Chapter 4 — ପରମାଣୁ ଗଠନ

Simple experiments show that matter contains electric charge. Rub a comb on dry hair and it attracts small pieces of paper; rub a glass rod with silk and it attracts a balloon rubbed with wool. The rubbing separates charges that were already present in the neutral atoms. So atoms are not indivisible: they contain charged particles, and since matter is normally neutral they must contain equal amounts of positive and negative charge.

The first of these particles was identified from the study of electricity passing through gases at very low pressure in a discharge tube — a sealed glass tube with two metal electrodes connected to a high voltage. When the pressure inside is reduced to a fraction of a millimetre of mercury, a stream of invisible rays travels from the negative electrode, the cathode, towards the positive electrode, the anode, and makes the glass glow green where it strikes. These were named cathode rays. In 1897 the English physicist J. J. Thomson showed that the rays are deflected towards the positive plate in an electric field and in the corresponding direction in a magnetic field, so they consist of negatively charged particles; that they cast sharp shadows and can turn a small paddle wheel, so they are material particles moving in straight lines; and, most remarkable, that the particles are exactly the same whatever gas fills the tube and whatever metal the cathode is made of. The particles were therefore a universal constituent of all matter. Thomson called them corpuscles; the name electron, proposed earlier by G. J. Stoney, was adopted.

Thomson measured the ratio of charge to mass of the electron, and Robert Millikan later measured its charge: 1.6 × 10⁻¹⁹ coulomb, the smallest unit of charge, taken as one unit of negative charge (−1). The mass of an electron is about 9.1 × 10⁻³¹ kg, which is 1/1840 of the mass of a hydrogen atom, so for practical purposes the mass of an electron is taken as negligible or zero in atomic mass units. The electron is represented as e⁻.

The discovery had immediate consequences. If atoms contain negatively charged electrons yet are neutral, they must also contain positive charge. If the electron is so light, nearly all the mass of the atom must belong to the positive part. And since electrons can be pulled out of atoms — by rubbing, by heating a cathode, by light — they must lie near the outside of the atom. The search for the positive particle, and for the arrangement of both, occupied the next thirty years and gave the models described in the topics that follow. Thomson received the Nobel Prize in 1906 for the discovery of the electron.

The positive particle was found in the same kind of apparatus. In 1886 the German physicist E. Goldstein used a discharge tube with a perforated cathode and observed a second set of rays travelling in the opposite direction, from the anode towards the cathode and through the holes in it. He called them canal rays (from the German for channel). These rays were deflected towards the negative plate and so carry positive charge; they are the positive ions left when the cathode rays knock electrons out of the gas atoms. Unlike cathode rays, their charge-to-mass ratio depended on the gas in the tube. The lightest positive particle, obtained when the gas was hydrogen, was named the proton by Rutherford in 1920. A proton has a charge of +1 unit — equal in size and opposite in sign to the electron — and a mass of 1.67 × 10⁻²⁷ kg, about 1840 times the mass of the electron, taken as 1 u. It is represented as p⁺. The hydrogen atom, the simplest of all, consists of one proton and one electron.

With two particles known, the next step was to propose how they are arranged. In 1898 J. J. Thomson proposed the first model of the atom. He suggested that the atom is a sphere of positive charge in which the negatively charged electrons are embedded, like the seeds in a watermelon or the raisins in a Christmas pudding — hence the name plum-pudding model or watermelon model. The red edible part is the positive charge spread uniformly through the whole atom; the seeds are the electrons studded through it. The negative and positive charges are equal in magnitude, so the atom as a whole is electrically neutral, and the mass of the atom is spread uniformly with the positive charge.

Thomson's model explained the neutrality of the atom and the fact that electrons can be removed from atoms. But it made a definite prediction — that the mass and positive charge are spread evenly through the atom — and that prediction could be tested. If a small fast charged particle were fired at such an atom, it would pass through a soft, uniform cloud of charge and be deflected only very slightly, like a bullet passing through fog. Ernest Rutherford, Thomson's own former student, set up exactly this test, and its result destroyed the model. The next topic describes that experiment.

A summary of the two particles so far: the electron, negative, negligible mass, found by Thomson from cathode rays in 1897; the proton, positive, mass 1 u, found from Goldstein's canal rays of 1886 and named by Rutherford. Both are present in every atom, in equal numbers when the atom is neutral.

Ernest Rutherford, working in Manchester in 1911 with his assistants Hans Geiger and Ernest Marsden, designed an experiment to look inside the atom. The probe was the alpha particle: a fast-moving, positively charged particle emitted by radioactive elements such as radium, having the mass of four hydrogen atoms and a charge of +2 (it is in fact a helium nucleus). The target was a gold foil, chosen because gold can be beaten so thin — about 1000 atoms thick — that the alpha particles would meet only a few atoms on their way through. A beam of alpha particles from a radioactive source was directed at the foil, and a movable screen coated with zinc sulphide, which gives a tiny flash of light wherever an alpha particle strikes it, was placed around the foil to detect where the particles went.

According to Thomson's model, the alpha particles should have passed through the soft, evenly spread positive charge of the gold atoms with at most a slight deflection. The observations were quite different.

Observation 1. Most of the alpha particles — the great majority — passed straight through the foil without any deflection at all. Observation 2. A small fraction were deflected through small angles. Observation 3. A very few — about one in 12,000 — were deflected through very large angles, and some bounced straight back towards the source. Rutherford said this was as incredible as if you had fired a fifteen-inch shell at a piece of tissue paper and it had come back and hit you.

From these facts Rutherford reasoned as follows. Conclusion 1. Since most alpha particles passed through undeflected, most of the space inside the atom is empty. Conclusion 2. Since some positively charged alpha particles were deflected, there must be a concentration of positive charge in the atom that repels them, occupying a very small volume. Conclusion 3. Since a very few particles bounced back, and a light particle cannot turn back a heavy one, that small positive region must contain nearly all the mass of the atom. He calculated that the radius of this central region, which he called the nucleus, is about 10⁻¹⁵ m, while the radius of the atom is about 10⁻¹⁰ m — the nucleus is 100,000 times smaller than the atom. If the atom were the size of a cricket stadium, the nucleus would be a pea at the centre.

The experiment is the classic example of science: a definite prediction from a model, an experiment designed to test it, an unexpected result, and a new model built to explain it. The student must be able to draw the apparatus, list the three observations and give the three conclusions; this is a standard five-mark question in the Odisha examination.

From his experiment Rutherford proposed the nuclear model of the atom in 1911, with these features:

1. There is a positively charged centre in the atom called the nucleus, in which nearly all the mass of the atom is concentrated. 2. The electrons revolve around the nucleus in well-defined orbits, as the planets revolve around the Sun — so the model is also called the planetary model. The electrostatic attraction between the positive nucleus and the negative electrons provides the force that keeps them in orbit, as gravity keeps the planets. 3. The size of the nucleus is very small compared with the size of the atom, and most of the atom is empty space. The positive charge of the nucleus equals the total negative charge of the electrons, so the atom is neutral.

The model was a great advance: it explained the scattering experiment completely and gave the atom a structure — a dense centre and a light, mostly empty outer region — that has stood ever since. But it had a serious flaw, pointed out at once by physicists who knew the laws of electromagnetism.

Drawback 1: the atom should collapse. An electron moving in a circular orbit is continuously changing direction, and a body whose direction changes is accelerating. According to the well-established laws of Maxwell, an accelerating charged particle must radiate energy as electromagnetic waves. So the revolving electron should lose energy continuously, its orbit should shrink in a spiral, and within about 10⁻⁸ second it should fall into the nucleus. The atom, in other words, should be highly unstable. But atoms are stable — we exist. Rutherford's model could not explain this.

Drawback 2: the spectrum should be continuous. If the electron spiralled inward, radiating as it went, it would emit light of continuously changing wavelength, giving a continuous band of colour. In fact, when the light emitted by hydrogen gas in a discharge tube is passed through a prism, it shows a few sharp lines of definite colour — a line spectrum — and each element has its own set of lines. Rutherford's model could not explain this either.

Drawback 3. The model said nothing about how the electrons are arranged — how many are in each orbit or how far out — and so it could not explain the chemical properties of the elements.

Rutherford's atom was therefore right about the nucleus and wrong, or silent, about the electrons. The problem of the electrons was solved two years later by Niels Bohr, a young Dane working in Rutherford's own laboratory, by introducing a wholly new idea into physics: that electrons are allowed only certain orbits. That is the next topic. The historical sequence — Thomson (1898), Rutherford (1911), Bohr (1913) — is worth remembering as a chain in which each model fixed the failure of the last.

In 1913 the Danish physicist Niels Bohr kept the nucleus of Rutherford's model and rescued the electrons by proposing rules that ordinary physics did not contain. His postulates are:

1. Electrons revolve around the nucleus only in certain definite circular paths called orbits or shells, and each orbit has a definite energy. These orbits are also called energy levels. 2. While an electron is revolving in one of these allowed orbits it does not radiate energy, so it does not spiral into the nucleus; the allowed orbits are called stationary orbits (stationary in energy, not in position). 3. An electron can jump from one orbit to another. When it absorbs a definite amount of energy it jumps to a higher orbit; when it falls back to a lower orbit it emits exactly that amount of energy as light of a definite wavelength. This is why an element gives a line spectrum: each line is a jump between two particular orbits.

The orbits are numbered outward from the nucleus, n = 1, 2, 3, 4, and lettered K, L, M, N. The K shell is nearest the nucleus and has the lowest energy; the energy increases as we go outward, and an electron in an outer shell is more loosely held. The number of electrons each shell can hold is fixed, which is the subject of the electron-distribution topic below.

Bohr's model explained the stability of the atom (postulate 2) and the line spectrum of hydrogen (postulate 3) with quantitative success: he calculated the wavelengths of the hydrogen lines and they matched experiment exactly. For this he received the Nobel Prize in 1922. The model also gave chemistry what Rutherford's could not — an arrangement of electrons in shells that, as later topics show, explains valency and the periodic table.

The model has limits, which higher classes address: it works exactly only for atoms with one electron, it treats orbits as circles though electrons do not move on simple paths, and it was replaced in the 1920s by the quantum mechanical model in which electrons occupy orbitals — regions of probability rather than tracks. But for the chemistry of Class 9 and 10, the Bohr picture — a nucleus of protons and neutrons with electrons in shells K, L, M, N of fixed capacity — is the working model, and every diagram of an atom in this course is drawn in it. A Bohr diagram shows the nucleus as a small circle with the numbers of protons and neutrons, surrounded by concentric circles for the shells, with the electrons drawn as dots or crosses on them.

Two particles did not account for the mass of atoms. A helium atom has two protons and two electrons, so its mass should be about 2 u; it is in fact 4 u. Rutherford suggested in 1920 that the nucleus must contain a neutral particle of about the mass of a proton, and in 1932 the English physicist James Chadwick, his student, found it. When beryllium was bombarded with alpha particles, a highly penetrating radiation came out that was not deflected by electric or magnetic fields and could knock protons out of paraffin wax; it consisted of neutral particles with a mass almost equal to that of a proton. Chadwick named it the neutron, represented as n. It has no charge and a mass of 1 u (1.675 × 10⁻²⁷ kg, very slightly more than a proton). Neutrons are present in the nucleus of every atom except ordinary hydrogen, whose nucleus is a single proton. Chadwick received the Nobel Prize in 1935.

The neutron completed the picture of the atom. The nucleus contains protons and neutrons, together called nucleons, packed tightly and held by a very strong nuclear force; it carries the positive charge (from the protons) and nearly all the mass (protons plus neutrons). The electrons occupy the shells outside the nucleus and contribute negligible mass. Neutrons add mass without charge, which explains why the mass of helium is 4 u — two protons and two neutrons — and also why atoms of the same element can have different masses, as the topic on isotopes shows.

Three simple rules follow for any neutral atom. The number of protons equals the number of electrons, so the charges cancel. The mass of the atom in atomic mass units is, to the nearest whole number, the number of protons plus the number of neutrons, since electrons weigh almost nothing. And the number of protons decides which element the atom is — a point developed under atomic number.

A worked illustration: a carbon atom has 6 protons, 6 neutrons and 6 electrons; its mass is 6 + 6 = 12 u; its nucleus has charge +6 and its 6 electrons are arranged 2 in K and 4 in L. An oxygen atom has 8 protons, 8 neutrons and 8 electrons, mass 16 u. A sodium atom has 11 protons, 12 neutrons and 11 electrons, mass 23 u. These numbers are the raw material for the electronic configurations and mass numbers of the following topics.

Bohr and the English chemist Charles Bury together proposed, in 1921, the rules that decide how many electrons each shell holds and in what order the shells fill. They are called the Bohr-Bury scheme.

Rule 1. The maximum number of electrons that a shell can hold is given by 2n², where n is the number of the shell counted from the nucleus. For the K shell, n = 1, the maximum is 2 × 1² = 2 electrons. For the L shell, n = 2, it is 2 × 2² = 8. For the M shell, n = 3, it is 2 × 3² = 18. For the N shell, n = 4, it is 2 × 4² = 32.

Rule 2. The outermost shell can hold at most 8 electrons, whatever its capacity by the 2n² rule. This is why the M shell, though it can hold 18, takes only 8 while it is the outermost shell.

Rule 3. Shells are filled in order from the inside: electrons enter the K shell first, and a new shell is started only when the inner shells are filled to the limits set by the rules above. (Strictly, the M shell is not completely filled before the N shell starts, but for the first twenty elements — which is all this class requires — the simple rule holds.)

Applying the rules gives the electronic configuration of each element, written as the number of electrons in each shell, K, L, M, N, separated by commas. For the first twenty elements:

Note how potassium's nineteenth electron goes into the N shell rather than making the M shell 9: the outermost shell may not exceed 8. The electrons of the outermost shell are called valence electrons and the shell itself the valence shell; these electrons take part in chemical reactions and decide the properties of the element. Helium (2), neon (2, 8) and argon (2, 8, 8) have completely filled outer shells and are the chemically inert noble gases. The student should be able to write the configuration of any of the first twenty elements from its atomic number and draw its Bohr diagram.

The previous chapter used valency — the combining capacity of an element — as a given number. The structure of the atom now explains where it comes from.

Atoms of the noble gases — helium (2), neon (2, 8), argon (2, 8, 8) — have completely filled outermost shells and are chemically inert; they do not combine with anything. Chemists concluded that a filled outer shell of 8 electrons (or 2 for the K shell) is a state of special stability, and that atoms of other elements react in order to reach it. This is the octet rule: atoms tend to gain, lose or share electrons so as to have eight electrons in their outermost shell (a duplet of two for the elements nearest helium). The valency of an element is the number of electrons its atom must gain, lose or share to achieve an octet — in other words, the number of electrons involved when it combines.

Elements with 1, 2 or 3 valence electrons — metals — reach an octet most easily by losing them, exposing the full shell beneath; their valency equals the number of valence electrons. Sodium (2, 8, 1) loses 1 electron to become Na⁺ with configuration 2, 8: valency 1. Magnesium (2, 8, 2) loses 2: valency 2. Aluminium (2, 8, 3) loses 3: valency 3. Potassium (2, 8, 8, 1): valency 1; calcium (2, 8, 8, 2): valency 2; lithium (2, 1): valency 1.

Elements with 5, 6 or 7 valence electrons — non-metals — reach an octet by gaining electrons; their valency is 8 minus the number of valence electrons. Chlorine (2, 8, 7) gains 1 to become Cl⁻ with 2, 8, 8: valency 8 − 7 = 1. Oxygen (2, 6) gains 2: valency 2. Nitrogen (2, 5) gains 3: valency 3. Fluorine (2, 7): valency 1; sulphur (2, 8, 6): valency 2; phosphorus (2, 8, 5): valency 3.

Elements with 4 valence electrons — carbon (2, 4) and silicon (2, 8, 4) — neither lose nor gain four electrons easily; they share four electrons with other atoms, and their valency is 4. Hydrogen (1) needs one more electron to reach the helium duplet, or can lose its one electron; either way its valency is 1.

Elements with 8 valence electrons, the noble gases, neither gain nor lose: valency 0. Helium, with its K shell full at 2, is also 0.

The rule to remember: valency = number of valence electrons if that number is 1 to 4; valency = 8 minus the number of valence electrons if it is 4 to 7; valency = 0 if the outer shell is full. This is why sodium chloride is NaCl (1 with 1), magnesium chloride is MgCl₂ (2 with 1), aluminium oxide is Al₂O₃ (3 with 2), and water is H₂O (1 with 2). The criss-cross formulae of the last chapter are simply the bookkeeping of electrons lost, gained or shared so that every atom reaches an octet.

Two numbers describe any atom completely.

The atomic number, symbol Z, is the number of protons in the nucleus of an atom. It is the identity card of the element: every atom of hydrogen has exactly 1 proton, every atom of carbon 6, every atom of oxygen 8, every atom of sodium 11, every atom of uranium 92, and no other element has those numbers. If the number of protons changes, the element changes. In a neutral atom the number of electrons equals the atomic number, so Z also gives the number of electrons and hence, through the Bohr-Bury rules, the electronic configuration. The English physicist Henry Moseley showed in 1913 that the atomic number, not the atomic mass, is the fundamental property that orders the elements, and the modern periodic table is arranged by Z.

The mass number, symbol A, is the total number of protons and neutrons in the nucleus — the number of nucleons. Since each proton and each neutron has a mass of about 1 u and the electrons weigh almost nothing, the mass number is the mass of the atom in atomic mass units to the nearest whole number. Carbon with 6 protons and 6 neutrons has A = 12; oxygen with 8 and 8 has A = 16; sodium with 11 protons and 12 neutrons has A = 23; chlorine-35 with 17 protons and 18 neutrons has A = 35.

The number of neutrons is therefore A − Z. This is the relation used in nearly every numerical question of the chapter.

An atom is written in the notation ^A_ZX: the symbol of the element X with the mass number as a superscript and the atomic number as a subscript at the left. Thus ¹²₆C, ¹⁶₈O, ²³₁₁Na, ³⁵₁₇Cl. Since the symbol itself fixes Z, the subscript is often omitted and the atom written carbon-12, oxygen-16, chlorine-35.

Worked examples. (1) An atom has Z = 17 and A = 35. Protons = 17, electrons = 17, neutrons = 35 − 17 = 18, configuration 2, 8, 7; it is chlorine, valency 1. (2) An atom has 12 protons and 12 neutrons. Z = 12, A = 24; it is magnesium, 2, 8, 2, valency 2. (3) The nucleus of an atom has 20 nucleons of which 10 are neutrons. Z = 10, A = 20; neon, 2, 8, valency 0. (4) Potassium has Z = 19 and A = 39: 19 protons, 19 electrons, 20 neutrons, configuration 2, 8, 8, 1. (5) An ion X²⁺ has 10 electrons and 12 neutrons: the neutral atom had 12 electrons, so Z = 12 and A = 24 — magnesium.

Note the distinction between mass number, which is a whole number for a particular atom, and atomic mass, which is the average for the element and may be fractional (chlorine 35.5). The reason for the difference is the subject of the next topic: atoms of the same element with the same Z can have different A.

Dalton said that all atoms of an element are identical. Once the structure of the nucleus was known, this was found to be untrue in one respect: atoms of the same element always have the same number of protons, but they may have different numbers of neutrons, and therefore different mass numbers. Such atoms are called isotopes (from the Greek for same place, since they occupy the same place in the periodic table). Isotopes are atoms of the same element having the same atomic number but different mass numbers.

Hydrogen has three isotopes: protium ¹₁H, with one proton and no neutron, which is 99.98 percent of natural hydrogen; deuterium ²₁H (or D), with one proton and one neutron; and tritium ³₁H (or T), with one proton and two neutrons, which is radioactive. Water made with deuterium is called heavy water and is used in nuclear reactors. Carbon has ¹²₆C (98.9 percent), ¹³₆C and the radioactive ¹⁴₆C. Chlorine has ³⁵₁₇Cl (about 75 percent) and ³⁷₁₇Cl (about 25 percent). Uranium has ²³⁵₉₂U and ²³⁸₉₂U. Oxygen has isotopes of mass 16, 17 and 18.

Because isotopes have the same number of protons and electrons, they have the same electronic configuration and hence the same chemical properties; chlorine-35 and chlorine-37 both form NaCl, both have valency 1, both are green gases. They differ only in physical properties that depend on mass — density, rate of diffusion, and the stability of the nucleus (some isotopes are radioactive).

Average atomic mass. Since a natural sample of an element is a mixture of its isotopes, the atomic mass used in calculations is the weighted average. For chlorine: (35 × 75 + 37 × 25) ÷ 100 = (2625 + 925) ÷ 100 = 3550 ÷ 100 = 35.5 u. This is why chlorine's atomic mass is fractional though every chlorine atom has a whole-number mass; no single chlorine atom has mass 35.5. Similarly, if an element has isotopes of mass 10 and 11 in the ratio 20 : 80, its atomic mass is (10 × 20 + 11 × 80) ÷ 100 = 10.8 u — this is boron.

Worked example on the reverse problem: bromine has isotopes of mass 79 and 81 and an atomic mass of 79.9 u. Let the fraction of Br-79 be x. Then 79x + 81(1 − x) = 79.9, giving 81 − 2x = 79.9, so 2x = 1.1 and x = 0.55: 55 percent Br-79 and 45 percent Br-81.

The discovery of isotopes corrected Dalton's third postulate but confirmed his deeper insight: it is the number of protons — the atomic number — that defines an element, not the mass. The next topic turns to the practical value of isotopes, especially the radioactive ones.

Isotopes whose nuclei are unstable break down spontaneously, emitting radiation; these are radioactive isotopes or radioisotopes. Because their radiation can be detected in tiny amounts and can destroy cells or release energy, radioisotopes have applications that touch every citizen.

In energy. The isotope uranium-235 is used as fuel in nuclear reactors: its nucleus splits when struck by a neutron, releasing enormous energy and more neutrons that split further nuclei in a chain reaction. Nuclear power stations, such as those at Kudankulam and Tarapur, and the atomic bomb both depend on it. Uranium-238, the common isotope, does not undergo fission in the same way and must be separated out or enriched.

In medicine. Cobalt-60 emits gamma rays that are directed at tumours to kill cancer cells in radiotherapy. Iodine-131 is used to treat and diagnose diseases of the thyroid gland, which naturally absorbs iodine: a small dose taken by the patient goes to the thyroid, where its radiation shows the gland's activity or destroys overactive tissue. Technetium-99 is used in imaging the heart, bones and other organs. Radioisotopes are also used to sterilise surgical instruments and to trace the path of a drug through the body.

In archaeology and geology. Carbon-14 is formed continuously in the upper atmosphere and taken up by all living things; when an organism dies, its carbon-14 decays at a known rate, halving every 5,730 years. Measuring the carbon-14 remaining in a piece of wood, bone or cloth gives its age — carbon dating — and has dated the timbers of ancient buildings and the remains of ancient settlements in Odisha and across the world. Uranium-lead dating gives the ages of rocks and of the Earth itself, 4.5 billion years.

In agriculture and industry. Radiation from cobalt-60 preserves food by killing microbes and stops potatoes and onions sprouting; radioactive phosphorus-32 traces how plants take up fertiliser; and radiation is used to check welds in pipelines and to measure the thickness of paper and metal sheet during manufacture. Deuterium, in heavy water, moderates the neutrons in India's pressurised heavy-water reactors.

Isobars. A second family of atoms must be distinguished from isotopes. Isobars are atoms of different elements that have the same mass number but different atomic numbers. Calcium ⁴⁰₂₀Ca and argon ⁴⁰₁₈Ar both have mass number 40, though calcium has 20 protons and 20 neutrons while argon has 18 protons and 22 neutrons; they are entirely different elements with different chemical properties. Other pairs are ¹⁴₆C and ¹⁴₇N, and ³₁H and ³₂He. The rule of thumb: isotopes — same Z, different A, same element, same chemistry; isobars — same A, different Z, different elements, different chemistry.

With this, the chapter has moved from the indivisible atom of Dalton to a nucleus of protons and neutrons ringed by shells of electrons, a structure that explains mass, charge, valency, the identity of elements and the existence of isotopes. The periodic table of Class 10 is the arrangement of the elements by this structure.

The examination tests this chapter mainly through short numerical and reasoning problems. This topic works through the standard types so that the method becomes routine. In every problem, first write down Z, A and the number of electrons, then derive the rest.

Problem 1. Write the electronic configuration and valency of an element with atomic number 15. Electrons = 15. Fill K with 2, L with 8, leaving 5 for M: configuration 2, 8, 5. Valence electrons = 5, which is more than 4, so valency = 8 − 5 = 3. The element is phosphorus.

Problem 2. The atomic number of an element is 12 and its mass number is 24. Find the number of protons, neutrons and electrons, its configuration and the ion it forms. Protons = 12, electrons = 12, neutrons = 24 − 12 = 12. Configuration 2, 8, 2; it loses 2 electrons to form Mg²⁺, which has configuration 2, 8 and 10 electrons.

Problem 3. Na⁺ has completely filled K and L shells. Explain. Sodium (Z = 11) has configuration 2, 8, 1. On losing its single M-shell electron it becomes Na⁺ with 10 electrons arranged 2, 8; both shells are full, giving the ion the stable configuration of neon. This is why sodium readily forms Na⁺.

Problem 4. If bromine atoms are available as two isotopes ⁷⁹₃₅Br (49.7 percent) and ⁸¹₃₅Br (50.3 percent), calculate the average atomic mass. (79 × 49.7 + 81 × 50.3) ÷ 100 = (3926.3 + 4074.3) ÷ 100 = 8000.6 ÷ 100 = 80.0 u.

Problem 5. The average atomic mass of a sample of element X is 16.2 u. What are the percentages of isotopes ¹⁶₈X and ¹⁸₈X in the sample? Let the percentage of X-16 be p. Then 16p + 18(100 − p) = 16.2 × 100; 16p + 1800 − 18p = 1620; −2p = −180; p = 90 percent of X-16 and 10 percent of X-18.

Problem 6. Compare the properties of electrons, protons and neutrons (table in the neutron topic): charge −1, +1, 0; mass 1/1840, 1, 1; location outside the nucleus, in it, in it.

Problem 7. Helium has 2 electrons in its valence shell yet its valency is 0. Why? Because the K shell is complete with 2 electrons; helium has a stable filled outermost shell and has no tendency to gain, lose or share electrons.

Problem 8. Two atoms have the compositions: X — 6 protons, 6 neutrons; Y — 6 protons, 8 neutrons. What is their relation, and what are their mass numbers? Same Z = 6, different neutrons: isotopes of carbon with mass numbers 12 and 14. They have identical chemical properties.

Problem 9. An atom has 8 protons and 8 neutrons, another has 8 protons and 10 neutrons, and a third has 9 protons and 9 neutrons. Identify isotopes and isobars. The first two are isotopes (oxygen-16 and oxygen-18); the second and third are isobars (mass number 18, but oxygen and fluorine).

Problem 10. Draw the Bohr diagram of chlorine-35. Nucleus: 17 protons, 18 neutrons. Shells: K 2, L 8, M 7. Draw three circles with 2, 8 and 7 dots. The seven valence electrons show that chlorine needs one more for an octet and has valency 1.

In every case the chain is the same: Z gives protons and electrons; A − Z gives neutrons; the 2n² and outer-shell-8 rules give the configuration; the valence electrons give the valency; and the same Z with different A means isotopes, the same A with different Z means isobars.