Chemistry deals with the composition, structure, and properties of matter, and the ways by which various forms of matter may be interconverted. Thus, it occupies a central place in the study and practice of science and technology. Chemists use the scientific method to perform experiments, pose hypotheses, and formulate laws and develop theories, so that they can better understand the behavior of the natural world. To do so, they operate in the macroscopic, microscopic, and symbolic domains.
Chemistry is sometimes referred to as "the central science" due to its interconnectedness with a vast array of other STEM disciplines. Chemistry and the language of chemists play vital roles in biology, medicine, materials science, forensics, environmental science, and many other fields. The basic principles of physics are essential for understanding many aspects of chemistry, and there is extensive overlap between many subdisciplines within the two fields, such as chemical physics and nuclear chemistry. Mathematics, computer science, and information theory provide important tools that help us calculate, interpret, describe, and generally make sense of the chemical world.
Chemical engineering, materials science, and nanotechnology combine chemical principles and empirical findings to produce useful substances, ranging from gasoline to fabrics to electronics. Agriculture, food science, veterinary science, and brewing and wine making help provide sustenance in the form of food and drink to the world's population. Medicine, pharmacology, biotechnology, and botany identify and produce substances that help keep us healthy. Environmental science, geology, oceanography, and atmospheric science incorporate many chemical ideas to help us better understand and protect our physical world. Chemical ideas are used to help understand the universe in astronomy and cosmology.
Knowledge of chemistry is central to understanding a wide range of scientific disciplines. Digesting and assimilating food, synthesizing polymers that are used to make clothing, containers, cookware, and credit cards, and refining crude oil into gasoline and other products are just a few examples of changes in matter that are essential to daily life. As you proceed through this course, you will discover many different examples of changes in the composition and structure of matter, how to classify these changes and how they occurred, their causes, the changes in energy that accompany them, and the principles and laws involved.
Chemistry is a science based on observation and experimentation. Doing chemistry involves attempting to answer questions and explain observations in terms of the laws and theories of chemistry, using procedures that are accepted by the scientific community. There is no single route to answering a question or explaining an observation, but there is an aspect common to every approach: Each uses knowledge based on experiments that can be reproduced to verify the results.
The scientific method follows a process similar to the one shown in the diagram. All the key components are shown, in roughly the right order. Scientific progress is seldom neat and clean: It requires open inquiry and the reworking of questions and ideas in response to findings.
Chemists study and describe the behavior of matter and energy in three different domains: macroscopic, microscopic, and symbolic. These domains provide different ways of considering and describing chemical behavior. The macroscopic domain is familiar to us: It is the realm of everyday things that are large enough to be sensed directly by human sight or touch. The microscopic domain includes everyday and laboratory chemistry, where we observe and measure physical and chemical properties such as density, solubility, and flammability. The symbolic domain contains the specialized language used to represent components of the macroscopic and microscopic domains.
A helpful way to understand the three domains is via the essential and ubiquitous substance of water. That water is a liquid at moderate temperatures, will freeze to form a solid at lower temperatures, and boil to form a gas at higher temperatures are macroscopic observations. But some properties of water fall into the microscopic domain—what cannot be observed with the naked eye. The description of water as comprising two hydrogen atoms and one oxygen atom, and the explanation of freezing and boiling in terms of attractions between these molecules, is within the microscopic arena. The formula H2O, which can describe water at either the macroscopic or microscopic levels, is an example of the symbolic domain. The abbreviations for gas, solid, and liquid are also symbolic.
Physical properties are characteristics of matter that can be observed without changing the chemical composition of a substance. Examples of physical properties include density, color, hardness, melting and boiling points, and electrical conductivity. Chemical properties, on the other hand, depend on the amount of matter present and describe how matter reacts or changes under different conditions.
Chemical properties are characteristics of matter that can be observed by changing the amount of matter present. Examples of chemical properties include flammability, toxicity, acidity, and many other types of reactivity. Chemical properties are often used to identify and classify elements and compounds based on their behavior under different conditions.
The difference between physical and chemical properties lies in the way they are observed and described. Physical properties are typically measured using standardized units and scales, while chemical properties are described using mathematical equations that relate the amount of matter present to the observed property.
Understanding the differences between physical and chemical properties is essential for studying chemistry. By recognizing the characteristics of different types of matter, scientists can better understand how elements and compounds interact with each other and their surroundings. This knowledge can be used to develop new technologies, materials, and processes that benefit society in various ways.
In conclusion, physical properties are inherent characteristics of matter that can be observed without changing its chemical composition. Chemical properties, on the other hand, depend on the amount of matter present and describe how matter reacts or changes under different conditions. Understanding the differences between these two types of properties is crucial for studying chemistry and developing new technologies and materials.
In chemistry, the factor-label method is a technique used to solve complex calculations involving conversions between different units of measurement. This method involves orienting all factors involved in the calculation so that their labels will appropriately cancel and/or combine to yield the desired unit in the result. The basic approach is the same for all calculations, regardless of the details; all factors involved in the calculation must be properly oriented to ensure that their labels will combine correctly to produce the desired unit in the result.
One common application of this method is in solving temperature conversions. Temperature is measured using different scales, such as Celsius and Fahrenheit. To convert between these scales, a linear equation must be derived based on the reference temperatures used to define each scale. For example, the freezing temperature of water on the Celsius scale is 0°C, while its boiling temperature is 100°C. On the Fahrenheit scale, the freezing point of water is defined as 32°F, and the boiling point is 212°F. The space between these two points on a Fahrenheit thermometer is divided into 180 equal parts.
The linear equation relating Celsius and Fahrenheit temperatures can be derived by representing the Celsius temperature as x and the Fahrenheit temperature as y, then computing the slope of the line using the following formula:
m = (y - 32°F) / (100°C - 0°C)
where m is the conversion factor. The equation relating the two scales can then be written as:
T (°F) = + 32 °F + (5 / 9) × T (°C)
Rearranging this equation yields the form useful for converting from Fahrenheit to Celsius:
T (°C) = (9 / 5) × T (°F) - 32
As mentioned earlier in this chapter, the SI unit of temperature is the kelvin. Unlike the Celsius and Fahrenheit scales, the kelvin scale is an absolute temperature scale in which 0 K corresponds to the lowest temperature that can theoretically be achieved. The early 19th-century discovery of the relationship between a gas's volume and temperature suggested that the volume of a gas would be zero at -273.15 °C. In 1848, British physicist William Thompson proposed an absolute temperature scale based on this concept. The freezing temperature of water on this scale is 273.15 K, and its boiling temperature is 373.15 K.
The equations for converting between the kelvin and Celsius temperature scales are:
T (K) = T (°C) + 273.15
T (°C) = T (K) - 273.15
In conclusion, the factor-label method is a useful technique for solving complex calculations involving conversions between different units of measurement. By properly orienting all factors involved in the calculation, this method ensures that the desired unit will be produced in the result. The linear equation relating Celsius and Fahrenheit temperatures can be derived using the reference temperatures used to define each scale, and the kelvin scale is an absolute temperature scale with 0 K corresponding to the lowest temperature theoretically achievable.
The development of modern atomic theory revealed much about the inner structure of atoms. It was learned that an atom contains a very small nucleus composed of positively charged protons and uncharged neutrons, surrounded by a much larger volume of space containing negatively charged electrons. The nucleus contains the majority of an atom's mass because protons and neutrons are much heavier than electrons, whereas electrons occupy almost all of an atom's volume. The diameter of an atom is on the order of 10 m, whereas the diameter of the nucleus is roughly 10 mâ€about 100,000 times smaller. For a perspective about their relative sizes, consider this: If the nucleus were the size of a blueberry, the atom would be about the size of a football stadium.
Atoms and subatomic particles are extremely small, so we use appropriately small units of measure, such as the atomic mass unit (amu) and the fundamental unit of charge (e), to describe their properties. The amu was originally defined based on hydrogen, the lightest element, then later in terms of oxygen. Since 1961, it has been defined with regard to the most abundant isotope of carbon, atoms of which are assigned masses of exactly 12 amu. Therefore, one amu = 1.67 x 10^-24 g. The unified atomic mass unit (A) is an alternative unit that is equivalent to the amu.
The proton has a mass of 1.0073 amu and a charge of 1+, while a neutron is slightly heavier with a mass of 1.0087 amu and no charge. The electron has a charge of 1∠and is much lighter than the other particles with a mass of about 0.00055 amu.
A chemical symbol is an abbreviation that we use to indicate an element or an atom of an element. For example, the symbol for mercury is Hg. We use the same symbol to indicate one atom of mercury or to label a container of many atoms of the element mercury.
Traditionally, the discoverer of a new element names the element. However, until the name is recognized by the International Union of Pure and Applied Chemistry (IUPAC), the recommended name of the new element is based on the Latin word for its atomic number. For example, element 106 was called unnilhexium , element 107 was called unnilseptium , and element 108 was called unniloctium for several years. These elements are now named after scientists; for example, element 106 is now known as seaborgium in honor of Glenn Seaborg, a Nobel Prize winner who was active in the discovery of several heavy elements. Element 109 was named in honor of Lise Meitner, who discovered nuclear fission, a phenomenon that would have world-changing impacts; Meitner also contributed to the discovery of some major isotopes.
The symbol for a specific isotope of any element is written by placing the mass number as a superscript to the left of the element symbol . The atomic number is sometimes written as a subscript preceding the symbol, but since this number defines the element's identity, as does its symbol, it is often omitted. For example, magnesium exists as a mixture of three isotopes, each with an atomic number of 12 and with mass numbers of 24, 25, and 26, respectively. These isotopes can be identified as Mg, Mg, and Mg. These isotope symbols are read as "magnesium-24," "magnesium-25," and "magnesium-26." All magnesium atoms have 12 protons in their nucleus. They differ only because a magnesium atom has 12 neutrons in its nucleus, a magnesium atom has 13 neutrons, and a magnesium atom has 14 neutrons.
Isotopes of an element are atoms with the same atomic number but different mass numbers; isotopes of an element, therefore, differ from each other only in the number of neutrons within the nucleus. When a naturally occurring element is composed of several isotopes, the atomic mass of the element represents the average of the masses of the isotopes involved. A chemical symbol identifies the atoms in a substance using symbols, which are one-, two-, or three-letter abbreviations for the atoms. The discovery of the periodic recurrence of similar properties among the elements led to the formulation of the periodic table, in which the elements are arranged in order of increasing atomic number in rows known as periods and columns known as groups. Elements in the same group of the periodic table have similar chemical properties. Elements can be classified as metals, metalloids, and nonmetals or as a main-group elements, transition metals, and inner transition metals. Groups are numbered 1–18 from left to right. The elements in group 1 are known as the alkali metals; those in group 2 are the alkaline earth metals; those in 15 are the pnictogens; those in 16 are the chalcogens; those in 17 are the halogens; and those in 18 are the noble gases.
The occurrence and natural abundances of isotopes can be experimentally determined using an instrument called a mass spectrometer. Mass spectrometry is widely used in chemistry, forensics, medicine, environmental science, and many other fields to analyze and help identify the substances in a sample of material. In a typical mass spectrometer, the sample is vaporized and exposed to a high-energy electron beam that causes the sample's atoms to become electrically charged, typically by losing one or more electrons. These cations then pass through a electric or magnetic field that deflects each cation's path to an extent that depends on both its mass and charge. The ions are detected, and a plot of the relative number of ions generated versus their mass-to-charge ratios is made. The height of each vertical feature or peak in a mass spectrum is proportional to the fraction of cations with the specified mass-to-charge ratio.
Dimitri Mendeleev is widely credited with creating the first periodic table of the elements. By the twentieth century, it became apparent that the periodic relationship involved atomic numbers rather than atomic masses. The modern statement of this relationship, the periodic law, is as follows: the properties of the elements are periodic functions of their atomic numbers. A modern periodic table arranges the elements in increasing order of their atomic numbers and groups atoms with similar properties in the same vertical column.
Ida Tacke and Walter Noddack set out to find the elements after German chemists predicted that there should be elements below Manganese in Group 7. They investigated ores containing minerals of ruthenium, tungsten, osmium, and so on, and were able to identify naturally occurring elements that helped complete the table. Rhenium was one of their discoveries, which was one of the last natural elements to be discovered and is the last stable element to be discovered.
In studying the periodic table, you might have noticed something about the atomic masses of some of the elements. Element 43, element 61, and most of the elements with atomic number 84 and higher have their atomic mass given in square brackets. This is done for elements that consist entirely of unstable, radioactive isotopes. The number in square brackets is the atomic mass number of the most stable isotope of that element.
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The mole is a convenient unit of measurement for expressing large numbers of atoms or molecules. The identity of a substance is defined by the types of atoms or ions it contains, as well as the quantity of each type. For example, water and hydrogen peroxide are alike in that they consist of hydrogen and oxygen atoms, but hydrogen peroxide has twice as many oxygen atoms. The mole provides a link between easily measured macroscopic properties and fundamental microscopic traits.
The formula mass of a substance is the sum of the average atomic masses of all the atoms represented in its chemical formula. For covalent compounds, the formula mass represents the molecular mass. The average mass of a chloroform molecule is 119.37 amu, and that of aspirin is 180.15 amu.
For ionic compounds, the formula mass is calculated in the same way as for covalent compounds. The average masses of sodium and chloride atoms were used to compute the formula mass of sodium chloride, which is 58.44 amu.
In calculating the formula mass of an ionic compound, it is acceptable to use the average masses of neutral atoms rather than the masses of charged atoms or ions. The missing or additional electrons can generally be ignored when computing the mass of an isolated ion, as their contribution to the overall mass is negligible and reflected only in the nonsignificant digits that will be lost when the computed mass is properly rounded.
In summary, the mole is a convenient unit of measurement for expressing large numbers of atoms or molecules, and the formula mass of a substance is the sum of the average atomic masses of all the atoms represented in its chemical formula.
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Light and other forms of electromagnetic radiation move through a vacuum with a constant speed, c, of 2.998 × 10 m/s. This radiation shows wavelike behavior, which can be characterized by a frequency, ν, and a wavelength, λ, such that c = λν. Light is an example of a traveling wave. Other important wave phenomena include standing waves, periodic oscillations, and vibrations. Standing waves exhibit quantization, since their wavelengths are limited to discrete integer multiples of some characteristic lengths. Electromagnetic radiation that passes through two closely spaced narrow slits having dimensions roughly similar to the wavelength will show an interference pattern that is a result of constructive and destructive interference of the waves. Electromagnetic radiation also demonstrates properties of particles called photons. The energy of a photon is related to the frequency of the radiation as E = hν , where h is Planck's constant. That light demonstrates both wavelike and particle-like behavior is known as wave-particle duality, which has superseded the classical view. All forms of electromagnetic radiation share these properties, although various forms including X-rays, visible light, microwaves, and radio waves interact differently with matter and have very different practical applications.
Early in the nineteenth century, Thomas Young demonstrated that light passing through narrow, closely spaced slits produced interference patterns that could not be explained in terms of Newtonian particles but could be easily explained in terms of waves. Later in the nineteenth century, after James Clerk Maxwell developed his theory of electromagnetic radiation and showed that light was the visible part of a vast spectrum of electromagnetic waves, the particle view of light became thoroughly discredited. By the end of the nineteenth century, scientists viewed the physical universe as roughly comprising two separate domains: matter composed of particles moving according to Newton's laws of motion, and electromagnetic radiation consisting of waves governed by Maxwell's equations. Today, these domains are referred to as classical mechanics and classical electrodynamics . Although there were a few physical phenomena that could not be explained within this framework, scientists at that time were so confident of the overall soundness of this framework that they viewed these aberrations as puzzling paradoxes that would ultimately be resolved somehow within this framework. As we shall see, these paradoxes led to a contemporary framework that intimately connects particles and waves at a fundamental level called wave-particle duality, which has superseded the classical view.
Visible light and other forms of electromagnetic radiation play important roles in chemistry, since they can be used to infer the energies of electrons within atoms and molecules. Much of modern technology is based on electromagnetic radiation. For example, radio waves from a mobile phone, X-rays used by dentists, the energy used to cook food in your microwave, the radiant heat from red-hot objects, and the light from your television screen are forms of electromagnetic radiation that all exhibit wavelike behavior. Waves need not be restricted to travel through matter. As Maxwell showed, electromagnetic waves consist of an electric field oscillating in step with a perpendicular magnetic field, both of which are perpendicular to the direction of travel. These waves can travel through a vacuum at a constant speed of 2.998 Ã — 10 m/s, the speed of light .
All waves, including forms of electromagnetic radiation, are characterized by, a wavelength, a frequency, and an amplitude. The product of a wave's wavelength and its frequency , c = λν, is the speed of the wave. Thus, for electromagnetic radiation in a vacuum, speed is equal to the fundamental constant, c:
Wavelength and frequency are inversely proportional: As the wavelength increases, the frequency decreases. The inverse proportionality is illustrated in Figure 7.2. This figure also shows the electromagnetic spectrum, the range of all types of electromagnetic radiation. Each of the various colors of visible light has specific frequencies and wavelengths associated with them, and you can see that visible light makes up only a small portion of the electromagnetic spectrum. Because the technologies developed to work in various parts of the electromagnetic spectrum are different, for reasons of convenience and historical legacies, different units are typically used for different parts of the spectrum. For example, radio waves are usually specified as frequencies , while the visible region is usually specified in wavelengths .
One particularly characteristic phenomenon of waves results when two or more waves come into contact: They interfere with each other. Figure 7.5 shows the interference patterns that arise when light passes through narrow slits closely spaced about a wavelength apart. The fringe patterns produced depend on the wavelength, with the fringes being more closely spaced for shorter wavelength light passing through a given set of slits. When the light passes through the two slits, each slit effectively acts as a new source, resulting in two closely spaced waves coming into contact at the detector . The dark regions in Figure 7.5 correspond to regions where the peaks for the wave from one slit happen to coincide with the troughs for the wave from the other slit, while the brightest regions correspond to regions where the peaks for both waves happen to coincide. Likewise, when two stones are tossed close together, they can create an interference pattern on a surface, such as a drum, that is visible as a result of constructive and destructive interference of the waves.
Not all waves exhibit wavelike behavior. Standing waves, which remain constrained within some region of space, also exhibit quantization. For example, when a vibrating string is divided into two parts that are close together but not touching, the resulting standing wave pattern can be seen as a series of nodes and antinodes. Similarly, when light passes through two closely spaced narrow slits, an interference pattern results from the constructive and destructive interference of the waves.
In conclusion, light and other forms of electromagnetic radiation exhibit wavelike behavior, which can be characterized by their wavelength, frequency, and amplitude. The speed of these waves is a fundamental constant, c. Waves can also exhibit standing wave patterns, which are constrained within some region of space and exhibit quantization. These phenomena have led to the development of contemporary frameworks that intimately connect particles and waves at a fundamental level, known as wave-particle duality.
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Electromagnetic radiation can be generated by exciting matter to higher energies, such as heating it. The emitted light can be either continuous or discrete. Continuous spectra often have distributions that can be approximated as blackbody radiation at some appropriate temperature. The line spectrum of hydrogen can be obtained by passing the light from an electrified tube of hydrogen gas through a prism.
The solar distribution is compared to a representative distribution, called a blackbody spectrum, that corresponds to a temperature of 5250 °C in Figure 8.1. The blackbody spectrum matches the solar spectrum quite well. A blackbody is a convenient, ideal emitter that approximates the behavior of many materials when heated. It is "ideal" in the same sense that an ideal gas is a convenient, simple representation of real gases that works well, provided that the pressure is not too high nor the temperature too low.
Figure 8.2 shows the resulting curves for some representative temperatures. Each distribution depends only on a single parameter: the temperature. The maxima in the blackbody curves shift to shorter wavelengths as the temperature increases, reflecting the observation that metals being heated to high temperatures begin to glow a darker red that becomes brighter as the temperature increases, eventually becoming white hot at very high temperatures as the intensities of all of the visible wavelengths become appreciable.
Physicists derived mathematical expressions for the blackbody curves using well-accepted concepts from the theories of classical mechanics and classical electromagnetism. The theoretical expressions as functions of temperature fit the observed experimental blackbody curves well at longer wavelengths, but showed significant discrepancies at shorter wavelengths. Not only did the theoretical curves not show a peak, they absurdly showed the intensity becoming infinitely large as the wavelength became smaller, which would imply that everyday objects at room temperature should be emitting large amounts of UV light. This became known as the "ultraviolet catastrophe" because no one could find any problems with the theoretical treatment that could lead to such unrealistic short-wavelength behavior.
Around 1900, Max Planck derived a theoretical expression for blackbody radiation that fit the experimental observations exactly. Planck developed his theoretical treatment by extending the earlier work that had been based on the premise that the atoms composing the oven vibrated at increasing frequencies as the temperature increased, with these vibrations being the source of the emitted electromagnetic radiation. By restricting the vibrational energies to discrete values for each frequency, Planck could derive an expression for blackbody radiation that correctly had the intensity dropping rapidly for the short wavelengths in the UV region.
The quantity h is a constant now known as Planck's constant, in his honor. Although Planck was pleased he had resolved the blackbody radiation paradox, he was disturbed that to do so, he needed to assume the vibrating atoms required quantized energies, which he was unable to explain. The value of Planck's constant is very small, 6.626 × 10 joule seconds, which helps explain why energy quantization had not been observed previously in macroscopic phenomena.
In the photoelectric effect, electrons were ejected from the clean surface of a metal when light having a frequency greater than some threshold frequency was shone on it. Surprisingly, the kinetic energy of the ejected electrons did not depend on the brightness of the light, but increased with increasing frequency of the light. Einstein argued that the quantized energies that Planck had postulated in his treatment of blackbody radiation could be applied to the light in the photoelectric effect so that the light striking the metal surface should not be viewed as a wave, but instead as a stream of particles whose energy depended on their frequency, according to Planck's formula. Electrons were ejected when hit by photons having sufficient energy. The greater the frequency, the greater the kinetic energy imparted to the escaping electrons by the collisions.
With Einstein's findings, the nature of light took on a new air of mystery. Although many light phenomena could be explained either in terms of waves or particles, certain phenomena, such as the interference patterns obtained when light passed through a double slit, were completely contrary to a particle view of light, while other phenomena, such as the photoelectric effect, were completely contrary to a wave view of light. Somehow, at a deep fundamental level still not fully understood, light is both wavelike and particle-like. This is known as wave-particle duality.
In this essay, I will discuss the historical context and significance of Bohr's model of the hydrogen atom. Bohr's model was a groundbreaking achievement in the field of physics, as it provided a theoretical explanation for the discrete energy levels observed in the spectra of elements. This model introduced several important features that are still used in modern atomic models, such as quantized electronic energies and an increase in electron energy with distance from the nucleus.
Bohr's model was developed in the early 1900s, a time when the classical mechanics theories of the day were unable to explain the discrete energy levels observed in the spectra of elements. Bohr's solution to this problem was to propose that the electrons in an atom move in quantized orbits around the nucleus, with each orbit having a specific energy level. This idea challenged the classical mechanics notion of precise orbits and introduced the concept of quantized energy levels, which is a fundamental aspect of quantum mechanics.
Bohr's model was able to explain many observed properties of atoms, such as the discrete energy levels in their spectra and the stability of the electron in the lowest energy level, known as the ground state. The model also predicted the existence of higher energy states, which were later confirmed through experimentation.
One of the most significant implications of Bohr's model was its introduction of the concept of quantized energy levels. This idea challenged the classical mechanics notion of precise orbits and introduced the concept of quantized energy levels, which is a fundamental aspect of quantum mechanics. The quantization of electronic energies in atoms laid the foundation for the development of quantum mechanical models of atoms, which are still used today to describe the behavior of electrons in atoms.
Bohr's model also introduced the idea that an electron's energy increases with increasing distance from the nucleus. This concept is known as the Bohr effect and is still observed in the spectra of elements today. The Bohr effect is a result of the electrostatic attraction between the electron and the nucleus, which decreases as the electron moves further away from the nucleus.
In conclusion, Bohr's model of the hydrogen atom was a groundbreaking achievement in the field of physics. It introduced several important features that are still used in modern atomic models, such as quantized electronic energies and an increase in electron energy with distance from the nucleus. The model challenged the classical mechanics notion of precise orbits and laid the foundation for the development of quantum mechanical models of atoms. Bohr's work won him a Nobel Prize in Physics and cemented his place as one of the most important figures in the history of physics.
In this chapter, we will explore the quantum mechanical model for where electrons reside in an atom. We will examine the electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom.
The quantum mechanical 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. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom.
The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principal quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion and the general region in which discrete energy levels of electrons in a multi-electron atom and ions are located.
Another quantum number is the secondary quantum number, which is an integer that may take the values, l = 0, 1, 2, etc. This means that an orbital with n = 1 can have only one value of l = 0, whereas n = 2 permits l = 0 and l = 1. Whereas the principal quantum number, n, defines the general size and energy of the orbital, the secondary quantum number specifies the shape of the orbital. Orbitals with the same value of l have a spherical distribution, while those with different values of l have a dumbbell shape.
There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ(r) is zero at this distance for this orbital. Such a distance is called a radial node. The number of radial nodes in an orbital is n … 1.
Consider the examples in Figure 10.5, which show the probability density of finding an electron for the s, p, d, and f orbitals as a function of distance from the nucleus. It can be seen from the graphs that there are 1 … 0 … 1 = 0 places where the density is zero for the s orbitals and 1 … 0 … 1 = 1 node for the p orbitals.
The s subshell electron density distribution is spherical, and the d subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found.
In Figure 10.6, we see the shapes of the s, p, d, and f orbitals. The s subshell can only have one value of l = 0, while the p subshell can have three values of l = 1, 2, or 3. Similarly, the d subshell can have five values of l = 0, 1, 2, 3, or 4, and the f subshell can have seven values of l = -1, 0, 1, 2, 3, or 4.
The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers. This means that each electron in an atom must occupy a unique orbital, and the probability density of finding an electron in a particular orbital is zero outside of that orbital.
In summary, the quantum mechanical model for electrons in atoms provides valuable insights into the behavior of electrons in atoms. The principal quantum number defines the size and energy of an orbital, while the secondary quantum number specifies its shape. The Pauli exclusion principle ensures that each electron occupies a unique orbital, and the probability density of finding an electron in a particular orbital is zero outside of that orbital.
In this chapter, we will explore the concept of electron configurations and how they relate to the periodic table. We will also discuss the Aufbau principle, which is a rule used to predict the order in which electrons are added to an atom's outer shell.
Electron Configuration:
An electron configuration is a way of describing the arrangement of electrons in an atom or molecule. It shows how many electrons are in each energy level (or shell) around the nucleus, and which subshell (or orbital) each electron occupies. The electron configuration can be represented using a series of numbers called quantum numbers, which describe the energy, spin, and spatial distribution of the electrons.
Periodic Table:
The periodic table is a tabular arrangement of elements that shows their atomic number (number of protons in the nucleus), electron configuration, and other properties. The elements are arranged in order of increasing atomic number, and the periodic table can be used to predict the properties of elements based on their position in the table.
Aufbau Principle:
The Aufbau principle is a rule that describes how electrons are added to an atom's outer shell. It states that the lowest-energy electron occupies the innermost energy level (or shell), and higher-energy electrons occupy higher-level shells. The electrons in each shell are filled in a specific order, based on their energy levels, until all of the electrons in the outermost shell are accounted for.
Electronic Configuration of Atoms:
The electronic configuration of an atom is determined by the number of electrons in its outer shell. Atoms with a full outer shell have 8 electrons (2 in the 1s subshell, 2 in the 2s subshell, and 4 in the 2p subshell). Atoms with fewer than 8 electrons in their outer shell can gain or lose electrons to achieve a full outer shell.
Electronic Configuration of Ions:
Ions are formed when atoms gain or lose electrons. A cation forms when one or more electrons are removed from a parent atom, while an anion forms when one or more electrons are added to a parent atom. The electronic configuration of ions is determined by the number of electrons in their outer shell, and can be represented using the same quantum numbers as atoms.
Electronic Configuration and the Periodic Table:
The periodic table arranges elements based on their atomic number, which is related to their electron configuration. Elements in the same group have the same number of valence electrons, and elements in different groups have different numbers of valence electrons. The periodic table can be used to predict the properties of elements based on their position in the table, including their electron configuration.
Conclusion:
In conclusion, electron configurations are a way of describing the arrangement of electrons in an atom or molecule, and the Aufbau principle is a rule used to predict how electrons are added to an atom's outer shell. The periodic table arranges elements based on their atomic number, which is related to their electron configuration, and can be used to predict the properties of elements based on their position in the table. Understanding electron configurations and the periodic table is essential for understanding the properties of elements and how they react with other elements.
In this chapter, we learned about the ionization energy (IE) and electron affinity (EA) of atoms. Ionization energy is the energy required to remove an electron from an atom, while electron affinity is the energy change for adding an electron to a gaseous atom to form an anion. We also discussed how these energies vary across a period and down a group in the periodic table.
The IE of an element decreases as the atomic number increases within a period, due to the increasing nuclear charge and the resulting penetration and shielding effects. Similarly, the EA of an element becomes more negative as the atomic number increases within a period, due to the increased effective nuclear charge. However, there are some deviations from these trends, such as the decrease in IE for boron compared to beryllium, despite the greater nuclear charge of boron.
The EA values also show some systematic deviations, such as the rapid increase in EA for Sc and Ga after the third ionization, due to the removal of core electrons. Additionally, we saw that the atom at the top of each group tends to have the most negative EA, which suggests that these atoms have the largest effective nuclear charges.
Overall, the properties discussed in this section are central to understanding chemical reactivity, as they determine the ease with which electrons can be removed from an atom and the resulting metallic character of an element.