Class 9 Science Chapter 8: Journey Inside the Atom

Acharya Kanada's name for the smallest particle of matter, reached by dividing dravya repeatedly. It is infinitely small, imperceptible to the senses, and joins in dyads and triads.

Rays travelling from the cathode to the anode when a high voltage is applied across a gas at very low pressure. They proved to be streams of negatively charged particles far lighter than atoms.

A sphere of positive charge with electrons distributed throughout it, likened to a plum pudding or a watermelon. The first genuine account of how an atom's charges stay balanced.

The deflection of alpha particles from their straight path on meeting a gold foil. It gives the gold foil experiment its other name, the alpha-ray scattering experiment.

The extremely small central region in which an atom's positive charge and most of its mass are concentrated. It is about $10^5$ times smaller than the atom itself.

Go on halving matter, or dravya, he argued, and you arrive at particles that will not halve again; parmanu was his word for them, and the Vaisesika Sutras preserve the argument. No sense can reach a parmanu, which is smaller than any size you can name, and it is by parmanus joining in twos and threes that everything material is built up. What the account does not specify is the proportions in which they combine to form different substances.

The earlier ideas from India and Greece originated as imaginary ideas rather than from experimental observations. Dalton's theory of 1808 was based on the scientific experiments of the time, which made it the first scientific description of how matter is made and the starting point for our present understanding.

He worked on how current passes through a gas thinned almost to nothing, in a glass tube carrying a pair of electrodes under a large voltage. Something streamed across it from the cathode towards the anode. Putting the streams through fields, electric and magnetic, told him what they were: particles each carrying a negative charge, each far lighter than any atom, and each thrown out by the atoms.

Because the nature of the cathode rays proved to be independent of the material of the cathode and of the gas filled in the tube. Since nothing about the particular setup made any difference, electrons must be a fundamental component of every element's atoms.

Having discovered negatively charged electrons, Thomson faced the puzzle that atoms are neutral, so the positive charge had to be accounted for. His answer was a ball of positive matter with the electrons scattered all through it — plums through a pudding, or seeds through the flesh of a watermelon.

In 1911 Geiger and Marsden, working under Rutherford, directed a fine beam of alpha particles onto a very thin gold foil. Most of the particles passed through undeflected, some were sharply deflected, and a few even bounced back. That deflection from the straight path is called scattering, which gives the experiment its other name.

He concluded that the positive charge is not spread throughout but concentrated in an extremely small region called the nucleus, that most of an atom is empty space, that the nucleus is dense and holds all the positive charge. Most of the mass, and that the electrons revolve around it as planets orbit the Sun. The nucleus is about $10^5$ times smaller than the atom, roughly $10^{-15}$ m against $10^{-10}$ m.

It could not explain the stability of the atom. Go round a circle and your direction is altering at every instant, which is acceleration; and a charge kept accelerating ought to shed energy. Shedding energy, the electron would wind inward until it struck the nucleus, so no atom could hold together at all. Since matter plainly stays intact, a new explanation was needed.

More than two thousand years ago, thinkers in two distant civilisations were pondering the same question: what is everything made up of?

In India, Acharya Kanada suggested that if matter, which he called dravya, is divided repeatedly, one reaches a stage of the smallest particles that can no longer be divided. Parmanu was his word for them, and the Vaisesika Sutras preserve the argument in Sanskrit. No sense can reach a parmanu, which is smaller than any size you can name. Parmanus join in twos to make dyads and in threes to make triads, and it is out of such joinings, on this account, that everything material is built up, living bodies among the rest.

One thing that account does not specify is the proportions in which parmanus combine to form different substances.

In Greece, Leucippus and Democritus proposed a similar idea, calling their indivisible particles atomos, which means indivisible in Greek.

What unites both is worth stressing: the concept of the atom originated as an imaginary idea rather than from experimental observations.

That is precisely what changed in 1808, when John Dalton proposed his atomic theory on the basis of the scientific experiments of his time. He held that all matter is composed of indivisible particles called atoms, the fundamental building blocks of matter. His was the first scientific description of how matter is made.

Right through to the closing years of the 1800s, an atom was taken to be as small as matter went and incapable of being split. Then certain elements were found to emit invisible energy and particles called radiation, a phenomenon known as radioactivity, which showed that atoms must be composed of smaller particles.

In 1897 J. J. Thomson was working on how current passes through a gas thinned almost to nothing. His apparatus was a glass tube carrying a pair of electrodes, across which he put a large voltage, and something streamed across it, leaving the cathode, which is the negative electrode, for the positive anode. These were called cathode rays.

Putting the streams through fields, electric and magnetic, told him what they were: particles each carrying a negative charge and each far lighter than any atom. Since the atoms themselves were throwing these out, an atom evidently has parts. The decisive detail was that the nature of the rays was independent of the material of the cathode and of the gas in the tube, which showed electrons to be a fundamental component of every element's atoms.

The find left a difficulty: an atom carries no net charge, so something in it must be positive. Thomson's answer was a ball of positive matter with the electrons scattered all through it — plums through a pudding, or seeds through the flesh of a watermelon. Though later replaced, it was the first genuine attempt to explain how the atom's charges stay balanced.

In 1911 Geiger and Marsden, working under Ernest Rutherford, set out to test Thomson's model. They aimed a narrow beam of alpha particles, which are tiny positively charged particles emitted by certain radioactive elements, at an extremely thin sheet of gold foil. On Thomson's model the positive charge was spread out evenly, so they expected the particles to pass straight through or be deflected only slightly. Instead, while most passed through undeflected, some were sharply deflected and a few even bounced back. That deflection from the straight path is called scattering, which is why the work is also known as the alpha-ray scattering experiment. Thomson's model failed to explain those results, particularly the deflection of some particles through large angles alongside the fact that most passed straight through. Rutherford's reading was that the positive charge sits packed into a region of extraordinarily small size rather than being spread about, and he named that region the nucleus. His model held that most of an atom is empty space, since most particles passed without deflection; that the nucleus is dense, containing all the positive charge. Most of the mass; and that the electrons revolve around the nucleus somewhat as planets orbit the Sun, which is why it is called the planetary model. The nucleus proved about $10^5$ times smaller than the atom, roughly $10^{-15}$ m against $10^{-10}$ m, so an atom the size of a cricket ground would have a peppercorn at its centre.

Placing a nucleus at the centre was a large step forward, but the model could not explain why atoms are stable.

The argument runs through the physics of motion. Go round a circle and your direction is altering at every instant, which is to say you are accelerating, however constant your speed. An electron carries charge, and a charge kept accelerating ought to shed energy.

Shedding energy, it would wind inward turn by turn until it struck the positive nucleus. Were that to happen, no atom could hold together at all.

But atoms are stable, which is precisely why the matter around us stays intact. Rutherford's picture, then, had a hole in it, and something else had to account for electrons that keep moving without ever winding in.

Before that explanation came another particle. Rutherford showed that the nucleus carries positive charge, and that this comes from particles called protons, which are much heavier than electrons and carry a charge equal and opposite to theirs. An atom shows no charge only when protons and electrons come to the same count — helium two and two, sodium eleven and eleven — and every atom is neutral on the same terms.

A permitted circular path in which an electron's energy stays constant although it is moving. Bohr laid this down as a postulate, and it is what keeps the atom from collapsing.

Another name for a shell, used because an electron in a given shell holds a definite quantity of energy. Energy rises with distance from the nucleus.

A particle of nearly the mass of a proton but no electrical charge, found by Chadwick in 1932. It lies in the nucleus of every atom except hydrogen.

The force binding the particles of a nucleus together. Neutrons strengthen it, and by coming between protons they also reduce the repulsion between them.

A one or two letter abbreviation for an element, approved by IUPAC. The first letter is capital, the second small, and many come from Latin, Greek or German names.

That electrons follow fixed circular paths called stationary states, orbits or shells rather than moving at random. That every shell carries its own fixed energy for an electron sitting in it, which is why shells are equally called energy levels. That electrons may revolve only in these allowed shells and never between them. And that so long as it keeps to its own shell, an electron sheds nothing.

They are labelled K, L, M, N and onward, or n = 1, 2, 3, 4 and onward. The K shell with n = 1 lies nearest the nucleus and has the least energy, and energy increases as one moves outward, so an L shell electron has more energy than a K shell electron.

In his model electrons still move in circular paths around a positive nucleus, exactly as in Rutherford's, so the question of energy loss had to be met directly. Bohr met it by introducing the stationary state as a postulate: in such a state an electron's energy remains constant although it is in motion. Nothing is lost, so nothing spirals inward.

Most of an atom's mass sits in the nucleus and the electrons are light enough to ignore, so the protons should settle the matter. But hydrogen has one proton and helium two, while helium weighs about four times hydrogen rather than twice. Something in the nucleus was adding mass without adding charge.

It is a subatomic particle whose mass is nearly equal to that of a proton but which carries no electrical charge, usually written n. Every atom except hydrogen carries neutrons in its nucleus, and together with the protons they supply nearly all of an atom's mass.

Every proton does repel every other, since all of them carry positive charge. Neutrons, being neutral, reduce that repulsion by coming between the protons and increasing the distance separating them, and they also strengthen the nuclear force that binds all the nuclear particles together. That is why heavier atoms need many more neutrons.

Dalton realised a standard way of representing elements and compounds was needed and introduced the first pictorial symbols in 1803. In 1813 Berzelius suggested deriving symbols from Latin names, which gave the alphabetic symbols we use. Today the International Union of Pure and Applied Chemistry approves all names and symbols.

Most of them are just the opening letter, or the opening pair, of the name itself. The first letter is always capital and the second, where there is one, always small, so aluminium is Al and cobalt is Co rather than AL or CO. Some take the first letter with a later letter instead of the second, as in Cl and Zn. And some come from Latin, Greek or German names, as Fe from ferrum, Hg from hydrargyros and W from wolfram.

Rutherford had left one problem unsolved: an electron circling the nucleus is constantly accelerating, so it ought to lose energy and spiral in, and atoms would not exist. Niels Bohr proposed a new model in 1913 to meet exactly this.

Electrons, on his account, are not wandering anywhere they please: each keeps to one circle and no other, a path called a stationary state, an orbit or a shell. Every shell carries its own fixed energy for an electron sitting in it, which is why the shells are equally called energy levels. The shells are written K, L, M, N and onward, or n = 1, 2, 3, 4 and onward.

Electrons may revolve only in these allowed shells and never in between, and each shell holds only a certain number of them. The K shell, n = 1, lies closest to the nucleus and has the least energy; energy increases outward, so an electron in the L shell has more energy than one in the K shell. To move from one shell to another, an electron absorbs or releases a fixed amount of energy set by the gap between the two levels.

Everything turns on the fourth postulate: so long as it keeps to its own shell, an electron sheds nothing. Bohr introduced this stationary state as a postulate, not as a derived result. In a stationary state the energy remains constant even though the electron is in motion, so nothing is shed and nothing spirals inward.

The model explained many experimental observations and was a major step in understanding atomic structure, though limits to it were found in turn and the quantum mechanical model followed.

Rutherford's model had put nearly all of an atom's mass in the nucleus, the revolving electrons being so light that their mass can be ignored. That should have made the proton count decisive for mass, and early in the twentieth century something did not fit.

A hydrogen atom has one proton and a helium atom has two, so helium ought to weigh twice what hydrogen weighs. It weighs about four times as much. Scientists were left asking whether, besides protons, something else in the nucleus was adding mass without affecting the charge.

In 1932 James Chadwick, a student of Ernest Rutherford working at the Cavendish Laboratory, solved it. What he turned up was a particle inside the atom with about as much mass as a proton and no charge whatever. This neutral particle was named the neutron and is usually written n. Every atom except hydrogen carries neutrons in its nucleus.

So an atom's mass comes mainly from its protons and neutrons packed tightly into the nucleus, which is exactly why atoms are heavier than their protons alone would account for. The three subatomic particles can now be tabulated: the electron e with charge minus one, the proton p with charge plus one, and the neutron n with charge zero.

Chadwick's work earned the Nobel Prize in Physics in 1935, and because neutrons carry no charge and penetrate nuclei easily it opened a new era in atomic physics.

Lighter atoms often carry an equal number of protons and neutrons. Carbon has six of each and oxygen eight of each. As atoms get heavier the pattern breaks: iron has 26 protons against 30 neutrons, and by uranium the nucleus holds 92 protons against 146 neutrons.

The reason lies in what the nucleus has to overcome. Every proton inside a nucleus pushes away every other proton, since all of them carry positive charge, and they are squeezed into an extremely small region.

Neutrons help in two distinct ways. Being neutral, they intervene between protons and increase the distance separating them, and since repulsion falls off with distance, that alone reduces the strain. Beyond this they strengthen the nuclear force, the force that binds all the particles of a nucleus together.

Put those together and the pattern follows. A nucleus with only a few protons has little repulsion to overcome, so equal numbers suffice. A nucleus with ninety-two protons faces an enormous amount of mutual repulsion, and needs far more neutrons to keep everything tightly bound.

This is also why the neutron mattered so much beyond bookkeeping. Carrying no charge, neutrons pass into nuclei easily, which led to artificial radioactive elements and to the splitting of uranium atoms, and so to both nuclear power and nuclear weapons.

By 1869 scientists knew of 69 elements, most of them found naturally on the Earth; today about 118 are known, some made artificially, and the search continues. A list that long needs a shorthand.

John Dalton realised that a standard way of representing elements and compounds would make the study of chemistry easier, and in 1803 he introduced the first pictorial symbols for the elements then known. In 1813 Berzelius suggested instead that symbols be derived from the Latin names of the elements, and alphabetic chemical symbols followed from that. Today the International Union of Pure and Applied Chemistry, IUPAC, approves the names and symbols of all elements.

Four rules govern how a symbol is written. Many symbols are simply the first letter, or the first two letters, of the element's name. The first letter is always a capital and the second, where there is one, is always small, so aluminium is Al and not AL, and cobalt is Co and not CO. Some symbols take the first letter together with a later letter that is not the second, as in Cl for chlorine and Zn for zinc. And some come from Latin, Greek or German names rather than English, so iron is Fe from ferrum, mercury is Hg from hydrargyros and tungsten is W from wolfram.

Symbols are used in place of full names because they are recognised internationally, which lets scientists anywhere communicate clearly whatever language they speak.

The number of protons in the nucleus of an atom. It determines the identity of the element and its chemical behaviour, and no two elements share a value.

The total number of protons and neutrons in the nucleus. Since a neutron weighs about what a proton weighs, this count accounts for an atom's mass.

A collective name for the protons and neutrons of a nucleus. The mass number is simply the number of nucleons.

An atom as a whole carries no charge, so its proton count equals its electron count. This is what lets the atomic number give both at once.

The symbol of the element with the mass number written above and the atomic number below, both on the left, as in $^{12}_{6}\text{C}$.

An element's atomic number is the count of protons in the nucleus of one of its atoms, and is written $Z$. It determines the identity of the element and its chemical behaviour, so elements with different atomic numbers are distinct and the atomic number identifies an element uniquely.

An atom taken altogether shows no charge, so whatever its proton count is, just as many electrons circle outside. So hydrogen with one proton has one electron, and helium with atomic number 2 has two protons and two electrons.

An atom's mass number, written $A$, is its protons and neutrons added together. The protons and neutrons in the nucleus are called nucleons, so the mass number is the number of nucleons. Mass number = number of protons + number of neutrons.

Because a neutron weighs about what a proton weighs, so every nucleon brings much the same amount and a head count does the job. An electron's mass is almost negligible in comparison, so electrons can be left out of the calculation altogether.

The symbol of the element is written with its mass number $A$ above and its atomic number $Z$ below, both to the left of the symbol. Carbon's symbol is C, its atomic number is 6 and its mass number is 12, so it is written $^{12}_{6}\text{C}$.

The atomic number gives 26 protons. Since the atom is neutral, it has 26 electrons. Nucleons means the mass number, so $A = 56$, and the neutrons number $56 - 26 = 30$.

The mass number is the protons plus the neutrons, so $A = 17 + 18 = 35$. Since the atom is neutral its electron count equals its proton count, which is 17.

The atom is neutral, so its proton count equals its electron count and is therefore 11, which makes its atomic number 11. The mass number given is 23. Since the mass number is the protons plus the neutrons, the neutrons number $23 - 11 = 12$.

Within an element the atoms match one another and differ from every other element's, and the respect in which they differ is how many protons and electrons they carry.

Count the protons in the nucleus of one of an element's atoms and that count is the element's atomic number, written $Z$. This number determines the identity of the element and its chemical behaviour.

One consequence follows immediately. An atom taken altogether shows no charge, so whatever its proton count is, just as many electrons circle outside. One proton and one electron give hydrogen its atomic number of 1. At 2, helium carries a pair of each. Lithium, with atomic number 3, has three of each.

So a single figure carries two counts. Give the atomic number and the proton count and the electron count both follow.

And because elements with different atomic numbers are distinct from each other, the atomic number identifies an element uniquely. No two elements share one. This is why the mass number cannot do the same work: an atom that gains a neutron changes its mass number while remaining the same element, since its proton count is untouched.

The atomic number alone leaves something unexplained. Two protons is what helium has, yet it weighs in at some four proton masses rather than two. The protons cannot account for it.

Add the protons to the neutrons in a nucleus and the total is that atom's mass number, written $A$. Anything sitting in the nucleus, proton or neutron, is a nucleon, so the mass number is nothing more than a head count of nucleons.

The formula is an addition: mass number = number of protons + number of neutrons.

It works because a neutron weighs about what a proton weighs, so every nucleon brings much the same amount to the total. Helium's mass is then accounted for by two protons and two neutrons together. The electron, in comparison, has almost negligible mass and can be ignored in these calculations.

A few examples make the pattern plain. Hydrogen has 1 proton and 0 neutrons, giving a mass number of 1. Helium has 2 protons and 2 neutrons, giving 4. Lithium has 3 protons and 4 neutrons, giving 7.

Run backwards, the same formula gives the neutrons: number of neutrons = mass number − atomic number.

In the standard notation for an atom, the symbol of the element, its atomic number $Z$ and its mass number $A$ are written together in one compact form. The mass number is placed above and the atomic number below, both to the left of the symbol, giving $^{A}_{Z}\text{X}$.

Take carbon. Its symbol is C, its atomic number is 6 and its mass number is 12, so in this notation it is written $^{12}_{6}\text{C}$.

Three counts can be read from it. The proton count is the atomic number, which is 6. The electron count is also 6, because the atom is neutral and its positive and negative particles must balance. The neutron count needs one subtraction: mass number minus atomic number, which is $12 - 6 = 6$.

The same reading works in reverse. If an atom is written $^{23}A$ and is said to have 11 electrons, then its proton count is 11 too, so $Z = 11$, and the neutrons number $23 - 11 = 12$.

One useful check follows from all this. Since a neutron count can be zero but never negative, the mass number can never be smaller than the atomic number. Hydrogen is the case where the two are equal, because it carries no neutrons.

Start from the atomic number. It is the proton count, so the atom has 20 protons.

The atom as a whole is neutral, so its electron count equals its proton count, giving 20 electrons.

The mass number is the protons plus the neutrons, so $A = 20 + 21 = 41$. Equivalently, the nucleus holds 41 nucleons.

In standard notation the mass number goes above and the atomic number below, both to the left of the symbol, so this atom is written $^{41}_{20}\text{X}$, where X stands for whichever element has atomic number 20.

Now add a neutron. The neutron count rises from 21 to 22, so the mass number rises from 41 to 42. But the atomic number is unchanged at 20, because no proton has been added or taken away.

That is the important consequence. Since the atomic number determines the identity of the element and its chemical behaviour, the atom is still the same element and still behaves the same way chemically. It is simply heavier. The new notation would read $^{42}_{20}\text{X}$, and the electron count would still be 20.

The maximum number of electrons a shell can hold, where $n$ is the shell number. K holds 2, L holds 8, M holds 18.

The distribution of an atom's electrons among its various shells, written shell by shell from the innermost outward, as in 2, 8, 1 for sodium.

The outermost shell of an atom that contains electrons. The electrons in it are the valence electrons, and they decide how the atom reacts.

A valence shell holding 8 electrons. Elements with a complete octet, or 2 in helium's case, are largely unreactive and more stable.

The number of electrons an atom gains, loses or shares in order to complete its octet. It is the same thing as its combining capacity.

First, the maximum number of electrons in a shell is $2n^2$, where $n$ is the shell number, so K holds 2, L holds 8 and M holds 18. Second, the outermost shell may hold no more than 8 electrons, and the first shell no more than 2 where it is the only one. Third, electrons fill stepwise from the shell nearest the nucleus outward, so the L shell fills only after the K shell is complete.

The formula $2n^2$ gives the M shell a capacity of 18, but the cap on the outermost shell is 8. So while M is the outermost shell of an atom it may hold at most 8, as in argon at 2, 8, 8. The full 18 becomes available only once a further shell has begun.

Atomic number 12 is magnesium, 2, 8, 2. Atomic number 16 is sulfur, 2, 8, 6. Atomic number 18 is argon, 2, 8, 8.

It is how many atoms of hydrogen, or of chlorine, a single atom of the element will take up in forming a compound. Those two are used because each of them itself possesses a combining capacity of one, which makes them a convenient unit to count against. In water, for instance, oxygen combines with two hydrogen atoms, so oxygen's combining capacity is two.

The valence shell is the outermost shell of an atom that contains electrons, and the electrons present in it are the valence electrons. If that shell holds 8 electrons it is called an octet, and elements with a complete octet, or 2 electrons in the case of helium, are largely unreactive and more stable.

An element with fewer than four valence electrons generally tends to lose them to complete its octet, since shedding a few is a shorter route than acquiring many. An element with more than four tends to gain electrons instead, for the same reason in reverse. An element sitting at exactly four can do neither easily, so it shares.

Sodium is 2, 8, 1, and gets an octet by losing one electron, so its valency is 1. Oxygen is 2, 6, and gains two electrons to attain an octet, so its valency is 2. Carbon is 2, 4, and cannot easily gain or lose, so it shares four electrons with other atoms, giving a valency of 4.

Nothing. It has no octet left to complete, so it will not try to lose or gain electrons and is largely unreactive. Neon at 2, 8 and argon at 2, 8, 8 are both such atoms. The one qualification is that an element with a single shell needs only two, which is helium's case.

Bohr and Bury gave three rules.

The first fixes capacity: the maximum number of electrons in a shell is $2n^2$, where $n$ is the number of the shell. So the K shell, $n = 1$, holds $2 \times 1^2 = 2$; the L shell, $n = 2$, holds $2 \times 2^2 = 8$; and the M shell, $n = 3$, holds $2 \times 3^2 = 18$.

The second caps the outside: the maximum that can be accommodated in the outermost shell is 8, and the first shell can accommodate at most two. This overrides the formula for whichever shell happens to be outermost.

The third fixes the order: electrons are filled stepwise, starting from the shell closest to the nucleus and moving outward in the order K, L, M, N. The L shell takes electrons only once K is full, and so on.

Applying them is a matter of adding one electron each time the atomic number rises by one. Hydrogen's single electron goes into K, giving 1. Helium's two fill K, giving 2. Lithium's third must start L, giving 2, 1, and the L shell then fills steadily through beryllium 2, 2, boron 2, 3, carbon 2, 4, nitrogen 2, 5, oxygen 2, 6 and fluorine 2, 7 until neon completes it at 2, 8.

Sodium's eleventh electron has nowhere left but M, giving 2, 8, 1, and M then fills in the same way through magnesium 2, 8, 2 to chlorine 2, 8, 7 and argon 2, 8, 8, where the outermost cap of eight stops it.

The outermost shell of an atom that contains electrons is its valence shell, and the electrons in it are its valence electrons. If that shell holds eight, it is called an octet.

The octet matters because of what it does to reactivity. Elements with a complete octet, or with two electrons in the case of helium, are largely unreactive and more stable. Atoms with incomplete valence shells are usually more reactive, and they lose, gain or share electrons in order to complete their octet.

That gives the definition. Count the electrons an element must take, give or share to arrive at that octet, and the count is its valency.

Which of the three routes an atom takes follows a rough rule. If it has fewer than four valence electrons it tends to lose them, since shedding a few is easier than acquiring many. If it has more than four it tends to gain instead. And at exactly four it can do neither easily, so it shares.

Three cases show this. Sodium is 2, 8, 1, and can reach an octet by losing one electron, so its valency is 1. Oxygen is 2, 6, and gains two to attain an octet, so its valency is 2. Carbon is 2, 4, and shares four electrons with other atoms, so its valency is 4.

Some compounds appear to violate the usual rule, which belongs to higher grades.

Molecules are built by atoms joining, whether they come from one element or several. Take one atom of an element and ask how many atoms of hydrogen, or of chlorine, it will take up in forming a compound: that figure is its combining capacity. Those two elements are the yardstick because both of them possess a combining capacity of one.

Read off a few formulae and the capacities follow. In water, $\text{H}_2\text{O}$, oxygen combines with two hydrogen atoms, so oxygen's combining capacity is two. In ammonia, $\text{NH}_3$, nitrogen combines with three, so nitrogen's is three. In magnesium chloride, $\text{MgCl}_2$, magnesium combines with two chlorines, so magnesium's is two.

Now take the same elements from the other side, through their configurations. Oxygen is 2, 6, and needs two electrons for an octet, giving a valency of two. Nitrogen is 2, 5, and needs three, giving three. Magnesium is 2, 8, 2, and loses two, giving two.

The two lists agree exactly, which is the point. Combining capacity is measured by experiment from the compounds an element forms, while valency is predicted from the electrons in its outermost shell. They are two routes to one number, and the agreement between them is what makes the electronic explanation convincing.

Magnesium and oxygen also make a useful pair. Both have a capacity of two, but magnesium reaches it by losing and oxygen by gaining.

Start with the configuration. The atomic number is 17, so there are 17 protons and, since the atom is neutral, 17 electrons. Filling stepwise, the K shell takes 2 and the L shell takes 8, which accounts for ten. The remaining seven go into M, so the configuration is 2, 8, 7. That element is chlorine.

Its valence shell is M and it has seven valence electrons. Since seven is more than four, the atom tends to gain rather than lose, and it needs only one electron to complete its octet. Its valency is therefore 1, and since it is one electron short of a full shell it should be markedly reactive.

That also explains why chlorine is used, alongside hydrogen, as a yardstick for combining capacity: a capacity of one is exactly what makes it a convenient unit.

Now atomic number 18. One more electron completes the M shell at eight, giving 2, 8, 8, which is argon. Its valence shell holds a complete octet, so there is nothing left to complete. It will not try to lose or gain electrons, and it is largely unreactive and more stable.

So a single electron separates the two, and that one electron is the whole difference between an element that reacts eagerly and one that hardly reacts at all.

Atoms of one element sharing an atomic number but differing in mass number, because they carry different numbers of neutrons. Their chemistry is alike; their physical properties are not.

The unit u, used because kilograms and grams are far too large for particles this small. It was formerly called the atomic mass unit, amu.

Each isotope's mass multiplied by its percentage abundance, and the results added. It reflects the element as it occurs in nature, unlike a simple mean.

Atoms of different elements that share a mass number but have different atomic numbers, such as argon 40, potassium 40 and calcium 40.

The modern picture that replaced fixed orbits. We can predict the regions where an electron is most likely to be, not exactly where it is.

Every atom of an element is a copy of every other, Dalton had said, mass included; but atoms of one element turned up agreeing in protons, and so in atomic number, while differing in neutrons and so in mass number. These twin atoms, alike in atomic number but different in mass number, are called isotopes.

Naturally occurring hydrogen is a mixture of three isotopes. Protium $^{1}{1}\text{H}$ makes up about 99.98 per cent and deuterium $^{2}{1}\text{H}$ about 0.015 per cent. Tritium $^{3}_{1}\text{H}$ occurs only in traces. All three contain one proton, and so one electron each, while protium has no neutron, deuterium has one and tritium has two.

Their electron counts agree and so do their electron arrangements; since chemistry turns chiefly on the valence electrons, a change inside the nucleus leaves it alone. Their physical properties, boiling and melting points among them, do differ, because those depend on mass.

Uranium's $^{235}{92}\text{U}$ is burned as reactor fuel, which is how a nuclear power plant raises electricity. Cobalt's radioactive $^{60}{27}\text{Co}$ is turned on tumours in the radiation treatment of cancer. Iodine's $^{131}{53}\text{I}$ serves against goitre and cancer of the thyroid. And carbon's $^{14}{6}\text{C}$ lets archaeologists and geologists put an age to fossils and artefacts.

It gives $(35 + 37) \div 2 = 36$ u. It fails because it treats the two isotopes as occurring in equal ratios, when in fact the lighter one makes up about 75 per cent and the heavier about 25 per cent.

Multiplying each mass by its abundance gives $35 \times \frac{75}{100} + 37 \times \frac{25}{100} = \frac{105}{4} + \frac{37}{4} = \frac{142}{4} = 35.5$ u. This does not mean any single chlorine atom has a fractional mass. It means that a million chlorine atoms would contain 7.5 lakh of the 35 u kind and 2.5 lakh of the 37 u kind.

Atoms of different elements that have the same mass number but different atomic numbers are called isobars. Calcium with atomic number 20, potassium with 19 and argon with 18 all have a mass number of 40, so their atoms hold the same number of nucleons altogether although they are different elements.

Bohr's account proved incomplete in its turn: no electron runs on a track of the kind his orbits described. They are understood today as electron clouds around the nucleus, so we can predict the regions where they are most likely to be, rather than exactly where they are.

Dalton proposed that all the atoms of one element are alike and carry equal mass. Scientists later discovered atoms of the same element that have the same number of protons, and so the same atomic number, yet different numbers of neutrons and therefore different mass numbers, since $A$ is the protons plus the neutrons. Such twin atoms are called isotopes.

Naturally occurring hydrogen is a mixture of three. Protium $^{1}{1}\text{H}$ makes up about 99.98 per cent, deuterium $^{2}{1}\text{H}$ about 0.015 per cent, and tritium $^{3}_{1}\text{H}$ occurs in traces. All three contain one proton each, and so one electron each, while protium has no neutron, deuterium has one and tritium has two.

Their chemical properties are similar, and the reason lies outside the nucleus. Their electron counts agree and so do their electron arrangements, and chemistry turns chiefly on the valence electrons. Adding a neutron changes the mass but leaves the electrons exactly as they were.

What does change is the physical properties, boiling and melting points among them, since those do depend on mass.

Carbon shows the same pattern. Its three isotopes $^{12}{6}\text{C}$, $^{13}{6}\text{C}$ and $^{14}{6}\text{C}$ each have six protons and six electrons, and differ only in the number of neutrons. $^{12}{6}\text{C}$ is the most abundant in nature.

Chlorine occurs in nature in two isotopic forms, one of mass 35 u and one of mass 37 u, in the ratio 3 : 1. That raises a question at once: should the mass of a chlorine atom be taken as 35 u or as 37 u?

One answer is to take the simple arithmetic mean of the two masses, calculated without accounting for how common each one is. That gives $(35 + 37) \div 2 = 36$ u.

Nature does not oblige with equal shares, so that figure misrepresents it. About three quarters of the chlorine about us is $^{35}\text{Cl}$ and the remaining quarter $^{37}\text{Cl}$.

The accurate figure is a weighted average atomic mass, found by multiplying the mass of each isotope by its percentage relative abundance and then adding the two values.

$35 \times \frac{75}{100} + 37 \times \frac{25}{100} = \frac{105}{4} + \frac{37}{4} = \frac{142}{4} = 35.5$ u.

One warning goes with the answer. No chlorine atom anywhere weighs 35.5 u; the figure belongs to no individual atom at all. What it says is that out of a million chlorine atoms, 7.5 lakh will be of the 35 u kind and 2.5 lakh of the 37 u kind, and weighting the two masses by those shares gives 35.5 u.

The comparison is the lesson: the simple average ignores abundance, while the weighted average reflects the element as it occurs in nature.

Isotopes belong to one element and share its atomic number while differing in mass number. Since the atomic number is the proton count, they share their protons and differ only in neutrons. Hydrogen's protium, deuterium and tritium are one example, and carbon's three isotopes another.

Isobars are the reverse. Atoms from two different elements that agree in mass number while differing in atomic number are called isobars. Calcium with atomic number 20, potassium with 19 and argon with 18 all have a mass number of 40. They have different numbers of protons, yet their atoms hold the same number of nucleons altogether.

Put side by side, the two cases make a point about the two numbers. The atomic number identifies the element: isotopes share it and are one element, while isobars differ in it and are three different elements. The mass number does not identify anything: isobars share it across three elements, and isotopes differ in it within one.

The chemistry follows the atomic number too. Isotopes of one element behave alike chemically, because they share an electron count and an electronic configuration. Isobars do not, because their electron counts differ, and it is the valence electrons that govern how an atom reacts.

Some isotopes have special properties that make them useful. Uranium's $^{235}{92}\text{U}$ is the fuel a reactor burns when a nuclear station makes electricity. Cobalt's radioactive $^{60}{27}\text{Co}$ supplies the radiation used against cancer. Iodine's $^{131}{53}\text{I}$ is given for goitre and for cancer of the thyroid. And carbon's $^{14}{6}\text{C}$ is what archaeologists and geologists date old fossils and old objects by.

It is worth noticing what makes these uses possible. Since isotopes of an element share their chemistry, a chosen isotope travels through the body or through a sample exactly as the common form would, while its nuclear behaviour is quite different. That is the whole basis of using one isotope where another would be useless.

As for the atom itself, the story does not end with Bohr. Bohr's account proved incomplete in its turn: no electron runs on a track of the kind his orbits described. What we now picture round a nucleus is a cloud of electron, so the most that can be given is where an electron is likeliest to be found, never where it is.

The chain of models runs from Dalton's indivisible particle through Thomson's charges, Rutherford's nucleus and Bohr's energy levels to the quantum mechanical model, and the exploration is still going on.

Go on halving matter, or dravya, he argued, and you arrive at particles that will not halve again; parmanu was his word for them, and the Vaisesika Sutras preserve the argument. No sense can reach a parmanu, which is smaller than any size you can name, and it is by parmanus joining in twos and threes that everything material is built up. What the account does not specify is the proportions in which they combine to form different substances.

The earlier ideas from India and Greece originated as imaginary ideas rather than from experimental observations. Dalton's theory of 1808 was based on the scientific experiments of the time, which made it the first scientific description of how matter is made and the starting point for our present understanding.

He worked on how current passes through a gas thinned almost to nothing, in a glass tube carrying a pair of electrodes under a large voltage. Something streamed across it from the cathode towards the anode. Putting the streams through fields, electric and magnetic, told him what they were: particles each carrying a negative charge, each far lighter than any atom, and each thrown out by the atoms.

That electrons follow fixed circular paths called stationary states, orbits or shells rather than moving at random. That every shell carries its own fixed energy for an electron sitting in it, which is why shells are equally called energy levels. That electrons may revolve only in these allowed shells and never between them. And that so long as it keeps to its own shell, an electron sheds nothing.

They are labelled K, L, M, N and onward, or n = 1, 2, 3, 4 and onward. The K shell with n = 1 lies nearest the nucleus and has the least energy, and energy increases as one moves outward, so an L shell electron has more energy than a K shell electron.

In his model electrons still move in circular paths around a positive nucleus, exactly as in Rutherford's, so the question of energy loss had to be met directly. Bohr met it by introducing the stationary state as a postulate: in such a state an electron's energy remains constant although it is in motion. Nothing is lost, so nothing spirals inward.

An element's atomic number is the count of protons in the nucleus of one of its atoms, and is written $Z$. It determines the identity of the element and its chemical behaviour, so elements with different atomic numbers are distinct and the atomic number identifies an element uniquely.

An atom taken altogether shows no charge, so whatever its proton count is, just as many electrons circle outside. So hydrogen with one proton has one electron, and helium with atomic number 2 has two protons and two electrons.

An atom's mass number, written $A$, is its protons and neutrons added together. The protons and neutrons in the nucleus are called nucleons, so the mass number is the number of nucleons. Mass number = number of protons + number of neutrons.

First, the maximum number of electrons in a shell is $2n^2$, where $n$ is the shell number, so K holds 2, L holds 8 and M holds 18. Second, the outermost shell may hold no more than 8 electrons, and the first shell no more than 2 where it is the only one. Third, electrons fill stepwise from the shell nearest the nucleus outward, so the L shell fills only after the K shell is complete.