar down each group.

The outer-shell electron configuration of calcium is similar to that of magnesium and beryllium.

To bring that shell from 18 electrons to a total of 32.

The number 15 is the atomic number of phosphorus.

There are 15 electrons in a phosphorus atom.

Predicting the electron configuration of an element can be done with the periodic table.

Small effects can lead to changes in the order of filling if the exceptions involve subshells with very similar energy.

In the case of Cu, half-filled and completely filled subshells seem to represent the conditions of preferred stability.

There are also other exceptions.
There is no simple method to predict the exceptions for atoms where the magnitude of the repulsions between electrons is greater than the small differences in energy between subshells.

The periodic table arranges atoms based on increasing atomic number so that elements have the same chemical properties.

The periodic recurrence of similar electron configurations in the outer shells of these elements can be seen when their electron configurations are added to the table.
The most important role in chemical reactions is played by valence electrons, who are in the outer shells of an atom.
The outer electrons have the highest energy of the electrons in an atom and are more easily lost or shared than the core electrons.

Some physical properties of the elements are determined by valence electrons.

The elements in any one group have the same number of electrons, with the exception of the alkaline earth metals and magnesium.

The chemical properties of elements in the same group are similar because they have the same number of electrons.
The loss, gain, or sharing of electrons is what defines how elements react.

The periodic table was developed on the basis of the chemical behavior of the elements before any idea of their atomic structure was available.

The arrangement of the periodic table puts elements with the same number of electrons in the same group.
The electron configuration of the last subshell is shown in periodic-table form in this arrangement.

The nonmetallic elements, as well as many metals and the intermediate semimetallic elements, are included in this category.

There are three valence electrons in 1, which is underlined.

There are two inner transition series.

When atoms gain or lose electrons, they form an ion.

A positively charged ion forms when electrons are removed from a parent atom.
The first electrons are removed from the main group elements.
An anion is formed when one or more electrons are added to a parent atom.
The added electrons fill the order predicted by the principle.