Properties of Light

The nuclear atomic model proposed by Rutherford was a great improvement over previous models, but was still not complete. It did not fully explain the location and behavior of the electrons in the vast space outside of the nucleus. In fact, it was well known that oppositely charged particles attract one another. Rutherford’s model did not explain why the electrons don’t simply move toward and eventually collide with the nucleus. Experiments in the early twentieth century began to focus on the absorption and emission of light by matter. These studies showed how certain phenomena associated with light reveal insight into the nature of matter, energy, and atomic structure.

Wave Nature of Light

In order to begin to understand the nature of the electron, we first need to look at the properties of light. Prior to 1900, scientists thought light behaved solely as a wave. As we will see later, this began to change as new experiments demonstrated that light also has some of the characteristics of a particle. First, we will examine the wavelike properties of light.

Visible light is one type of electromagnetic radiation, which is a form of energy that exhibits wavelike behavior as it moves through space. Other types of electromagnetic radiation include gamma rays, x-rays, ultraviolet light, infrared light, microwaves, and radio waves. The figure below shows the electromagnetic spectrum , which is all forms of electromagnetic radiation. Notice that visible light makes up only a very, very small portion of the entire electromagnetic spectrum. All electromagnetic radiation moves through a vacuum at a constant speed of 2.998 × 10 ⁸  m/s. While the presence of air molecules slows the speed of light by a very small amount, we will use the value of 3.00 × 10 ⁸  m/s as the speed of light in air.

Figure 1 shows how the electromagnetic spectrum displays a wide variation in wavelength and frequency. Radio waves have wavelengths of as long as hundreds of meters, while the wavelength of gamma rays are on the order of 10⁻¹²  m. The corresponding frequencies range from 10⁶ to 10²¹ Hz. Visible light can be split into colors with the use of a prism (Figure 2), yielding the visible spectrum of light. Red light has the longest wavelength and lowest frequency, while violet light has the shortest wavelength and highest frequency. Visible light wavelength ranges from about 400–700 nm with frequencies in the range of 10 ¹⁴  Hz.

Wavelength and Frequency Calculations

Waves

Waves are characterized by their repetitive motion. Imagine a toy boat riding the waves in a wave pool. As the water wave passes under the boat, it moves up and down in a regular and repeated fashion. While the wave travels horizontally, the boat only travels vertically up and down. Figure 3 shows two examples of waves.

A wave cycle consists of one complete wave – starting at the zero point, going up to a wave crest , going back down to a wave trough , and back to the zero point again. The wavelength of a wave is the distance between any two corresponding points on adjacent waves. It is easiest to visualize the wavelength of a wave as the distance from one wave crest to the next. In an equation, wavelength is represented by the Greek letter lambda . Depending on the type of wave, wavelength can be measured in meters, centimeters, or nanometers (1 m = 10 ⁹  nm). The frequency , represented by the Greek letter nu , is the number of waves that pass a certain point in a specified amount of time. Typically, frequency is measured in units of cycles per second or waves per second. One wave per second is also called a Hertz (Hz) and in SI units is a reciprocal second (s ^-1 ).

Figure B above shows an important relationship between the wavelength and frequency of a wave. The top wave clearly has a shorter wavelength than the second wave. However, if you picture yourself at a stationary point watching these waves pass by, more waves of the first kind would pass by in a given amount of time. Thus the frequency of the first waves is greater than that of the second waves. Wavelength and frequency are therefore inversely related. As the wavelength of a wave increases, its frequency decreases. The equation that relates the two is:

The variable is the speed of light. For the relationship to hold mathematically, if the speed of light is used in m/s, the wavelength must be in meters and the frequency in Hertz.

Quantization of Energy

Every so often you hear a commercial or a news story with the words “quantum leap” in it. The quantum leap is supposed to be a major breakthrough, a big change, something extraordinarily large. The reality is far different. Instead of the big, extravagant change the “quantum” that scientists know about is a very small difference in the location of an electron around a nucleus – hardly an enormous shift at all.

German physicist Max Planck (1858–1947) studied the emission of light by hot objects. You have likely seen a heated metal object glow an orange-red color (see Figure 4).

Classical physics, which explains the behavior of large, everyday objects, predicted that a hot object would emit electromagnetic energy in a continuous fashion. In other words, every wavelength of light could possibly be emitted. Instead, what Planck found by analyzing the spectra was that the energy of the hot body could only be lost in small discrete units. A quantum is the minimum quantity of energy that can either be lost or gained by an atom. An analogy is that a brick wall can only undergo a change in height by units of one or more bricks and not by any possible height. Planck showed that the amount of radiant energy absorbed or emitted by an object is directly proportional to the frequency of the radiation.

In the equation, is the energy, in joules, of a quantum of radiation, is the frequency, and is a fundamental constant called Planck’s constant . The value of Planck’s constant is . The energy of any system must increase or decrease in units of . A small energy change results in the emission or absorption of low-frequency radiation, while a large energy change results in the emission or absorption of high-frequency radiation.

Photoelectric Effect

Photoelectric Effect and the Particle Nature of Light

In 1905 Albert Einstein (1879–1955) proposed that light be described as quanta of energy that behave as particles. A photon is a particle of electromagnetic radiation that has zero mass and carries a quantum of energy. The energy of photons of light is quantized according to the equation. For many years light had been described using only wave concepts, and scientists trained in classical physics found this wave-particle duality of light to be a difficult idea to accept. A key experiment that was explained by Einstein using light’s particle nature was called the photoelectric effect.

The photoelectric effect is a phenomenon that occurs when light shined onto a metal surface causes the ejection of electrons from that metal. It was observed that only certain frequencies of light are able to cause the ejection of electrons. If the frequency of the incident light is too low (red light, for example), then no electrons were ejected even if the intensity of the light was very high or it was shone onto the surface for a long time. If the frequency of the light was higher (green light, for example), then electrons were able to be ejected from the metal surface even if the intensity of the light was very low or it was shone for only a short time. This minimum frequency needed to cause electron ejection is referred to as the threshold frequency.

Classical physics was unable to explain the photoelectric effect. If classical physics applied to this situation, the electron in the metal could eventually collect enough energy to be ejected from the surface even if the incoming light was of low frequency. Einstein used the particle theory of light to explain the photoelectric effect as shown in Figure 5.

Consider the E = hv  equation. The E is the minimum energy that is required in order for the metal’s electron to be ejected.

• If the incoming light’s frequency, v, is below the threshold frequency, there will never be enough energy to cause electron to be ejected.
• If the frequency is equal to or higher than the threshold frequency, electrons will be ejected.

As the frequency increases beyond the threshold, the ejected electrons simply move faster. An increase in the intensity of incoming light that is above the threshold frequency causes the number of electrons that are ejected to increase, but they do not travel any faster.

The photoelectric effect is applied in devices called photoelectric cells, which are commonly found in everyday items such as a calculator which uses the energy of light to generate electricity.

Atomic Emission Spectra

The electrons in an atom tend to be arranged in such a way that the energy of the atom is as low as possible. The ground state of an atom is the lowest energy state of the atom. When those atoms are given energy, the electrons absorb the energy and move to a higher energy level. These energy levels of the electrons in atoms are quantized, meaning again that the electron must move from one energy level to another in discrete steps rather than continuously. An excited state of an atom is a state where its potential energy is higher than the ground state. An atom in the excited state is not stable. When it returns back to the ground state, it releases the energy that it had previously gained in the form of electromagnetic radiation.

So how do atoms gain energy in the first place? One way is to pass an electric current through an enclosed sample of a gas at low pressure. Since the electron energy levels are unique for each element, every gas discharge tube will glow with a distinctive color depending on the identity of the gas (see Figure 7).

“Neon” signs are familiar examples of gas discharge tubes. However, only signs that glow with the red-orange color seen in the figure are actually filled with neon. Signs of other colors contain different gases or mixtures of gases.

Scientists studied the distinctive pink color of the gas discharge created by hydrogen gas. When a narrow beam of this light was viewed through a prism, the light was separated into four lines of very specific wavelengths (and frequencies since and are inversely related). An atomic emission spectrum is the pattern of lines formed when light passes through a prism to separate it into the different frequencies of light it contains. Figure 8 shows the atomic emission spectrum of hydrogen.

Classical theory was unable to explain the existence of atomic emission spectra, also known as line-emission spectra. According to classical physics, a ground state atom would be able to absorb any amount of energy rather than only discrete amounts. Likewise, when the atoms relaxed back to a lower energy state, any amount of energy could be released. This would result in what is known a continuous spectrum , where all wavelengths and frequencies are represented. White light viewed through a prism and a rainbow are examples of continuous spectra. Atomic emission spectra were more proof of the quantized nature of light and led to a new model of the atom based on quantum theory.

Bohr’s Atomic Model

Following the discoveries of hydrogen emission spectra and the photoelectric effect, the Danish physicist Niels Bohr (1885–1962) proposed a new model of the atom in 1915. Bohr proposed that electrons do not radiate energy as they orbit the nucleus, but exist in states of constant energy which he called stationary states. This means that the electrons orbit at fixed distances from the nucleus (see Figure 9). Bohr’s work was primarily based on the emission spectra of hydrogen. This is also referred to as the planetary model of the atom. It explained the inner workings of the hydrogen atom. Bohr was awarded the Nobel Prize in physics in 1922 for his work.

Bohr explained that electrons can be moved into different orbits with the addition of energy. When the energy is removed, the electrons return back to their ground state, emitting a corresponding amount of energy—a quantum of light, or photon. This was the basis for what later became known as quantum theory. This is a theory based on the principle that matter and energy have the properties of both particles and waves. It accounts for a wide range of physical phenomena, including the existence of discrete packets of energy and matter, the uncertainty principle, and the exclusion principle.

According to the Bohr model, often referred to as a planetary model, the electrons encircle the nucleus of the atom in specific allowable paths called orbits. When the electron is in one of these orbits, its energy is fixed. The ground state of the hydrogen atom, where its energy is lowest, is when the electron is in the orbit that is closest to the nucleus. The orbits that are further from the nucleus are all of successively greater energy. The electron is not allowed to occupy any of the spaces in between the orbits. An everyday analogy to the Bohr model is the rungs of a ladder. As you move up or down a ladder, you can only occupy specific rungs and cannot be in the spaces in between rungs. Moving up the ladder increases your potential energy, while moving down the ladder decreases your energy.

Bohr’s work had a strong influence on our modern understanding of the inner workings of the atom. However, his model worked well for an explanation for the emissions of the hydrogen atom, but was seriously limited when applied to other atoms. Shortly after Bohr published his planetary model of the atom, several new discoveries were made, which resulted in, yet again, a revised view of the atom.

Spectral Lines of Hydrogen

Bohr’s model explains the spectral lines of the hydrogen atomic emission spectrum. While the electron of the atom remains in the ground state, its energy is unchanged. When the atom absorbs one or more quanta of energy, the electron moves from the ground state orbit to an excited state orbit that is further away. Energy levels are designated with the variable . The ground state is , the first excited state is , and so on. The energy that is gained by the atom is equal to the difference in energy between the two energy levels. When the atom relaxes back to a lower energy state, it releases energy that is again equal to the difference in energy of the two orbits.

In Figure 10, electron is shown transitioning from the n = 3 energy level to the n = 2 energy level. The photon of light that is emitted has a frequency that corresponds to the difference in energy between the two levels.

The change in energy, , then translates to light of a particular frequency being emitted according to the equation . Recall that the atomic emission spectrum of hydrogen had spectral lines consisting of four different frequencies. This is explained in the Bohr model by the realization that the electron orbits are not equally spaced. As the energy increases further and further from the nucleus, the spacing between the levels gets smaller and smaller.

Based on the wavelengths of the spectral lines, Bohr was able to calculate the energies that the hydrogen electron would have in each of its allowed energy levels. He then mathematically showed which energy level transitions corresponded to the spectral lines in the atomic emission spectrum (Figure 11).

He found that the four visible spectral lines corresponded to transitions from higher energy levels down to the second energy level . This is called the Balmer series. Transitions ending in the ground state are called the Lyman series, but the energies released are so large that the spectral lines are all in the ultraviolet region of the spectrum. The transitions called the Paschen series and the Brackett series both result in spectral lines in the infrared region because the energies are too small.

Bohr’s model was a tremendous success in explaining the spectrum of the hydrogen atom. Unfortunately, when the mathematics of the model was applied to atoms with more than one electron, it was not able to correctly predict the frequencies of the spectral lines. While Bohr’s model represented a great advancement in the atomic model and the concept of electron transitions between energy levels is valid, improvements were needed in order to fully understand all atoms and their chemical behavior.

de Broglie Wave Equation

Bohr’s model of the atom was valuable in demonstrating how electrons were capable of absorbing and releasing energy and how atomic emission spectra were created. However, the model did not really explain why electrons should exist only in fixed circular orbits rather than being able to exist in a limitless number of orbits all with different energies. In order to explain why atomic energy states are quantized, scientists needed to rethink the way in which they viewed the nature of the electron and its movement.

Planck’s investigation of the emission spectra of hot objects and the subsequent studies into the photoelectric effect had proven that light was capable of behaving both as a wave and as a particle. It seemed reasonable to wonder if electrons could also have a dual wave-particle nature. In 1924, French scientist Louis de Broglie (1892–1987) derived an equation that described the wave nature of any particle. Particularly, the wavelength (λ) of any moving object is given by:

[latex]\lambda = \frac{h}{mv}[/latex]

In this equation, h is Planck’s constant, is the mass of the particle in kg, and v is the velocity of the particle in m/s. The problem below shows how to calculate the wavelength of the electron.

If we were to calculate the wavelength of a 0.145 kg baseball thrown at a speed of 40 m/s, we would come up with an extremely short wavelength on the order of 10 ^-34 m. This wavelength is impossible to detect even with advanced scientific equipment. Indeed, while all objects move with wavelike motion, we never notice it because the wavelengths are far too short. On the other hand, particles with measurable wavelengths are all very small. However, the wave nature of the electron proved to be a key development in a new understanding of the nature of the electron. An electron that is confined to a particular space around the nucleus of an atom can only move around that atom in such a way that its electron wave “fits” the size of the atom correctly. This means that the frequencies of electron waves are quantized . Based on the equation, the quantized frequencies means that electrons can only exist in an atom at specific energies, as Bohr had previously theorized.

Quantum Mechanics

How do you study something that seemingly makes no sense? We talk about electrons being in orbits and it sounds like we can tell where that electron is at any moment. We can draw pictures of electrons in orbit, but the reality is that we just don’t know exactly where they are. We are going to take a quick look at an area of science that even leaves scientists puzzled. When asked about quantum mechanics, Niels Bohr (who proposed the Bohr model of the atom) said: “Anyone who is not shocked by quantum theory has not understood it”. Richard Feynman (one of the founders of modern quantum theory) stated: “I think I can safely say that nobody understands quantum theory”. So, let’s take a short trip into a land that challenges our every-day world.

The study of motion of large objects such as baseballs is called mechanics, or more specifically classical mechanics. Because the quantum nature of the electron and other tiny particles moving at high speeds, classical mechanics is inadequate to accurately describe their motion.

 

Quantum mechanics is the study of the motion of objects that are atomic or subatomic in size and thus demonstrate wave-particle duality. In classical mechanics, the size and mass of the objects involved effectively obscures any quantum effects so that such objects appear to gain or lose energies in any amounts. Particles whose motion is described by quantum mechanics gain or lose energy in the small pieces called quanta.

One of the fundamental (and hardest to understand) principles of quantum mechanics is that the electron is both a particle and a wave. In the everyday macroscopic world of things we can see, something cannot be both. But this duality can exist in the quantum world of the submicroscopic at the atomic scale.

At the heart of quantum mechanics is the idea that we cannot specify accurately the location of an electron. All we can say is that there is a probability that it exists within this certain volume of space. The scientist Erwin Schrödinger developed an equation that deals with these calculations, which we will not pursue at this time.

Heisenberg Uncertainty Principle

Another feature that is unique to quantum mechanics is the uncertainty principle. The Heisenberg Uncertainty Principle states that it is impossible to determine simultaneously both the position and the velocity of a particle. The detection of an electron, for example, would be made by way of its interaction with photons of light. Since photons and electrons have nearly the same energy, any attempt to locate an electron with a photon will knock the electron off course, resulting in uncertainty about where the electron is located (see Figure below ). We do not have to worry about the uncertainty principle with large everyday objects because of their mass. If you are looking for something with a flashlight, the photons coming from the flashlight are not going to cause the thing you are looking for to move. This is not the case with atomic-sized particles, leading scientists to a new understanding about how to envision the location of the electrons within atoms.

Quantum Mechanical Atomic Model

In 1926, Austrian physicist Erwin Schrödinger (1887–1961) used the wave-particle duality of the electron to develop and solve a complex mathematical equation that accurately described the behavior of the electron in a hydrogen atom. The quantum mechanical model of the atom comes from the solution to Schrödinger’s equation. Quantization of electron energies is a requirement in order to solve the equation. This is unlike the Bohr model, in which quantization was simply assumed with no mathematical basis.

Recall that in the Bohr model, the exact path of the electron was restricted to very well-defined circular orbits around the nucleus. The quantum mechanical model is a radical departure from that. Solutions to the Schrödinger wave equation, called wave functions, give only the probability of finding an electron at a given point around the nucleus. Electrons do not travel around the nucleus in simple circular orbits.

The location of the electrons in the quantum mechanical model of the atom is often referred to as an electron cloud . The electron cloud can be thought of in the following way: Imagine placing a square piece of paper on the floor with a dot in the circle representing the nucleus. Now take a marker and drop it onto the paper repeatedly, making small marks at each point the marker hits. If you drop the marker many, many times, the overall pattern of dots will be roughly circular. If you aim toward the center reasonably well, there will be more dots near the nucleus and progressively fewer dots as you move away from it. Each dot represents a location where the electron could be at any given moment. Because of the uncertainty principle, there is no way to know exactly where the electron is. An electron cloud has variable densities: a high density where the electron is most likely to be and a low density where the electron is least likely to be (Figure 15).

In order to specifically define the shape of the cloud, it is customary to refer to the region of space within which there is a 90% probability of finding the electron. This is called an orbital , the three-dimensional region of space that indicates where there is a high probability of finding an electron.

Quantum Numbers

We use a series of specific numbers, called quantum numbers, to describe the location of an electron in an associated atom. Quantum numbers specify the properties of the atomic orbitals and the electrons in those orbitals. An electron in an atom or ion has four quantum numbers to describe its state. Think of them as important variables in an equation which describes the three-dimensional position of electrons in a given atom.

Principal Quantum Number [latex](n)[/latex]

The principal quantum number, signified by [latex](n)[/latex], is the main energy level occupied by the electron. Energy levels are fixed distances from the nucleus of a given atom. They are described in whole number increments (e.g., 1, 2, 3, 4, 5, 6, …). At location , an electron would be closest to the nucleus, while the electron would be farther, and farther yet. As we will see, the principal quantum number corresponds to the row number for an atom on the periodic table.

Angular Momentum Quantum Number [latex](l)[/latex]

The angular momentum quantum number , signified as [latex](l)[/latex], describes the general shape or region an electron occupies—its orbital shape. The value of l depends on the value of the principle quantum number n. The angular momentum quantum number can have positive values of zero to . If , could be either 0 or 1.

Magnetic Quantum Number [latex](m_l)[/latex]

The magnetic quantum number, signified as [latex](m_l)[/latex], describes the orbital orientation in space. Electrons can be situated in one of three planes in three dimensional space around a given nucleus and . For a given value of the angular momentum quantum number l, there can be values for  [latex](m_l)[/latex]. As an example:

or 1

for

for

Principal Energy Levels and Sublevels

Principal energy level	Number of possible sublevels	Possible Angular Momentum Quantum Numbers	Orbital Designation by Principal Energy Level and Sublevel
	1		1 s
	2		2 s 2 p
	3		3 s 3 p 3 d
	4		4 s 4 p 4 d 4 f

Table above shows the possible magnetic quantum number values [latex](m_l)[/latex]  for the corresponding angular momentum quantum numbers [latex](l)[/latex] of and .

Spin Quantum Number [latex](m_s)[/latex]

The spin quantum number describes the spin for a given electron. An electron can have one of two associated spins, spin, or spin. An electron cannot have zero spin. We also represent spin with arrows or . A single orbital can hold a maximum of two electrons and each must have opposite spin.

Orbitals

We can apply our knowledge of quantum numbers to describe the arrangement of electrons for a given atom. We do this with something called electron configurations. They are effectively a map of the electrons for a given atom. We look at the four quantum numbers for a given electron and then assign that electron to a specific orbital.

s Orbitals

For any value of n, a value of places that electron in an s orbital. This orbital is spherical in shape:

p Orbitals

From Table below we see that we can have three possible orbitals when . These are designated as p orbitals and have dumbbell shapes. Each of the p orbitals has a different orientation in three-dimensional space.

d Orbitals

When , values can be -2, -1, 0, +1, +2 for a total of five d orbitals . Note that all five of the orbitals have specific three-dimensional orientations.

f Orbitals

The most complex set of orbitals are the f orbitals . When , values can be -3, -2, -1, 0, +1, +2, +3 for a total of seven different orbital shapes. Again, note the specific orientations of the different f orbitals.

Electron Arrangement Within Energy Levels

Principal Quantum Number	Allowable Sublevels	Number of Orbitals per Sublevel	Number of Orbitals per Principal Energy Level	Number of Electrons per Sublevel	Number of Electrons per Principal Energy Level
1	s	1	1	2	2
2	s p	1 3	4	2 6	8
3	s p d	1 3 5	9	2 6 10	18
4	s p d f	1 3 5 7	16	2 6 10 14	32

Aufbau Principle

In order to create ground state electron configurations for any element, it is necessary to know the way in which the atomic sublevels are organized in order of increasing energy. The Figure below shows the order of increasing energy of the sublevels.

The lowest energy sublevel is always the 1 s sublevel, which consists of one orbital. The single electron of the hydrogen atom will occupy the 1 s orbital when the atom is in its ground state. As we proceed with atoms with multiple electrons, those electrons are added to the next lowest sublevel: 2 s , 2 p , 3 s , and so on. The Aufbau principle states that an electron occupies orbitals in order from lowest energy to highest. The Aufbau (German: “building up, construction”) principle is sometimes referred to as the “building-up” principle. It is worth noting that in reality atoms are not built by adding protons and electrons one at a time and that this method is merely an aid for us to understand the end result.

As seen in the Figure above , the energies of the sublevels in different principal energy levels eventually begin to overlap. After the 3 p sublevel, it would seem logical that the 3 d sublevel should be the next lowest in energy. However, the 4 s sublevel is slightly lower in energy than the 3 d sublevel and thus fills first. Following the filling of the 3 d sublevel is the 4 p , then the 5 s and the 4 d . Note that the 4 f sublevel does not fill until just after the 6 s sublevel. The Figure below is a useful and simple aid for keeping track of the order of fill of the atomic sublevels.

Pauli Exclusion Principle

When we look at the orbital possibilities for a given atom, we see that there are different arrangements of electrons for each different type of atom. Since each electron must maintain its unique identity, we intuitively sense that the four quantum numbers for any given electron must not match up exactly with the four quantum numbers for any other electron in that atom.

For the hydrogen atom, there is no problem since there is only one electron in the H atom. However, when we get to helium we see that the first three quantum numbers for the two electrons are the same: same energy level, same spherical shape. What differentiates the two helium electrons is their spin. One of the electrons has spin while the other electron has spin. So the two electrons in the 1s orbital are each unique and distinct from one another because their spins are different. This observation leads to the Pauli exclusion principle , which states that no two electrons in an atom can have the same set of four quantum numbers. The energy of the electron is specified by the principal, angular momentum, and magnetic quantum numbers. If those three numbers are identical for two electrons, the spin numbers must be different in order for the two electrons to be differentiated from one another. The two values of the spin quantum number allow each orbital to hold two electrons. The figure below shows how the electrons are indicated in a diagram.

In an orbital filling diagram, a square represents an orbital, while arrows represent electrons. An arrow pointing upward represents one spin direction, while an arrow pointing downward represents the other spin direction.

Hund’s Rule and Orbital Filling Diagrams

Hund’s Rule

The last of the three rules for constructing electron arrangements requires electrons to be placed one at a time in a set of orbitals within the same sublevel. This minimizes the natural repulsive forces that one electron has for another. Hund’s rule states that orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron and that each of the single electrons must have the same spin. The Figure below shows how a set of three p orbitals is filled with one, two, three, and four electrons.

Orbital Filling Diagrams

An orbital filling diagram is the more visual way to represent the arrangement of all the electrons in a particular atom. In an orbital filling diagram, the individual orbitals are shown as circles (or squares) and orbitals within a sublevel are drawn next to each other horizontally. Each sublevel is labeled by its principal energy level and sublevel. Electrons are indicated by arrows inside the circles. An arrow pointing upwards indicates one spin direction, while a downward pointing arrow indicates the other direction. The orbital filling diagrams for hydrogen, helium, and lithium are shown in Figure below .

According to the Aufbau process, sublevels and orbitals are filled with electrons in order of increasing energy. Since the s sublevel consists of just one orbital, the second electron simply pairs up with the first electron as in helium. The next element is lithium and necessitates the use of the next available sublevel, the 2 s .

The filling diagram for carbon is shown in the Figure below . There are two 2 p electrons for carbon and each occupies its own 2 p orbital.

Oxygen has four 2 p electrons. After each 2 p orbital has one electron in it, the fourth electron can be placed in the first 2 p orbital with a spin opposite that of the other electron in that orbital.

Electron Configurations

Electron configuration notation eliminates the boxes and arrows of orbital filling diagrams. Each occupied sublevel designation is written followed by a superscript that is the number of electrons in that sublevel. For example, the hydrogen configuration is 1 s ¹ , while the helium configuration is 1 s ² . Multiple occupied sublevels are written one after another. The electron configuration of lithium is 1 s ² 2 s ¹ . The sum of the superscripts in an electron configuration is equal to the number of electrons in that atom, which is in turn equal to its atomic number.

Second Period Elements

Periods refer to the horizontal rows of the periodic table. Looking at a periodic table you will see that the first period contains only the elements hydrogen and helium. This is because the first principal energy level consists of only the s sublevel and so only two electrons are required in order to fill the entire principal energy level. Each time a new principal energy level begins, as with the third element lithium, a new period is started on the periodic table. As one moves across the second period, electrons are successively added. With beryllium (Z = 4), the 2 s sublevel is complete and the 2 p sublevel begins with boron (Z = 5). Since there are three 2 p orbitals and each orbital holds two electrons, the 2 p sublevel is filled after six elements. The Table below shows the electron configurations of the elements in the second period.

Electron Configurations of Second-Period Elements

Element Name	Symbol	Atomic Number	Electron Configuration
Lithium	Li	3	1 s 2 2 s 1
Beryllium	Be	4	1 s 2 2 s 2
Boron	B	5	1 s 2 2 s 2 2 p 1
Carbon	C	6	1 s 2 2 s 2 2 p 2
Nitrogen	N	7	1 s 2 2 s 2 2 p 3
Oxygen	O	8	1 s 2 2 s 2 2 p 4
Fluorine	F	9	1 s 2 2 s 2 2 p 5
Neon	Ne	10	1 s 2 2 s 2 2 p 6

Valence Electrons

Electron Configurations of Second-Period Elements

Element Name	Symbol	Atomic Number	Electron Configuration
Lithium	Li	3	1 s 2 2 s 1
Beryllium	Be	4	1 s 2 2 s 2
Boron	B	5	1 s 2 2 s 2 2 p 1
Carbon	C	6	1 s 2 2 s 2 2 p 2
Nitrogen	N	7	1 s 2 2 s 2 2 p 3
Oxygen	O	8	1 s 2 2 s 2 2 p 4
Fluorine	F	9	1 s 2 2 s 2 2 p 5
Neon	Ne	10	1 s 2 2 s 2 2 p 6

In the study of chemical reactivity, we will find that the electrons in the outermost principal energy level are very important and so they are given a special name. Valence electrons are the electrons in the highest occupied principal energy level of an atom. In the second period elements listed above, the two electrons in the 1 s sublevel are called inner-shell electrons and are not involved directly in the element’s reactivity or in the formation of compounds. Lithium has a single electron in the second principal energy level and so we say that lithium has one valence electron. Beryllium has two valence electrons. How many valence electrons does boron have? You must recognize that the second principal energy level consists of both the 2 s and the 2 p sublevels and so the answer is three. In fact, the number of valence electrons goes up by one for each step across a period until the last element is reached. Neon, with its configuration ending in s ²p ⁶ , has eight valence electrons.

Noble Gas Configuration

Sodium, element number eleven, is the first element in the third period of the periodic table. Its electron configuration is 1 s ² 2 s ² 2 p ⁶ 3 s ¹ . The first ten electrons of the sodium atom are the inner-shell electrons and the configuration of just those ten electrons is exactly the same as the configuration of the element neon (Z = 10). This provides the basis for a shorthand notation for electron configurations called the noble gas configuration. The elements that are found in the last column of the periodic table are an important group of elements that are called the noble gases. They are helium, neon, argon, krypton, xenon, and radon. A noble gas configuration of an atom consists of the elemental symbol of the last noble gas prior to that atom, followed by the configuration of the remaining electrons. So for sodium, we make the substitution of [Ne] for the 1 s ² 2 s ² 2 p ⁶ part of the configuration. Sodium’s noble gas configuration becomes [Ne]3 s ¹ . Table below shows the noble gas configurations of the third period elements.

Electron Configurations of Third-Period Elements

Element Name	Symbol	Atomic Number	Noble Gas Electron Configuration
Sodium	Na	11	[Ne]3 s 1
Magnesium	Mg	12	[Ne]3 s 2
Aluminum	Al	13	[Ne]3 s 2 3 p 1
Silicon	Si	14	[Ne]3 s 2 3 p 2
Phosphorus	P	15	[Ne]3 s 2 3 p 3
Sulfur	S	16	[Ne]3 s 2 3 p 4
Chlorine	Cl	17	[Ne]3 s 2 3 p 5
Argon	Ar	18	[Ne]3 s 2 3 p 6

Again, the number of valence electrons increases from one to eight across the third period.

The fourth and subsequent periods follow the same pattern except for using a different noble gas. Potassium has nineteen electrons, one more than the noble gas argon, so its configuration could be written as [Ar]4 s ¹ . In a similar fashion, strontium has two more electrons than the noble gas krypton, which would allow us to write its electrons distribution as [Kr]5 s ² . All the elements can be represented in this fashion.