Chem 101 - Theoretical PDF

General chemistry (I) General chemistry (I) For first Year Students Collected and prepared By Assoc. prof. Nagwa hussien Dr. Mohamed Abdel-sabour...

General chemistry (I) General chemistry (I) For first Year Students Collected and prepared By Assoc. prof. Nagwa hussien Dr. Mohamed Abdel-sabour Fahmy Chemistry Department Faculty of Science Luxor University 2024/2025 1 General chemistry (I) Book data Faculty: Faculty of Science Group: 1st Students Natural Science, Biology and Geology groups 2 General chemistry (I) Content Chapter 1. Structure of Atom-Classical Mechanics Chapter 2. Structure of Atom-Wave Mechanical Approach Chapter 3. Chemical Bonding-Types of Bonds Chapter 4. Hybridization-Type of Hybridization 3 General chemistry (I) Atomic Theory and Structure Pure substances are classified as elements or compounds, but just what makes a substance possess its unique properties? How small a piece of salt will still taste salty? Carbon dioxide puts out fires, is used by plants to produce oxygen, and forms dry ice when solidified. But how small a mass of this material still behaves like carbon dioxide? Substances are in their simplest identifiable form at the atomic, ionic, or molecular level. Further division produces a loss of characteristic properties. What particles lie within an atom or ion? How are these tiny particles alike? How do they differ? How far can we can we continue to divide them? Alchemists began the quest, early chemists laid the foundation, and modern chemists continue to build and expand on models of the atom. Dalton’s Model of the Atom More than 2000 years after Democritus, the English schoolmaster John Dalton (1766–1844) revived the concept of atoms and proposed an atomic model based on facts and experimental evidence (Figure 5.1). His theory, described in a series of papers published from 1803 to 1810, rested on the idea of a different kind of atom for each element. The essence of Dalton’s atomic model may be summed up as follows: 1. Elements are composed of minute, indivisible particles called atoms. 2. Atoms of the same element are alike in mass and size. 3. Atoms of different elements have different masses and sizes. 4. Chemical compounds are formed by the union of two or more atoms of different elements. 5. Atoms combine to form compounds in simple numerical ratios, such as one to one, one to two, two to three, and so on. 4 General chemistry (I) 6. Atoms of two elements may combine in different ratios to form more than one compound. Fig 1.(a) Dalton’s atoms were individual particles, the atoms of each element being alike in mass and size but different in mass and size from other elements. (b) and (c) Dalton’s atoms combine in specific ratios to form compounds. Composition of Compounds A large number of experiments extending over a long period have established the fact that a particular compound always contains the same elements in the same proportions by mass. For example, water always contains 11.2% hydrogen and 88.8% oxygen by mass (see Figure 1b). The fact that water contains hydrogen and oxygen in this particular ratio does not mean that hydrogen and oxygen cannot combine in some other ratio but rather that a compound with a different ratio would not be water. In fact, hydrogen peroxide is made up of two atoms of hydrogen and two atoms of oxygen per molecule and contains 5.9% hydrogen and 94.1% oxygen by mass; its properties are markedly different from those of water (see Figure 1c). We often summarize our general observations regarding nature into a statement called a natural law. In the case of the composition of a compound, we use the law of definite composition, which states that a compound always contains two or more elements chemically combined in a definite proportion by mass. 5 General chemistry (I) Let’s consider two elements, oxygen and hydrogen, that form more than one compound. In water, 8.0 g of oxygen are present for each gram of hydrogen. In hydrogen peroxide, 16.0 g of oxygen are present for each gram of hydrogen. The masses of oxygen are in the ratio of small whole numbers, 16: 8 or 2: 1. Hydrogen peroxide has twice as much oxygen (by mass) as does water. Using Dalton’s atomic model, we deduce that hydrogen peroxide has twice as many oxygen atoms per hydrogen atom as water. In fact, we now write the formulas for water as and for hydrogen peroxide H2O2 as See Figure 1b and c. The law of multiple proportions states atoms of two or more elements may combine in different ratios to produce more than one compound. The Nature of Electric Charge You’ve probably received a shock after walking across a carpeted area on a dry day. You may have also experienced the static electricity associated with combing your hair and have had your clothing cling to you. These phenomena result from an accumulation of electric charge. This charge may be transferred from one object to another. The properties of electric charge are as follows: 1. Charge may be of two types, positive and negative. 2. Unlike charges attract (positive attracts negative), and like charges repel (negative repels negative and positive repels positive). 3. Charge may be transferred from one object to another, by contact or induction. 4. The less the distance between two charges, the greater the force of attraction between unlike charges (or repulsion between identical charges). The force of attraction(F) can be expressed using the following equation: 6 General chemistry (I) F = kq1q2/ r2 where q1 and q2 are the charges, r is the distance between the charges, and k is a constant. Discovery of Ions English scientist Michael Faraday (1791–1867) made the discovery that certain substances when dissolved in water conduct an electric current. He also noticed that certain compounds decompose into their elements when an electric current is passed through the compound. Atoms of some elements are attracted to the positive electrode, while atoms of other elements are attracted to the negative electrode. Faraday concluded that these atoms are electrically charged. He called them ions after the Greek word meaning “wanderer.” Any moving charge is an electric current. The electrical charge must travel through a substance known as a conducting medium. The most familiar conducting media are metals formed into wires. The Swedish scientist Svante Arrhenius (1859–1927) extended Faraday’s work. Arrhenius reasoned that an ion is an atom (or a group of atoms) carrying a positive or negative charge. When a compound such as sodium chloride is melted, it conducts electricity. Water is unnecessary. Arrhenius’s explanation of this conductivity was that upon melting, the sodium chloride dissociates, or breaks up, into charged ions Na+ and Cl-, the Na+ ions move toward the negative electrode (cathode), whereas the Cl-ions migrate toward the positive electrode (anode). Thus positive ions are called cations, and negative ions are called anions. From Faraday’s and Arrhenius’s work with ions, Irish physicist G. J. Stoney (1826–1911) realized there must be some fundamental unit of electricity associated with atoms. He named this unit the electron in 1891. Unfortunately, he had no means of supporting his idea with experimental 7 General chemistry (I) proof. Evidence remained elusive until 1897, when English physicist J. J. Thomson (1856–1940) was able to show experimentally the existence of the electron. Subatomic Parts of the Atom The concept of the atom—a particle so small that until recently it could not be seen even with the most powerful microscope—and the subsequent determination of its structures and among the greatest creative intellectual human achievements. Any visible quantity of an element contains a vast number of identical atoms. But when we refer to an atom of an element, we isolate a single atom from the multitude in order to present the element in its simplest form. What is this tiny particle we call the atom? The diameter of a single atom ranges from 0.1 to 0.5 nanometer (1 nm = 1x10-9 m). Hydrogen, the smallest atom, has a diameter of about 0.1 nm. To arrive at some idea of how small an atom is, consider this dot ( ), which has a diameter of about 1 mm, or 1x106 nm. It would take 10 million hydrogen atoms to form a line of atoms across this dot. As inconceivably small as atoms are, they contain even smaller particles, the subatomic particles, including electrons, protons, and neutrons. The development of atomic theory was helped in large part by the invention of new instruments. For example, the Crookes tube, developed by Sir William Crookes (1832–1919) in 1875, opened the door to the subatomic structure of the atom (Figure 2). The emissions generated in a Crookes tube are called cathode rays. J. J. Thomson demonstrated in 1897 that cathode rays (1) travel in straight lines, (2) are negative in charge, (3) are deflected by electric and magnetic fields, (4) produce sharp shadows, 8 General chemistry (I) and (5) are capable of moving a small paddle wheel. This was the experimental discovery of the fundamental unit of charge—the electron. Fig 2. Crookes tube (cathode rays) The electron(e-) is a particle with a negative electrical charge and a mass of9.110 x 10-28 g. This mass is the mass1/1837 of a hydrogen atom. Although the actual charge of an electron is known, its value is too cumbersome for practical use and has therefore been assigned a relative electrical charge -1 of the size of an electron has not been determined exactly, but its diameter is believed to be less than10-12 cm. Protons were first observed by German physicist Eugen Goldstein (1850–1930) in1886. However, it was Thomson who discovered the nature of the proton. He showed that the proton is a particle, and he calculated its mass to be about 1837 times that of an electron. The proton (p) is a particle with actual mass of its 1.673x10-24g.relative charge is (+1) equal in magnitude, but opposite in sign, to the charge on the electron. The mass of a proton is only very slightly less than that of a hydrogen atom. Thomson had shown that atoms contain both negatively and positively charged particles. Clearly, the Dalton model of the atom was no longer acceptable. Atoms are not indivisible but are instead composed of smaller parts. Thomson proposed a new model of the atom. 9 General chemistry (I) In the Thomson model of the atom, the electrons are negatively charged particles embedded in the positively charged atomic sphere. A neutral atom could become an ion by gaining or losing electrons. Positive ions were explained by assuming that the neutral atom loses electrons. An atom with a net charge +1 of (for example, Na+ or Li+) has lost one electron. An atom with a net charge of +3 (for example Al3+) has lost three electrons (Figure 3a). Negative ions were explained by assuming that additional electrons can be added to atoms. A net charge of (for example, or) is produced by the addition of one electron. A net charge of -1(for example, Cl- or F-) requires the addition of two electrons (Figure 3b). The third major subatomic particle was discovered in 1932 by James Chadwick (1891–1974). This particle, the neutron(n), has neither a positive nor a negative charge and has an actual mass which is only very slightly greater than that of a proton. The properties of these three subatomic particles are summarized in Table 1. Fig. 3. Thomson model of the atom Nearly all the ordinary chemical properties of matter can be explained in terms of atoms consisting of electrons, protons, and neutrons. The discussion of atomic structure that follows is based on the assumption that atoms contain only these principal subatomic particles. 10 General chemistry (I) Many other subatomic particles, such as mesons, positrons, neutrinos, and antiprotons, have been discovered, but it is not yet clear whether all these Particles are actually present in the atom or whether they are produced by reactions occurring within the nucleus. The fields of atomic and high- energy physics have produced a long list of subatomic particles. Ions: Positive ions were explained by assuming that a neutral atom loses electrons.Negative ions were explained by assuming that atoms gain electrons Table 1. Electrical charge and relative mass of electrons, protons and neutrons. The Nuclear Atom The discovery that positively charged particles are present in atoms came soon after the discovery of radioactivity by Henri Becquerel (1852– 1908) in 1896. Radioactive elements spontaneously emit alpha particles, beta particles, and gamma rays from their nuclei by Rutherford (1907) found that alpha particles emitted by certain radioactive elements were helium nuclei. CATHODE RAYS – THE DISCOVERY OF ELECTRON The knowledge about the electron was derived as a result of the study of the electric discharge in the discharge tube (J.J. Thomson, 1896). The discharge tube consists of a glass tube with metal electrodes fused in the 11 General chemistry (I) walls. Through a glass side-arm air can be drawn with a pump. The electrodes are connected to a source of high voltage (10,000 Volts) and the air partially evacuated. The electric discharge passes between the electrodes and the residual gas in the tube begins to glow. If virtually all the gas is evacuated from within the tube, the glow is replaced by faintly luminous ‘rays’ which produce fluorescence on the glass at the end far from the cathode. The rays which proceed from the cathode and move away from it at right angles in straight lines are called Cathode Rays. By counterbalancing the effect of magnetic and electric field on cathode rays. Thomson was able to work out the ratio of the charge and mass (e/m) of the cathode particle. In SI units the value of e/m of cathode particles is – 1.76 × 108 coulombs per gram. As a result of several 12 General chemistry (I) experiments, Thomson showed that the value of e/m of the cathode particle was the same regardless of both the gas and the metal of which the cathode was made. This proved that the particles making up the cathode rays were all identical and were constituent parts of the various atoms. Dutch Physicist H.A. Lorentz named them Electrons. Electrons are also obtained by the action of X-rays or ultraviolet light on metals and from heated filaments. These are also emitted as β-particles by radioactive substances. Thus it is concluded that electrons are a universal constituent of all atoms. MEASUREMENT OF e/m FOR ELECTRONS The ratio of charge to mass (e/m) for an electron was measured by J.J. Thomson (1897) using the apparatus shown. Electrons produce a bright luminous spot at X on the fluorescent screen. Magnetic field is applied first and causes the electrons to be deflected in a circular path while the spot is shifted to Y. The radius of the circular path can be obtained from the dimensions of the apparatus, the current and number of turns in the coil of the electromagnet and the angle of deflection of the spot. An electrostatic field of known strength is 13 General chemistry (I) then applied so as to bring back the spot to its original position. Then from the strength of the electrostatic field and magnetic field, it is possible to calculate the velocity of the electrons. Equating magnetic force on the electron beam to centrifugal force. where B = magnetic field strength v = velocity of electrons e = charge on the electron m = mass of the electron r = radius of the circular path of the electron in the magnetic field. This means The value of r is obtained from the dimensions of the tube and the displacement of the electron spot on the fluorescent screen. When the electrostatic field strength and magnetic field strength are counterbalanced, Bev = Ee where E is the strength of the electrostatic field. Thus 14 General chemistry (I) If E and B are known, v can be calculated and on substitution in equation (1), we get the value of e/m. All the quantities on the right side of the equation can be determined experimentally. Using this procedure, the ratio e/m works out to be – 1.76 × 108 per gram. or e/m for the electron = – 1.76 × 108 coulomb/g DETERMINATION OF THE CHARGE ON AN ELECTRON The absolute value of the charge on an electron was measured by R.A. Milikan (1908) by what is known as the Milikan’s Oil-drop Experiment. The apparatus used by him is shown in: 15 General chemistry (I) He sprayed oil droplets from an atomizer into the apparatus. An oil droplet falls through a hole in the upper plate. The air between the plates is then exposed to X-rays which eject electrons from air molecules. Some of these electrons are captured by the oil droplet and it acquires a negative charge. When the plates are earthed, the droplet falls under the influence of gravity. He adjusted the strength of the electric field between the two charged plates so that a particular oil drop remained suspended, neither rising nor falling. At this point, the upward force due to the negative charge on the drop, just equalled the weight of the drop. As the X-rays struck the air molecules, electrons are produced. The drop captures one or more electrons and gets a negative charge, Q. Thus, Q = ne where n = number of electrons and e = charge of the electron. From measurement with different drops, Milikan established that electron has the charge – 1.60 × 10– 19 coulombs. Mass of Electron By using the Thomson’s value of e/m and the Milikan’s value of e, the absolute mass of an electron can be found. Mass of an Electron relative to H 16 General chemistry (I) Avogadro number, the number of atoms in one gram atom of any element is 6.023 × 1023. From this we can find the absolute mass of hydrogen atom. Mass of 6.023 × 1023 atoms of hydrogen = 1.008 g Thus an atom of hydrogen is 1835 times as heavy as an electron. In other words, the mass of an electron is 1/1835 th of the mass of hydrogen atom. DEFINITION OF AN ELECTRON Having known the charge and mass of an electron, it can be defined as : An electron is a subatomic particle which bears charge – 1.60 × 10–19 coulomb and has mass 9.1 × 10– 28 g. Alternatively, an electron may be defined as : A particle which bears one unit negative charge and mass 1/1835 th of a hydrogen atom. Since an electron has the smallest charge known, it was designated as unit charge by Thomson. POSITIVE RAYS In 1886 Eugen Goldstein used a discharge tube with a hole in the cathode 17 General chemistry (I) He observed that while cathode rays were streaming away from the cathode, there were coloured rays produced simultaneously which passed through the perforated cathode and caused a glow on the wall opposite to the anode. Thomson studied these rays and showed that they consisted of particles carrying a positive charge. He called them Positive rays. How are Positive rays produced? When high-speed electrons (cathode rays) strike molecule of a gas placed in the discharge tube, they knock out one or more electrons from it. Thus a positive ion results M + e− → M+ + 2e− These positive ions pass through the perforated cathode and appear as positive rays. When electric discharge is passed through the gas under 18 General chemistry (I) high electric pressure, its molecules are dissociated into atoms and the positive atoms (ions) constitute the positive rays. Conclusions from the study of Positive rays From a study of the properties of positive rays, Thomson and Aston (1913) concluded that atom consists of at least two parts: (a) the electrons; and (b) a positive residue with which the mass of the atom is associated. PROTONS E. Goldstein (1886) discovered protons in the discharge tube containing hydrogen. H → H+ + e– It was J.J. Thomson who studied their nature. He showed that: (1) The actual mass of proton is 1.672 × 10 – 24 gram. On the relative scale, proton has mass 1 atomic mass unit (amu). (2) The electrical charge of proton is equal in magnitude but opposite to that of the electron. Thus proton carries a charge +1.60 × 10–19 coulombs or + 1 elementary charge unit. Since proton was the lightest positive particle found in atomic beams in the discharge tube, it was thought to be a unit present in all other atoms. Protons were also obtained in a variety of nuclear reactions indicating further that all atoms contain protons. 19 General chemistry (I) Thus a proton is defined as a subatomic particle which has a mass of 1 amu and charge + 1 elementary charge unit. A proton is a subatomic particle which has one unit mass and one unit positive charge. NEUTRONS In 1932 Sir James Chadwick discovered the third subatomic particle. He directed a stream of alpha particles ( 24He) at a beryllium target. He found that a new particle was ejected. It has almost the same mass (1.674 × 10– 24 g) as that of a proton and has no charge. He named it neutron. The assigned relative mass of a neutron is approximately one atomic mass unit (amu). Thus : A neutron is a subatomic particle which has a mass almost equal to that of a proton and has no charge. The reaction which occurred in Chadwick’s experiment is an example of artificial transmutation where an atom of beryllium is converted to a carbon atom through the nuclear reaction. Rutherford experiment 20 General chemistry (I) In 1911 performed experiments that shot a stream of alpha particles at a gold foil. Most of the alpha particles passed through the foil with little or no deflection. He found that a few were deflected at large angles and some alpha particles even bounced back An electron with a mass of 1/1837 amu could not have deflected an alpha particle with a mass of 4 amu. Rutherford knew that like charges repel. Rutherford concluded that each gold atom contained a positively charged mass that occupied a tiny volume. He called this mass the nucleus. Most of the alpha particles passed through the gold foil. This led Rutherford to conclude that a gold atom was mostly empty space. General Arrangement of Subatomic Particles 21 General chemistry (I) Rutherford’s experiment showed that an atom had a dense, positively charged nucleus. Chadwick’s work in 1932 demonstrated that the atom contains neutrons. Rutherford also noted that light, negatively charged electrons were present in an atom and offset the positive nuclear charge. Rutherford put forward a model of the atom in which a dense, positively charged nucleus is located at the atom’s center. The negative electrons surround the nucleus. The nucleus contains protons and neutrons. The atom and the location of its subatomic particles were devised in which each atom consists of a nucleus surrounded by electrons (see above). The nucleus contains protons and neutrons but does not contain electrons. In a neutral atom the positive charge of the nucleus (due to protons) is exactly offset by the negative electrons. Because the charge of an electron is equal to, but of opposite sign than, the charge of a proton, a neutral atom must contain exactly the same number of electrons as protons. However, this model of atomic structure provides no information on the arrangement of electrons within the atom. A neutral atom contains the same number of protons and electrons. Atomic Numbers of the Elements The atomic number of an element is the number of protons in the nucleus of an atom of that element. The atomic number determines the identity of an atom. For example, every atom with an atomic number of 1 is a hydrogen atom; it contains one proton in its nucleus. Every atom with an atomic number of 6 is a carbon atom; it contains 6 protons in its nucleus. Every atom with an atomic number of 92 is a uranium atom; it contains 92 protons in its nucleus. The atomic number tells us not only the number of positive charges in the nucleus but also the number of 22 General chemistry (I) electrons in the neutral atom, since a neutral atom contains the same number of electrons and protons. In the nuclear model of the atom, protons and neutrons are located in the nucleus. The electrons are found in the remainder of the atom (which is mostly empty space because electrons are very tiny).You don’t need to memorize the atomic numbers of the elements because a periodic table is usually provided in texts, in laboratories, and on examinations. The atomic numbers of all elements are shown in the periodic table on the inside front cover of this book and are also listed in the table of atomic masses on the inside front endpapers. Atomic number 1H 1 proton in the nucleus Atomic number 6C6 proton in the nucleus Atomic number 92U92 proton in the nucleus Isotopes of the Elements Shortly after Rutherford’s conception of the nuclear atom, experiments were performed to determine the masses of individual atoms. These experiments showed that the masses of nearly all atoms were greater than could be accounted for by simply adding up the masses of all the protons and electrons that were known to be present in an atom. This fact led to the concept of the neutron, a particle with no charge but with a mass about the same as that of a proton. Because this particle has no charge, it was very difficult to detect, and the existence of the neutron was not proven experimentally until 1932. All atomic nuclei except that of the simplest hydrogen atom contain neutrons. All atoms of a given element have the same number of protons. Experimental evidence has shown that, in most cases, all atoms of a given element do not have 23 General chemistry (I) identical masses. This is because atoms of the same element may have different numbers of neutrons in their nuclei. Atoms of an element having the same atomic number but different atomic masses are called isotopes of that element. Atoms of the various isotopes of an element therefore have the same number of protons and electrons but different numbers of neutrons. Three isotopes of hydrogen (atomic number 1) are known. Each has one proton in the nucleus and one electron. The first isotope (protium), without a neutron, has amass number of 1; the second isotope (deuterium), with one neutron in the nucleus, has a mass number of 2; the third isotope (tritium), with two neutrons, has a mass number of 3. The three isotopes of hydrogen may be represented by the symbols11H, 12H and 13H and indicating an atomic number of 1 and mass numbers of 1, 2, and 3, respectively. This method of representing atoms is called isotopic notation. The subscript (Z) is the atomic number; the superscript (A) is the mass number, which is the sum of the number of protons and the number of neutrons in the nucleus. The hydrogen isotopes may also be referred to as referred to as hydrogen-1, hydrogen-2, and hydrogen-3. Mass number: (sum. of protons and neutrons in the nucleus) Z E Symbol of element A Atomic number (number of protons in the nucleus) The mass number of an element is the sum of the protons and neutrons in the nucleus. Most of the elements occur in nature as mixtures of isotopes. However, not all isotopes are stable; some are radioactive and are continuously decomposing to for mother elements. For example, of the seven known isotopes of carbon, only two, carbon-12 and carbon-13 24 General chemistry (I) 16 17 are stable. Of the seven known isotopes of oxygen, only three 8O 8O and188O, are stable. Of the fifteen known isotopes of arsenic, is the only one that is stable.7533As. is the only one that is stable. Atomic Mass The mass of a single atom is far too small to measure on a balance, but fairly precise determinations of the masses of individual atoms can be made with an instrument called a mass spectrometer. The mass of a single hydrogen atom is 1.673 x 10-24 g. However, it is neither convenient nor practical to compare the actual masses of atoms expressed in grams; therefore, a table of relative atomic masses using atomic mass units was devised. (The term atomic weight is sometimes used instead of atomic mass). The carbon isotope having six protons and six neutrons and designated carbon-12, or126C, was chosen as the standard for atomic masses. This reference isotope was assigned a value of exactly 12 atomic mass units (amu). Thus, 1 atomic mass unit is defined as equal to exactly of the mass of a carbon-12 atom. The actual mass of a carbon-12 atom is1.9927 x 10-23gand that of one atomic mass unit is1.6606 x 10-24 g. In the table of atomic masses, all elements then have values that are relative to the mass assigned to the reference isotope, carbon-12. Hydrogen atoms, with a mass of about 1/12 that of a carbon atom, have an average atomic mass of 1.00794 amu on this relative scale. Magnesium atoms, which are about twice as heavy as carbon, have an average mass of 24.305 amu. The average atomic mass of oxygen is 15.9994 amu. Since most elements occur as mixtures of isotopes with different masses, the atomic mass determined for an element represents the average relative mass of all the naturally occurring isotopes of that element. The atomic masses of the individual isotopes are approximately whole 25 General chemistry (I) numbers, because the relative masses of the protons and neutrons are approximately 1.0 amu each. Yet we find that the atomic masses given for many of the elements deviate considerably from whole numbers. For example, the atomic mass of rubidium is 85.4678 amu, that of copper is63.546 amu, and that of magnesium is 24.305 amu. The deviation of an atomic mass from a whole number is due mainly to the unequal occurrence of the various isotopes of an element. 63 The two principal isotopes of copper are 29Cu and6529Cu. Copper used in everyday objects, and the Liberty Bell contains a mixture of these two isotopes. It is apparent thatcopper-63 atoms are the more abundant isotope, since the atomic mass of copper,63.546 amu, is closer to 63 than to 65 amu. The average atomic mass can be calculated by multiplying the atomic mass of each isotope by the fraction of each isotope present and adding the results. The calculation for copper is (62.9298 amu)(0.6909) =43.48 amu (64.9278 amu)(0.3091) =20.07 amu 63.55 amu The atomic mass of an element is the average relative mass of the isotopes of that element compared to the atomic mass of carbon-12 (exactly 12.0000 amu). The relationship between mass number and atomic number is such that if we subtract the atomic number from the mass number of a given isotope, we obtain the number of neutrons in the nucleus of an atom of that isotope. For example, the fluorine atom(199F), atomic number 9, having a mass of 19 amu, contains 10 neutrons: Mass number 19 atomic number 9 number of neutrons 10 26 General chemistry (I) The atomic masses given in the table on the front endpapers of this book are values accepted by international agreement. You need not memorize atomic masses. In the calculations in this book, the use of atomic masses rounded to four significant figures will give results of sufficient accuracy. Modern Atomic Theory and the Periodic Table Chemists have the same dilemma when they study the atom. Atoms are so very small that it isn’t possible to use the normal senses to describe them. We are essentially working in the dark with this package we call the atom. However, our improvements in instruments (X-ray machines and scanning tunneling microscopes) and measuring devices (spectro- photometers and magnetic resonance imaging, MRI) as well as in our mathematical skills are bringing us closer to revealing the secrets of the atom. A Brief History In the last 200 years, vast amounts of data have been accumulated to support atomic theory. When atoms were originally suggested by the early Greeks, no physical evidence existed to support their ideas. Early chemists did a variety of experiments, which culminated in Dalton’s model of the atom. Because of the limitations of Dalton’s model, modifications were proposed first by Thomson and then by Rutherford, which eventually led to our modern concept of the nuclear atom. These early models of the atom work reasonably well-in fact, we continue to use them to visualize a variety of chemical concepts. There remain questions that these models cannot answer, including an explanation of how atomic structure relates to the periodic table. In this chapter, we will present our modern model of the atom; we will see how it varies from and improves upon the earlier atomic models. 27 General chemistry (I) Electromagnetic Radiation Scientists have studied energy and light for centuries, and several models have been proposed to explain how energy is transferred from place to place. One way energy travels through space is by electro- magnetic radiation. Examples of electromagnetic radiation include light from the sun, X-rays in your dentist’s office, microwaves from your microwave oven, radio and television waves, and radiant heat from your fireplace. While these examples seem quite different, they are all similar in some important ways. Each shows wavelike behavior, and all travel at the same speed in a vacuum (3.00 x 108 m/s). Light is one form of electromagnetic radiation and is usually classified by its wave length, as shown in Figure 4. Visible light, as you can see, is only a tiny part of the electromagnetic spectrum. Some examples of electromagnetic radiation involved in energy transfer outside the visible region are hot coals in your backyard grill, which transfer infrared radiation to cook your food, and microwaves, which transfer energy to water molecules in the food, causing them to move more quickly and thus raise the temperature of your food. Fig. 4. The Bohr Atom As scientists struggled to understand the properties of electromagnetic radiation, evidence began to accumulate that atoms could radiate light. At high temperatures, or when subjected to high voltages, elements in the gaseous state give off colored light. Brightly colored neon signs illustrate this property of matter very well. When the light emitted by a gas is passed through a prism or diffraction grating, a set of brightly 28 General chemistry (I) colored lines called a line spectrum results (Figure 5). These colored lines indicate that the light is being emitted only at certain wavelengths, or frequencies, that correspond to specific colors. Each element possesses a unique set of these spectral lines that is different from the sets of all the other elements. Fig. 5 line spectrum In 1912–1913, while studying the line spectrum of hydrogen, Niels Bohr (1885–1962), a Danish physicist, made a significant contribution to the rapidly growing knowledge of atomic structure. His research led him to believe that electrons exist in specific regions at various distances from the nucleus. He also visualized the electrons as revolving in orbits around the nucleus, like planets rotating around the sun. Bohr’s first paper in this field dealt with the hydrogen atom, which he described as a single electron revolving in an orbit about a relatively heavy nucleus. He applied the concept of energy quanta, proposed in 1900 by the German physicist Max Planck (1858–1947), to the observed line spectrum of hydrogen. Planck stated that energy is never emitted in a continuous stream but only in small, discrete packets called quanta. From this, Bohr theorized that electrons have several possible energies corresponding to several possible orbits at different distances from the nucleus. Therefore, an electron has to be in one specific energy level; it cannot exist between energy levels. In other words, the energy of the electron is said to be quantized. Bohr also stated that when a hydrogen atom absorbed one or more quanta of energy, its electron would “jump” to a higher energy level. 29 General chemistry (I) Bohr was able to account for spectral lines of hydrogen this way. A number of energy levels are available, the lowest of which is called the ground state. When an electron falls from a high energy level to a lower one (say, from the fourth to the second), a quantum of energy is emitted as light at a specific frequency, or wavelength5. This light corresponds to one of the lines visible in the hydrogen spectrum (Figure 5). Several lines are visible in this spectrum, each one corresponding to a specific electron energy-level shift within the hydrogen atom. The chemical properties of an element and its position in the periodic table depend on electron behavior within the atoms. In turn, much of our knowledge of the behavior of electrons within atoms is based on spectroscopy. Niels Bohr contributed a great deal to our knowledge of atomic structure by: (1) Suggesting quantized energy levels for electrons and (2) Showing that spectral lines result from the radiation of small increments of energy (Planck’s quanta) when electrons shift from one energy level to another. Bohr’s calculations succeeded very well in correlating the experimentally observed spectral lines with electron energy levels for the hydrogen atom. However, Bohr’s methods of calculation did not succeed for heavier atoms. More theoretical work on atomic structure was needed. In 1924, the French physicist Louis de Broglie suggested a surprising hypothesis: All objects have wave properties. De Broglie used sophisticated mathematics to show that the wave properties for an object of ordinary size, such as a baseball, are too small to be observed. But for smaller objects, such as an electron, the wave properties become significant. Other scientists confirmed de Broglie’s hypothesis, showing that electrons do exhibit wave properties. In 1926, Erwin Schrqdinger, an Austrian physicist, created a mathematical model that described electrons 30 General chemistry (I) as waves. Using Schrqdinger’s wave mechanics, we can determine the probability of finding an electron in a certain region around the nucleus of the atom. This treatment of the atom led to a new branch of physics called wave mechanics or quantum mechanics, which forms the basis for our modern understanding of atomic structure. Although the wave- mechanical description of the atom is mathematical, it can be translated, at least in part, into a visual model. It is important to recognize that we cannot locate an electron precisely within an atom; however, it is clear that electrons are not revolving around the nucleus in orbits as Bohr postulated. Postulates of Bohr’s Theory (1) Electrons travel around the nucleus in specific permitted circular orbits and in no others. Electrons in each orbit have a definite energy and are at a fixed distance from the nucleus. The orbits are given the letter designation n and each is numbered 1, 2, 3, etc. (or K, L, M, etc.) as the distance from the nucleus increases. (2) While in these specific orbits, an electron does not radiate (or lose) energy. Therefore, in each of these orbits the energy of an electron remains the same i.e. it neither loses nor gains energy. Hence the specific orbits available to the electron in an atom are referred to as stationary energy levels or simply energy levels. (3) An electron can move from one energy level to another by quantum or photon jumps only. When an electron resides in the orbit which is lowest in energy (which is also closest to the nucleus), the electron is said to be in the ground state. When an electron is supplied energy, it absorbs one quantum or photon of 31 General chemistry (I) energy and jumps to a higher energy level. The electron then has potential energy and is said to be in an excited state. The quantum or photon of energy absorbed or emitted is the difference between the lower and higher energy levels of the atom where h is Planck’s constant and ν the frequency of a photon emitted or absorbed energy. (4) The angular momentum (mvr) of an electron orbiting around the nucleus is an integral multiple of Planck’s constant divided by 2π. where m = mass of electron, v = velocity of the electron, r = radius of the orbit ; n = 1, 2, 3, etc., and h = Planck’s constant. By putting the values 1, 2, 3, etc., for n, we can have respectively the angular momentum 32 General chemistry (I) There can be no fractional value of h/2π. Thus the angular momentum is said to be quantized. The integer n in equation (2) can be used to designate an orbit and a corresponding energy level n is called the atom’s Principal quantum number. Using the above postulates and some classical laws of Physics, Bohr was able to calculate the radius of each orbit of the hydrogen atom, the energy associated with each orbit and the wavelength of the radiation emitted in transitions between orbits. The wavelengths calculated by this method were found to be in excellent agreement with those in the actual spectrum of hydrogen, which was a big success for the Bohr model. Calculation of radius of orbits Consider an electron of charge e revolving around a nucleus of charge Ze, where Z is the atomic number and e the charge on a proton. Let m be the mass of the electron, r the radius of the orbit and ν the tangential velocity of the revolving electron. The electrostatic force of attraction between the nucleus and the electron (Coulomb’s law), 33 General chemistry (I) The centrifugal force acting on the electron Bohr assumed that these two opposing forces must be balancing each other exactly to keep the electron in orbit. Thus, For hydrogen Z = 1, therefore, (1) Multiplying both sides by r (2) 34 General chemistry (I) According to one of the postulates of Bohr’s theory, angular momentum of the revolving electron is given by the expression (3) Substituting the value of ν in equation (2), (4) Since the value of h, m and e had been determined experimentally, substituting these values in (4), we have r = n2 × 0.529 × 10–8 cm (5) where n is the principal quantum number and hence the number of the orbit. When n = 1, the equation (5) becomes r = 0.529 × 10–8 cm = α0 (6) This last quantity, α0 called the first Bohr radius was taken by Bohr to be the radius of the hydrogen atom in the ground state. This value is reasonably consistent with other information on the size of atoms. When n = 2, 3, 4 etc., the value of the second and third orbits of hydrogen comprising the electron in the excited state can be calculated. 35 General chemistry (I) Energy of electron in each orbit For hydrogen atom, the energy of the revolving electron, E is the sum of its kinetic energy and potential energy are: , (7) From equation (1) Substituting the value of mv2 in (7) (8) Substituting the value of r from equation (4) in (8) (9) Substituting the values of m, e, and h in (9), (10) 36 General chemistry (I) Bohr’s Explanation of Hydrogen Spectrum The solitary electron in hydrogen atom at ordinary temperature resides in the first orbit (n = 1) and is in the lowest energy state (ground state). When energy is supplied to hydrogen gas in the discharge tube, the electron moves to higher energy levels viz., 2, 3, 4, 5, 6, 7, etc., depending on the quantity of energy absorbed. From these high energy levels, the electron returns by jumps to one or other lower energy level. In doing so the electron emits the excess energy as a photon. This gives an excellent explanation of the various spectral series of hydrogen. Lyman series is obtained when the electron returns to the ground state i.e., n = 1 from higher energy levels (n2 = 2, 3, 4, 5, etc.). Similarly, Balmer, Paschen, Brackett and Pfund series are produced when the electron returns to the second, third, fourth and fifth energy levels respectively as shown in: 37 General chemistry (I) Value of Rydberg’s constant is the same as in the original empirical Balmer’s equation According to equation (1), the energy of the electron in orbit n1 (lower) and n2 (higher) is Calculation of wavelengths of the spectral lines of Hydrogen in the visible region These lines constitute the Balmer series when n1 = 2. Now the equation (3) above can be written as 38 General chemistry (I) Thus the wavelengths of the photons emitted as the electron returns from energy levels 6, 5, 4 and 3 were calculated by Bohr. The calculated values corresponded exactly to the values of wavelengths of the spectral lines already known. This was, in fact, a great success of the Bohr atom. SOMMERFELD’S MODIFICATION OF BOHR ATOM When spectra were examined with spectrometers, each line was found to consist of several closely packed lines. The existence of these multiple spectral lines could not be explained on the basis of Bohr’s theory. Sommerfeld modified Bohr’s theory as follows. Bohr considered electron orbits as circular but Sommerfeld postulated the presence of elliptic orbits also. An ellipse has a major and minor axis. A circle is a special case of an ellipse with equal major and minor axis. The angular momentum of an electron moving in an elliptic orbit is also supposed to be quantized. Thus, only a definite set of values is permissible. It is further assumed that the angular momentum can be an integral part of h/2π units, where h is Planck’s constant. Or that, where k is called the azimuthal quantum number, whereas the quantum number used in Bohr’s theory is called the principal quantum number. The two quantum numbers n and k are related by the expression: 39 General chemistry (I) The values of k for a given value of n are k = n – 1, n – 2, n – 3 and so on. A series of elliptic orbits with different eccentricities result for the different values of k. When n = k, the orbit will be circular. In other words k will have n possible values (n to 1) for a given value of n. However, calculations based on wave mechanics have shown that this is incorrect and the Sommerfeld’s modification of Bohr atom fell through. Bohr-Bury Scheme In 1921, Bury put forward a modification of Langmuir scheme which is in better agreement with the physical and chemical properties of certain elements. At about the same time as Bury developed his scheme on chemical grounds, Bohr (1921) published independently an almost identical scheme of the arrangement of extra-nuclear electrons. He based his conclusions on a study of the emission spectra of the elements. Bohr- Bury scheme as it may be called, can be summarized as follows: 40 General chemistry (I) Rule 1. The maximum number of electrons which each orbit can contain is 2 × n2, where n is the number of orbit. The first orbit can contain 2 × 12 = 2 ; second 2 × 22 = 8 ; third 2 × 32 = 18 ; fourth 2 × 42 = 32, and so on. Rule 2. The maximum number of electrons in the outermost orbit is 8 and in the next-to-the outermost 18. Rule 3. It is not necessary for an orbit to be completed before another commences to be formed. In fact, a new orbit begins when the outermost orbit attains 8 electrons. 41 General chemistry (I) Rule 4. The outermost orbit cannot have more than 2 electrons and next- to-outermost cannot have more than eight so long as the next inner orbit, in each case, has not received the maximum electrons as required by rule (1). WAVE MECHANICAL CONCEPT OF ATOM Bohr, undoubtedly, gave the first quantitative successful model of the atom. But now it has been superseded completely by the modern Wave Mechanical Theory. The new theory rejects the view that electrons move in closed orbits, as was visualized by Bohr. The Wave mechanical theory gave a major breakthrough by suggesting that the electron motion is of a complex nature best described by its wave properties and probabilities. While the classical ‘mechanical theory’ of matter considered matter to be made of discrete particles (atoms, electrons, protons etc.), another theory called the ‘Wave theory’ was necessary to interpret the nature of radiations like X-rays and light. According to the wave theory, radiations as X-rays and light, consisted of continuous collection of waves travelling in space. The wave nature of light, however, failed completely to explain the photoelectric effect i.e. the emission of electron from metal surfaces by the action of light. In their attempt to find a plausible explanation of 42 General chemistry (I) radiations from heated bodies as also the photoelectric effect, Planck and Einstein (1905) proposed that energy radiations, including those of heat and light, are emitted discontinuously as little ‘bursts’, quanta, or photons. This view is directly opposed to the wave theory of light and it gives particle-like properties to waves. According to it, light exhibits both a wave and a particle nature, under suitable conditions. This theory which applies to all radiations, is often referred to as the ‘Wave Mechanical Theory’. With Planck’s contention of light having wave and particle nature, the distinction between particles and waves became very hazy. In 1924 Louis de Broglie advanced a complimentary hypothesis for material particles. According to it, the dual character–the wave and particle–may not be confined to radiations alone but should be extended to matter as well. In other words, matter also possessed particle as well as wave character. This gave birth to the ‘Wave mechanical theory of matter’. This theory postulates that electrons, protons and even atoms, when in motion, possessed wave properties and could also be associated with other characteristics of waves such as wavelength, wave-amplitude and frequency. The new quantum mechanics, which takes into account the particulate and wave nature of matter, is termed the Wave mechanics. de BROGLIE’S EQUATION de Broglie had arrived at his hypothesis with the help of Planck’s Quantum Theory and Einstein’s Theory of Relativity. He derived a relationship between the magnitude of the wavelength associated with the mass ‘m’ of a moving body and its velocity. According to Planck, the photon energy ‘E’ is given by the equation 43 General chemistry (I) (1) where h is Planck’s constant and v the frequency of radiation. By applying Einstein’s mass-energy relationship, the energy associated with photon of mass ‘m’ is given as (2) where c is the velocity of radiation Comparing equations (1) and (2) The equation (iii) is called de Broglie’s equation and may be put in words as: The momentum of a particle in motion is inversely proportional to wavelength, Planck’s constant ‘h’ being the constant of proportionality. The wavelength of waves associated with a moving material particle (matter waves) is called de Broglie’s wavelength. The de Broglie’s equation is true for all particles, but it is only with very small particles, such as electrons, that the wave-like aspect is of any significance. Large particles in motion though possess wavelength, but it is not measurable or observable. Let us, for instance consider de Broglie’s wavelengths associated with two bodies and compare their values. (a) For a large mass Let us consider a stone of mass 100 g moving with a velocity of 1000 cm/sec. The de Broglie’s wavelength λ will be given as follows: 44 General chemistry (I) This is too small to be measurable by any instrument and hence no significance. (b) For a small mass Let us now consider an electron in a hydrogen atom. It has a mass = 9.1091 × 10– 28 g and moves with a velocity 2.188 × 10– 8 cm/sec. The de Broglie’s wavelength λ is given as This value is quite comparable to the wavelength of X-rays and hence detectable. It is, therefore, reasonable to expect from the above discussion that everything in nature possesses both the properties of particles (or discrete units) and also the properties of waves (or continuity). The properties of large objects are best described by considering the particulate aspect while properties of waves are utilized in describing the essential characteristics of extremely small objects beyond the realm of our perception, such as electrons. Therefore, that electrons not only behave like ‘particles’ in motion but also have ‘wave properties’ associated with them. 45 General chemistry (I) HEISENBERG’S UNCERTAINTY PRINCIPLE One of the most important consequences of the dual nature of matter is the uncertainty principle developed by Werner Heisenberg in 1927. This principle is an important feature of wave mechanics and discusses the relationship between a pair of conjugate properties (those properties that are independent) of a substance. According to the uncertainty principle, it is impossible to know simultaneously both the conjugate properties accurately. For example, the position and momentum of a moving particle are interdependent and thus conjugate properties also. Both the position and the momentum of the particle at any instant cannot be determined with absolute exactness or certainty. If the momentum (or velocity) be measured very accurately, a measurement of the position of the particle correspondingly becomes less precise. On the other hand, if position is determined with accuracy or precision, the momentum becomes less accurately known or uncertain. Thus, certainty of determination of one property introduces uncertainty of 46 General chemistry (I) determination of the other. The uncertainty in measurement of position, Δx, and the uncertainty of determination of momentum, Δp (or Δmv), are related by Heisenberg’s relationship as: where h is Planck’s constant. It may be pointed out here that there exists a clear difference between the behaviour of large objects like stone and small particles such as electrons. The uncertainty product is negligible in case of large objects. For a moving ball of iron weighing 500 g, the uncertainty expression assumes the form which is very small and thus negligible. Therefore, for large objects, the uncertainty of measurements is practically nil. But for an electron of mass m = 9.109 × 10–28 g, the product of the uncertainty of measurements is quite large as This value is large enough in comparison with the size of the electron and is thus in no way 47 General chemistry (I) negligible. If position is known quite accurately i.e., Δx is very small, the uncertainty regarding velocity Δv becomes immensely large and vice versa. It is therefore very clear that the uncertainty principle is only important in considering measurements of small particles comprising an atomic system. Physical Concept of Uncertainty Principle The physical concept of uncertainty principle becomes illustrated by considering an attempt to measure the position and momentum of an electron moving in Bohr’s orbit. To locate the position of the electron, we should devise an instrument ‘supermicroscope’ to see the electron. A substance is said to be seen only if it could reflect light or any other radiation from its surface. Because the size of the electron is too small, its position at any instant may be determined by a supermicroscope employing light of very small wavelength (such as X-rays or γ-rays). A photon of such a radiation of small λ, has a great energy and therefore has quite large momentum. As one such photon strikes the electron and is reflected, it instantly changes the momentum of electron. Now the momentum gets changed and becomes more uncertain as the position of the electron is being determined. 48 General chemistry (I) Thus, it is impossible to determine the exact position of an electron moving with a definite velocity (or possessing definite energy). It appears clear that the Bohr’s picture of an electron as moving in an orbit with fixed velocity (or energy) is completely untenable. As it is impossible to know the position and the velocity of any one electron on account of its small size, the best we can do is to speak of the probability or relative chance of finding an electron with a probable velocity. The old classical concept of Bohr has now been discarded in favour of the probability approach. SCHRÖDINGER’S WAVE EQUATION In order to provide sense and meaning to the probability approach, Schrödinger derived an equation known after his name as Schrödinger’s Wave Equation. Calculation of the probability of finding the electron at various points in an atom was the main problem before Schrödinger. His equation is the keynote of wave mechanics and is based upon the idea of the electron as ‘standing wave’ around the nucleus. The equation for the standing wave, comparable with that of a stretched string is: where ψ (pronounced as sigh) is a mathematical function representing the amplitude of wave (called wave function) x, the displacement in a given direction, and λ, the wavelength and A is a constant. By differentiating equation (a) twice with respect to x, we get: 49 General chemistry (I) The K.E. of the particle of mass m and velocity ν is given by the relation According to Broglie’s equation Substituting the value of m2v2, we have From equation (3), we have Substituting the value of λ2 in equation (5) The total energy E of a particle is the sum of kinetic energy and the potential energy 50 General chemistry (I) This is Schrödinger’s equation in one dimension. It need be generalized for a particle whose motion is described by three space coordinates x, y and z. Thus, This equation is called the Schrödinger’s Wave Equation. The first three terms on the left-hand side are represented by Δ2ψ CHARGE CLOUD CONCEPT AND ORBITALS The Charge Cloud Concept finds its birth from wave mechanical theory of the atom. The wave equation for a given electron, on solving gives a three-dimensional arrangement of points where it can possibly lie. There are regions where the chances of finding the electron are relatively greater. Such regions are expressed in terms of ‘cloud of negative charge’. We need not know the specific location of the electrons in space but are concerned with the negative charge density regions. Electrons in atoms are assumed to be vibrating in space, moving haphazardly but at the same time are constrained to lie in regions of highest probability for 51 General chemistry (I) most of the time. The charge cloud concept simply describes the high probability region. The three-dimensional region within which there is higher probability that an electron having a certain energy will be found, is called an orbital. An orbital is the most probable space in which the electron spends most of its time while in constant motion. In other words, it is the spatial description of the motion of an electron corresponding to a particular energy level. The energy of electron in an atomic orbital is always the same. QUANTUM NUMBERS Bohr’s electronic energy shells or levels, designated as Principal Quantum Numbers ‘n’, could hardly explain the hydrogen spectrum adequately. Spectra of other elements that are quite complex, also remained unexplained by this concept. To explain these facts, it is necessary to increase the number of ‘possible orbits’ where an electron can be said to exist within an atom. In other words, it is necessary to allow more possible energy changes within an atom (or a larger number of energy states) to account for the existence of a larger number of such observed spectral lines. Wave mechanics makes a provision for three more states of an electron in addition to the one proposed by Bohr. Like 52 General chemistry (I) the energy states of Bohr, designated by n = 1, 2, 3..., these states are also identified by numbers and specify the position and energy of the electron. Thus there are in all four such identification numbers called quantum numbers which fully describe an electron in an atom. Each one of these refers to a particular character. Principal Quantum Number ‘n’ This quantum number denotes the principal shell to which the electron belongs. This is also referred to as major energy level. It represents the average size of the electron cloud i.e., the average distance of the electron from the nucleus. This is, therefore, the main factor that determines the values of nucleus-electron attraction, or the energy of the electron. In our earlier discussion, we have found that the energy of the electron and its distance from the nucleus for hydrogen atom are given by where n is the principal quantum number of the shell. The principal quantum number ‘n’ can have non-zero, positive, integral values n = 1, 2, 3... increasing by integral numbers to infinity. Although the quantum number ‘n’ may theoretically assume any integral value from 1 to ∝ , only values from 1 to 7 have so far been established for the atoms of the known elements in their ground states. In a polyelectron atom or ion, the electron that has a higher principal quantum number is at a higher energy level. An electron with n = 1 has the lowest energy and is bound most firmly to the nucleus. The letters K, L, M, N, O, P and Q are also used to designate the energy levels or shells of electrons with a n value of 1, 2, 3, 4, 5, 6, 7 respectively. There is a limited number of electrons in an atom which can 53 General chemistry (I) have the same principal quantum number and is given by 2n2, where n is the principal quantum number concerned. Thus, Azimuthal Quantum number ‘l ’ This is also called secondary or subsidiary quantum number. It defines the spatial distribution of the electron cloud about the nucleus and describes the angular momentum of the electron. In other words, the quantum number l defines the shape of the orbital occupied by the electron and the angular momentum of the electron. It is for this reason that ‘l’ is sometimes referred to as orbital or angular quantum number. For any given value of the principal quantum number n, the azimuthal quantum number l may have all integral values from 0 to n – 1, each of which refers to an Energy sublevel or Sub-shell. The total number of such possible sublevels in each principal level is numerically equal to the principal quantum number of the level under consideration. These sublevels are also symbolized by letters s, p, d, f etc. For example, for principal quantum number n = 1, the only possible value for l is 0 i.e., there is only one possible subshell i.e. s- subshell (n = 1, l = 0). For n = 2, there are two possible values of l, l = 0 and l = 2 – 1 = 1. This means that there are two subshells in the second energy shell with n = 2. These subshells are designated as 2s and 2p. Similarly, when n = 3, l can have three values i.e. 0, 1 and 2. Thus there are three subshells in third energy shell with designations 3s, 3p and 3d respectively. For n = 4, there are four possible values of azimuthal quantum number l (= 0, 1, 2, and 3) each representing a different sublevel. In other words, the fourth 54 General chemistry (I) energy level consists of four subshells which are designated as 4s, 4p, 4d and 4f. Thus, for different values of principal quantum numbers we have For a given value of principal quantum number the order of increasing energy for different subshells is: s < p < d < f (except for H atom) Magnetic Quantum Number ‘m’ This quantum number has been proposed to account for the splitting up of spectral lines (Zeeman Effect). An application of a strong magnetic field to an atom reveals that electrons with the same values of principal quantum number ‘n’ and of azimuthal quantum number ‘l’, may still differ in their behaviour. They must, therefore, be differentiated by introducing a new quantum number, the magnetic quantum number m. This is also called Orientation Quantum Number because it gives the orientation or distribution of the electron cloud. For each value of the azimuthal quantum number ‘l’, the magnetic quantum number m, may assume all the integral values between + l to – l through zero i.e., + l, (+ l – l),... 0..., (– l + 1), – l. Therefore for each value of l there will be (2l + 1) values of ml. Thus when l = 0, m = 0 and no other value. This means that for each value of principal quantum number ‘n’, there is only one orientation for l = 0 (s orbital) or there is only one s orbital. For s orbital, there being only one orientation, it must be spherically symmetrical about the nucleus. There is only one spherically symmetrical orbital for each value of n whose radius depends upon the value of n. 55 General chemistry (I) For l = 1 (p orbital), the magnetic quantum number m will have three values : + 1, 0 and – 1; so there are three orientations for p orbitals. These three types of p orbitals differ only in the value of magnetic quantum number and are designated as px, py, pz depending upon the axis of orientation. The subscripts x, y and z refer to the coordinate axes. In the absence of a magnetic field, these three p orbitals are equivalent in energy and are said to be three-fold degenerate or triply degenerate (Different orbitals of equivalent energy are called degenerate orbitals and are grouped together). In presence of an external magnetic field the relative energies of the three p orbitals vary depending upon their orientation or magnetic quantum number. This probably accounts for the existence of more spectral lines under the influence of an external magnetic field. The p orbital are of dumb-bell shape consisting of two lobes. The two lobes of a p orbital extend outwards and away from the nucleus along the axial line. Thus the two lobes of a p orbital may be separated by a plane that contains the nucleus and is perpendicular to the corresponding axis. Such plane is called a nodal plane. There is no likelihood of finding the electron on this plane. For a px orbital, the yz plane is the nodal plane. The shapes and orientations of the p orbitals are given in: 56 General chemistry (I) For l = 2 (d orbital), the magnetic quantum number are five (2 × 2 + 1); + 2, + 1, 0, – 1, – 2. Thus, there are five possible orientations for d orbitals which are equivalent in energy so long as the atom is not under the influence of a magnetic field and are said to be five-fold degenerate (Different orbitals of equivalent energy are called degenerate orbitals and are grouped together). The five d orbitals are designated as: 57 General chemistry (I) These orbitals have complex geometrical shapes as compared to p orbitals. The conventional boundary surfaces or shapes of five dz2 orbitals are shown in the above Fig. The shape of the dz orbitals is different from others. When l = 3 (f orbital) the magnetic quantum number m can have seven (2 × 3 + 1) values as + 3, + 2, + 1, 0, – 1, – 2 and – 3. These seven orientations give rise to a set of seven-fold degenerate orbitals. These seven orbitals possess very complicated shapes and orientation in space. The shapes of s, p and d orbitals only are of interest to chemists. Spin Quantum Number ‘s’ This quantum number has been introduced to account for the spin of electrons about their own axis. Since an electron can spin clockwise or anticlockwise (in two opposite directions), there are two possible values of s that are equal and opposite. As quantum numbers can differ only by unity from each other, there are two values given to s; +1/2 and–1/2 depending upon whether the electron spins in one direction or the other. These spins are also designated by arrows pointing upwards and downward as ↓↑. Two electrons with the same sign of the spin quantum numbers are said to have parallel spins while those having opposite signs of the spin quantum numbers are said to have opposite spin or antiparallel spin or paired-up spin. Since a spinning charge is associated with a magnetic field, an electron must have a magnetic moment associated with it. 58 General chemistry (I) Atomic Structures of the First 18 Elements We have seen that hydrogen has one electron that can occupy a variety of orbitals indifferent principal energy levels. Now let’s consider the structure of atoms with more than one electron. Because all atoms contain orbitals similar to those found in hydrogen, we can describe the structures of atoms beyond hydrogen by systematically placing electrons in these hydrogen-like orbitals. We use the following guidelines: 59 General chemistry (I) 1. No more than two electrons can occupy one orbital. 2. Electrons occupy the lowest energy orbitals available. They enter a higher energy orbital only when the lower orbitals are filled. For the atoms beyond hydrogen, orbital energies vary as s