Three Similar Elements Where the Middle Mass Is the Average
Test a set of three elements against the law of triads with real atomic masses, see why the law of octaves ran out at calcium, and find out what atomic number fixed in the older periodic table.
Why did chemists start arranging the elements in the first place?
Learning chemistry element by element is hopeless. There are more than a hundred of them, each with its own melting point, its own valency and its own set of reactions, and no student could hold all of that separately in their head.
But suppose the elements are not really separate. Suppose that if you line them up in the right order, similar ones fall into the same column — so that learning one column teaches you about all the elements in it.
That is the whole ambition of a periodic table, and it is why the arrangement matters so much more than the list.
Getting there took several attempts, each of which worked for a while and then broke. Groups of three similar elements were noticed first, then a pattern that repeated every eighth element, then an arrangement by atomic mass that was good enough to predict elements nobody had found — and finally an arrangement by atomic number that removed the last of the contradictions.
Each attempt failed for a specific, nameable reason, and the reasons are the examinable part of this topic — not the arrangements themselves.
This page covers the first part of the ICSE Class 9 Chemistry chapter on the periodic table: the law of triads and how to test one, the law of octaves and its limitations, Mendeleev's periodic law with its merits and its failures, and the Modern Periodic Law.
But suppose the elements are not really separate. Suppose that if you line them up in the right order, similar ones fall into the same column — so that learning one column teaches you about all the elements in it.
That is the whole ambition of a periodic table, and it is why the arrangement matters so much more than the list.
Getting there took several attempts, each of which worked for a while and then broke. Groups of three similar elements were noticed first, then a pattern that repeated every eighth element, then an arrangement by atomic mass that was good enough to predict elements nobody had found — and finally an arrangement by atomic number that removed the last of the contradictions.
Each attempt failed for a specific, nameable reason, and the reasons are the examinable part of this topic — not the arrangements themselves.
This page covers the first part of the ICSE Class 9 Chemistry chapter on the periodic table: the law of triads and how to test one, the law of octaves and its limitations, Mendeleev's periodic law with its merits and its failures, and the Modern Periodic Law.
How do you check whether three elements really form a triad?
Dobereiner's law of triads: when three chemically similar elements are arranged in order of increasing atomic mass, the atomic mass of the middle element is approximately the arithmetic mean of the other two.
So the test has two parts, and both must hold. The three elements must be chemically similar, and the arithmetic must work.
Worked verification 1 — lithium, sodium, potassium. Taking , and :
The mean is , which is exactly the atomic mass of sodium. All three are soft, highly reactive metals with valency 1. This is a triad.
Worked verification 2 — calcium, strontium, barium. With and :
Strontium's atomic mass is about , so the prediction is out by half a unit. The law says approximately, and all three are reactive metals of valency 2. This is a triad.
Worked verification 3 — chlorine, bromine, iodine. With and :
Bromine is about . Again close, and all three are reactive non-metals of valency 1. This is a triad.
Worked verification 4 — sulphur, selenium, tellurium. With and :
Selenium is about . A triad.
Now a set that fails. Take sodium, potassium and rubidium — all three genuinely similar metals. With and :
Potassium is , not . The chemistry is right and the arithmetic is wrong, so this is not a triad.
And a set that fails the other way. Take carbon, nitrogen and oxygen, with , and :
The arithmetic is perfect. But carbon is a solid that forms four bonds, nitrogen is an unreactive gas of valency 3 and oxygen is a reactive gas of valency 2 — they are not chemically similar at all, so this is not a triad either.
That is the trap in every triad question. The arithmetic is easy and it is only half the test. A set passes only if the three elements resemble one another and the middle mass comes out near the mean — and an examiner who gives you carbon, nitrogen and oxygen is checking whether you remembered the chemical condition.
The limitation of the law is simply how few triads exist. Only a handful of sets of three satisfy both conditions, so the law arranged a small fraction of the known elements and left the rest untouched. It was a real pattern that was far too narrow to be a classification.
So the test has two parts, and both must hold. The three elements must be chemically similar, and the arithmetic must work.
Worked verification 1 — lithium, sodium, potassium. Taking , and :
The mean is , which is exactly the atomic mass of sodium. All three are soft, highly reactive metals with valency 1. This is a triad.
Worked verification 2 — calcium, strontium, barium. With and :
Strontium's atomic mass is about , so the prediction is out by half a unit. The law says approximately, and all three are reactive metals of valency 2. This is a triad.
Worked verification 3 — chlorine, bromine, iodine. With and :
Bromine is about . Again close, and all three are reactive non-metals of valency 1. This is a triad.
Worked verification 4 — sulphur, selenium, tellurium. With and :
Selenium is about . A triad.
Now a set that fails. Take sodium, potassium and rubidium — all three genuinely similar metals. With and :
Potassium is , not . The chemistry is right and the arithmetic is wrong, so this is not a triad.
And a set that fails the other way. Take carbon, nitrogen and oxygen, with , and :
The arithmetic is perfect. But carbon is a solid that forms four bonds, nitrogen is an unreactive gas of valency 3 and oxygen is a reactive gas of valency 2 — they are not chemically similar at all, so this is not a triad either.
That is the trap in every triad question. The arithmetic is easy and it is only half the test. A set passes only if the three elements resemble one another and the middle mass comes out near the mean — and an examiner who gives you carbon, nitrogen and oxygen is checking whether you remembered the chemical condition.
The limitation of the law is simply how few triads exist. Only a handful of sets of three satisfy both conditions, so the law arranged a small fraction of the known elements and left the rest untouched. It was a real pattern that was far too narrow to be a classification.
What is the law of octaves, and why did it run out at calcium?
Newlands' law of octaves: when the elements are arranged in order of increasing atomic mass, every eighth element has properties similar to the first.
The name comes from music, where the eighth note of a scale sounds like the first. Here the claim is that chemical properties repeat with the same spacing.
Worked illustration. Counting lithium as the first:
- (1), (2), (3), (4), (5), (6), (7), (8)
Sodium is the eighth, and sodium does resemble lithium — both are soft reactive metals of valency 1.
Start again at sodium and the same thing happens:
- (1), (2), (3), (4), (5), (6), (7), (8)
Potassium is the eighth, and potassium resembles sodium.
So for the lighter elements the pattern is real, and it is the same repetition the modern table's short periods still show. The idea was sound; the arrangement built on it was not.
The limitations, which are the examinable part.
- It held only up to calcium. Beyond calcium the eighth element no longer resembled the first, so the pattern simply stopped working
- It assumed no more elements would be found. The arrangement was built for the elements then known, and there was no room in it for others. Many more were found afterwards, and they could not be fitted in
- Dissimilar elements were forced into the same slot. To keep the count of eight working, cobalt and nickel were put in the same position as the halogens fluorine, chlorine and bromine — metals sharing a slot with reactive non-metals
- Similar elements were separated. Iron, which resembles cobalt and nickel, was placed well away from them
Every one of those failures has the same root cause: the arrangement was rigid. A fixed pattern of eight with no spare places cannot survive the arrival of a new element, and cannot bend when the chemistry does not cooperate. The next attempt succeeded largely because it was willing to leave gaps — and that single change of attitude is what the following section is about.
The name comes from music, where the eighth note of a scale sounds like the first. Here the claim is that chemical properties repeat with the same spacing.
Worked illustration. Counting lithium as the first:
- (1), (2), (3), (4), (5), (6), (7), (8)
Sodium is the eighth, and sodium does resemble lithium — both are soft reactive metals of valency 1.
Start again at sodium and the same thing happens:
- (1), (2), (3), (4), (5), (6), (7), (8)
Potassium is the eighth, and potassium resembles sodium.
So for the lighter elements the pattern is real, and it is the same repetition the modern table's short periods still show. The idea was sound; the arrangement built on it was not.
The limitations, which are the examinable part.
- It held only up to calcium. Beyond calcium the eighth element no longer resembled the first, so the pattern simply stopped working
- It assumed no more elements would be found. The arrangement was built for the elements then known, and there was no room in it for others. Many more were found afterwards, and they could not be fitted in
- Dissimilar elements were forced into the same slot. To keep the count of eight working, cobalt and nickel were put in the same position as the halogens fluorine, chlorine and bromine — metals sharing a slot with reactive non-metals
- Similar elements were separated. Iron, which resembles cobalt and nickel, was placed well away from them
Every one of those failures has the same root cause: the arrangement was rigid. A fixed pattern of eight with no spare places cannot survive the arrival of a new element, and cannot bend when the chemistry does not cooperate. The next attempt succeeded largely because it was willing to leave gaps — and that single change of attitude is what the following section is about.
What did Mendeleev's table get right, and where did it break?
Mendeleev's periodic law: the physical and chemical properties of elements are a periodic function of their atomic masses.
The elements were set out in order of increasing atomic mass in a table of horizontal periods and vertical groups, with chemically similar elements in the same group. The two chief guides used were the formula of the oxide and the formula of the hydride of each element — that is, its valency.
Merit 1 — gaps were left for elements not yet known. Where the next element in mass order did not fit the chemistry of a group, the position was left empty rather than filled with the wrong element. The properties expected of the missing element were set down in advance from its neighbours. Elements were later found that fitted those empty places, and their measured properties agreed closely with what the table had predicted — scandium, gallium and germanium among them.
That is a genuinely remarkable thing for a classification to do. A table that merely organises what you already know is useful; a table that tells you what you have not yet found is a statement about nature rather than about bookkeeping. It is the strongest single argument in the law's favour, and it is the merit an examiner most often asks for.
Merit 2 — doubtful atomic masses were corrected. Some elements would not fit the group their accepted mass put them in. Beryllium had been given a mass of about on the assumption of valency 3, which placed it awkwardly. Its position in the table demanded valency 2, giving a mass of about — and the corrected value proved right. The masses of indium, gold and platinum were revised the same way.
Merit 3 — the noble gases were accommodated without disturbance. When helium, neon, argon and the rest were discovered, they were placed in a new zero group at the end of each period, and nothing already in the table had to move. A classification that can absorb an entire new family of elements untouched is telling you that its organising principle is sound.
Now the limitations.
- Hydrogen had no fixed position. It has one valence electron like the alkali metals of group I, and it is a diatomic non-metal like the halogens of group VII. Both placements can be defended, and the table could not decide
- Isotopes had no place. Isotopes of one element have different atomic masses, so a table ordered by mass should give them different slots. It does not — they are the same element and occupy one position
- Anomalous pairs. In several places a heavier element had to be put before a lighter one to keep the chemistry right: argon (about ) before potassium (about ); cobalt (about ) before nickel (about ); tellurium (about ) before iodine (about )
- Some dissimilar elements shared a group — copper and silver were placed with the alkali metals — and some similar ones were separated
- The law explained nothing. It recorded that properties repeat without saying why they repeat
Look at what the anomalous pairs actually mean. Three times over, the chemistry insisted on an order that the atomic masses forbade — and the chemistry was right each time. So the fault was not in the table but in the quantity chosen to order it by, and the obvious conclusion is that atomic mass is not quite the fundamental property of an element. The next section names the one that is.
The elements were set out in order of increasing atomic mass in a table of horizontal periods and vertical groups, with chemically similar elements in the same group. The two chief guides used were the formula of the oxide and the formula of the hydride of each element — that is, its valency.
Merit 1 — gaps were left for elements not yet known. Where the next element in mass order did not fit the chemistry of a group, the position was left empty rather than filled with the wrong element. The properties expected of the missing element were set down in advance from its neighbours. Elements were later found that fitted those empty places, and their measured properties agreed closely with what the table had predicted — scandium, gallium and germanium among them.
That is a genuinely remarkable thing for a classification to do. A table that merely organises what you already know is useful; a table that tells you what you have not yet found is a statement about nature rather than about bookkeeping. It is the strongest single argument in the law's favour, and it is the merit an examiner most often asks for.
Merit 2 — doubtful atomic masses were corrected. Some elements would not fit the group their accepted mass put them in. Beryllium had been given a mass of about on the assumption of valency 3, which placed it awkwardly. Its position in the table demanded valency 2, giving a mass of about — and the corrected value proved right. The masses of indium, gold and platinum were revised the same way.
Merit 3 — the noble gases were accommodated without disturbance. When helium, neon, argon and the rest were discovered, they were placed in a new zero group at the end of each period, and nothing already in the table had to move. A classification that can absorb an entire new family of elements untouched is telling you that its organising principle is sound.
Now the limitations.
- Hydrogen had no fixed position. It has one valence electron like the alkali metals of group I, and it is a diatomic non-metal like the halogens of group VII. Both placements can be defended, and the table could not decide
- Isotopes had no place. Isotopes of one element have different atomic masses, so a table ordered by mass should give them different slots. It does not — they are the same element and occupy one position
- Anomalous pairs. In several places a heavier element had to be put before a lighter one to keep the chemistry right: argon (about ) before potassium (about ); cobalt (about ) before nickel (about ); tellurium (about ) before iodine (about )
- Some dissimilar elements shared a group — copper and silver were placed with the alkali metals — and some similar ones were separated
- The law explained nothing. It recorded that properties repeat without saying why they repeat
Look at what the anomalous pairs actually mean. Three times over, the chemistry insisted on an order that the atomic masses forbade — and the chemistry was right each time. So the fault was not in the table but in the quantity chosen to order it by, and the obvious conclusion is that atomic mass is not quite the fundamental property of an element. The next section names the one that is.
How did the atomic number fix the anomalies?
The Modern Periodic Law: the physical and chemical properties of elements are a periodic function of their atomic numbers.
One word changed — mass became number — and every anomaly of the previous section disappeared.
Why atomic number is the better choice. The atomic number is the number of protons in the nucleus. It is a whole number, it is unique to each element, and it cannot be a fraction or an average of anything. Atomic mass, by contrast, is an average over a mixture of isotopes, which is why it comes out fractional and why it occasionally puts two elements in the wrong order.
The anomalous pairs resolve themselves.
- Argon has atomic number and potassium , so argon comes first — the order the chemistry demanded, now required by the law
- Cobalt is and nickel , so cobalt comes first
- Tellurium is and iodine , so tellurium comes first
In all three cases the heavier element genuinely has the lower atomic number, so no exception has to be made and no apology offered. The pairs stopped being anomalies and became ordinary entries — which is the clearest possible sign that the new ordering quantity was the right one.
Isotopes get one place. All isotopes of an element have the same number of protons, so they have the same atomic number and therefore one position in the table. Chlorine-35 and chlorine-37 both sit at . The problem that a mass-ordered table could not solve does not even arise.
And the repetition is finally explained. Atomic number fixes the number of electrons, which fixes the electronic configuration, and it is the configuration of the outermost shell that decides how an element behaves. Elements in the same group have the same number of valence electrons, so they behave alike — and the properties repeat because the outermost-shell arrangement repeats.
That is the deepest change of the three. The older law said properties repeat; the modern law says why, and the reason is the electron arrangement of the previous chapter. So the periodic table is not a separate topic from atomic structure — it is atomic structure sorted into a grid.
One problem survived. Hydrogen still has a single valence electron like an alkali metal and still behaves in some ways like a halogen, and the modern law does not settle where it belongs. Its anomalous position is a limitation of the modern table too, and a question asking for a limitation of the modern arrangement is usually asking for exactly this.
One word changed — mass became number — and every anomaly of the previous section disappeared.
Why atomic number is the better choice. The atomic number is the number of protons in the nucleus. It is a whole number, it is unique to each element, and it cannot be a fraction or an average of anything. Atomic mass, by contrast, is an average over a mixture of isotopes, which is why it comes out fractional and why it occasionally puts two elements in the wrong order.
The anomalous pairs resolve themselves.
- Argon has atomic number and potassium , so argon comes first — the order the chemistry demanded, now required by the law
- Cobalt is and nickel , so cobalt comes first
- Tellurium is and iodine , so tellurium comes first
In all three cases the heavier element genuinely has the lower atomic number, so no exception has to be made and no apology offered. The pairs stopped being anomalies and became ordinary entries — which is the clearest possible sign that the new ordering quantity was the right one.
Isotopes get one place. All isotopes of an element have the same number of protons, so they have the same atomic number and therefore one position in the table. Chlorine-35 and chlorine-37 both sit at . The problem that a mass-ordered table could not solve does not even arise.
And the repetition is finally explained. Atomic number fixes the number of electrons, which fixes the electronic configuration, and it is the configuration of the outermost shell that decides how an element behaves. Elements in the same group have the same number of valence electrons, so they behave alike — and the properties repeat because the outermost-shell arrangement repeats.
That is the deepest change of the three. The older law said properties repeat; the modern law says why, and the reason is the electron arrangement of the previous chapter. So the periodic table is not a separate topic from atomic structure — it is atomic structure sorted into a grid.
One problem survived. Hydrogen still has a single valence electron like an alkali metal and still behaves in some ways like a halogen, and the modern law does not settle where it belongs. Its anomalous position is a limitation of the modern table too, and a question asking for a limitation of the modern arrangement is usually asking for exactly this.
Exam tip
Exam tip: a triad needs both conditions, and every limitation needs its reason
For a triad, check chemical similarity AND the arithmetic. Carbon, nitrogen and oxygen satisfy and are not a triad, because they are chemically unlike.
Show the mean calculation as a fraction: for lithium, sodium and potassium.
For octaves, say "every eighth element" and give a run of eight — Li to Na, or Na to K.
Learn the octaves limitations as four points: valid only up to calcium; assumed no further elements would be found; dissimilar elements in one slot (cobalt and nickel with the halogens); iron separated from cobalt and nickel.
State the two laws with the right quantity. Mendeleev's law uses atomic masses; the Modern Periodic Law uses atomic numbers. Mixing them up loses the mark outright.
Learn Mendeleev's three merits: gaps left with predicted properties (scandium, gallium, germanium); doubtful atomic masses corrected (beryllium from about to about ); noble gases accommodated in a new zero group without disturbance.
Learn the limitations with their reasons. Hydrogen — resembles both group I and group VII. Isotopes — different masses would need different places. Anomalous pairs — name a pair with its masses, such as argon before potassium.
Explain the resolution in one line: atomic number is a whole number, unique, and not an average over isotopes, so the pairs fall into the correct order and isotopes share one place.
And remember that hydrogen's position is still unsettled in the modern table — that is the limitation to quote if asked.
Show the mean calculation as a fraction: for lithium, sodium and potassium.
For octaves, say "every eighth element" and give a run of eight — Li to Na, or Na to K.
Learn the octaves limitations as four points: valid only up to calcium; assumed no further elements would be found; dissimilar elements in one slot (cobalt and nickel with the halogens); iron separated from cobalt and nickel.
State the two laws with the right quantity. Mendeleev's law uses atomic masses; the Modern Periodic Law uses atomic numbers. Mixing them up loses the mark outright.
Learn Mendeleev's three merits: gaps left with predicted properties (scandium, gallium, germanium); doubtful atomic masses corrected (beryllium from about to about ); noble gases accommodated in a new zero group without disturbance.
Learn the limitations with their reasons. Hydrogen — resembles both group I and group VII. Isotopes — different masses would need different places. Anomalous pairs — name a pair with its masses, such as argon before potassium.
Explain the resolution in one line: atomic number is a whole number, unique, and not an average over isotopes, so the pairs fall into the correct order and isotopes share one place.
And remember that hydrogen's position is still unsettled in the modern table — that is the limitation to quote if asked.
Did you know
Why the noble gases were the real test of the table
Put yourself in the position of someone defending a classification of the elements, and ask what would destroy it.
Not a missing element. A gap is survivable, and a gap that later gets filled by exactly the element you predicted is a triumph rather than a wound.
What would destroy it is a whole family of elements that nobody had allowed for — several of them, chemically unlike anything already in the table, all needing places at once.
That is precisely what the noble gases were. Helium, neon, argon, krypton and xenon are gases that will not react with anything, form no ordinary compounds, and have a valency of zero. Nothing in the table resembled them. There was no column they belonged to and no obvious reason their masses should fall anywhere convenient.
And they fitted.
Each one dropped neatly into place at the end of a period, and a new zero group at the edge of the table held all of them in mass order, with helium above neon above argon just as the pattern required. Not a single element already placed had to be moved.
A classification that can absorb an unanticipated family without rearrangement is telling you something. A filing system invented for the elements would have had to be rebuilt; an arrangement that reflects how atoms are actually built would not.
There is a second point hiding in this, which the modern table makes obvious. The noble gases sit at the end of each period because that is where a shell finishes filling — a complete octet, or the duplet of helium. So the zero group is not an appendix bolted on at the edge. It is the natural boundary between one period and the next, and every period in the modern table ends with a noble gas for exactly that reason.
The group that looked like the hardest case turned out to mark where the periods divide.
Not a missing element. A gap is survivable, and a gap that later gets filled by exactly the element you predicted is a triumph rather than a wound.
What would destroy it is a whole family of elements that nobody had allowed for — several of them, chemically unlike anything already in the table, all needing places at once.
That is precisely what the noble gases were. Helium, neon, argon, krypton and xenon are gases that will not react with anything, form no ordinary compounds, and have a valency of zero. Nothing in the table resembled them. There was no column they belonged to and no obvious reason their masses should fall anywhere convenient.
And they fitted.
Each one dropped neatly into place at the end of a period, and a new zero group at the edge of the table held all of them in mass order, with helium above neon above argon just as the pattern required. Not a single element already placed had to be moved.
A classification that can absorb an unanticipated family without rearrangement is telling you something. A filing system invented for the elements would have had to be rebuilt; an arrangement that reflects how atoms are actually built would not.
There is a second point hiding in this, which the modern table makes obvious. The noble gases sit at the end of each period because that is where a shell finishes filling — a complete octet, or the duplet of helium. So the zero group is not an appendix bolted on at the edge. It is the natural boundary between one period and the next, and every period in the modern table ends with a noble gas for exactly that reason.
The group that looked like the hardest case turned out to mark where the periods divide.
Exam relevance
How does the periodic table carry into JEE Main and NEET?
Because periodicity is the framework every later chapter of inorganic chemistry hangs on.
This is the foundation for Class 11 Chemistry Classification of Elements and Periodicity in Properties, examined in both JEE Main and NEET. That chapter restates the Modern Periodic Law and then makes the reason for periodicity precise through electronic configuration — the s-, p-, d- and f-blocks, and the connection between a block and the subshell being filled. The qualitative reason given here becomes a rule for locating any element from its configuration.
The historical attempts remain examinable as recall. Assertion-reason and match-the-column questions on the law of triads, the law of octaves, Mendeleev's merits and limitations, and the anomalous pairs appear in NEET and in JEE Main. The anomalous pairs are the single most reused fact from this page — argon before potassium, cobalt before nickel, tellurium before iodine — because they make a clean statement about why atomic number replaced atomic mass.
Mendeleev's predictions are asked by name. Questions link eka-boron, eka-aluminium and eka-silicon to scandium, gallium and germanium. The pairing is worth memorising in that order.
Periodic trends become the heart of the topic. Class 11 turns the qualitative trends into named quantities — atomic and ionic radii, ionisation enthalpy, electron gain enthalpy and electronegativity — each with its trend across a period and down a group, and each with its own irregularities to explain. Ranking four elements by ionisation enthalpy is among the commonest JEE Main question types in inorganic chemistry, and every such ranking starts from the position in the table.
The blocks then organise two whole years of chemistry. Class 11 The s-Block Elements and The p-Block Elements and Class 12 The d- and f-Block Elements are all group-by-group studies, and the diagonal relationship, the inert-pair effect and the anomalous behaviour of the first member of a group are recurring JEE Advanced themes. None of them can be stated without the grid.
For NEET, periodicity is examined as recall and reasoning rather than calculation: identify the group and period from a configuration, pick the element with the largest atomic radius, name the most electronegative element, or match a historical law to its limitation. Biology needs the table too — the essential mineral elements of Mineral Nutrition and the ions of Transport in Plants are read off it.
What the questions look like. For board work, expect state the law of triads and verify a given set, state the law of octaves with an example and its limitations, give three merits and three limitations of Mendeleev's table, state the Modern Periodic Law, and explain how atomic number removed the anomalies. Definitions must name the correct ordering quantity. For JEE Main and NEET, expect block identification, trend rankings, assertion-reason items on periodicity, and the eka-element pairings.
How board and competitive emphasis differ. A board paper rewards the stated law with its reason and a named example. A competitive paper assumes the history and asks you to rank four elements on a trend or locate one from its configuration.
The single trap that costs the most marks. Writing the Modern Periodic Law with atomic mass in it. The whole point of the modern law is that it uses atomic number, and a definition with the wrong quantity contradicts everything the anomalous pairs establish. The defence is to recite the two laws as a pair — mass for the older, number for the modern — so that the contrast is what you remember rather than the wording of either one alone.
This is the foundation for Class 11 Chemistry Classification of Elements and Periodicity in Properties, examined in both JEE Main and NEET. That chapter restates the Modern Periodic Law and then makes the reason for periodicity precise through electronic configuration — the s-, p-, d- and f-blocks, and the connection between a block and the subshell being filled. The qualitative reason given here becomes a rule for locating any element from its configuration.
The historical attempts remain examinable as recall. Assertion-reason and match-the-column questions on the law of triads, the law of octaves, Mendeleev's merits and limitations, and the anomalous pairs appear in NEET and in JEE Main. The anomalous pairs are the single most reused fact from this page — argon before potassium, cobalt before nickel, tellurium before iodine — because they make a clean statement about why atomic number replaced atomic mass.
Mendeleev's predictions are asked by name. Questions link eka-boron, eka-aluminium and eka-silicon to scandium, gallium and germanium. The pairing is worth memorising in that order.
Periodic trends become the heart of the topic. Class 11 turns the qualitative trends into named quantities — atomic and ionic radii, ionisation enthalpy, electron gain enthalpy and electronegativity — each with its trend across a period and down a group, and each with its own irregularities to explain. Ranking four elements by ionisation enthalpy is among the commonest JEE Main question types in inorganic chemistry, and every such ranking starts from the position in the table.
The blocks then organise two whole years of chemistry. Class 11 The s-Block Elements and The p-Block Elements and Class 12 The d- and f-Block Elements are all group-by-group studies, and the diagonal relationship, the inert-pair effect and the anomalous behaviour of the first member of a group are recurring JEE Advanced themes. None of them can be stated without the grid.
For NEET, periodicity is examined as recall and reasoning rather than calculation: identify the group and period from a configuration, pick the element with the largest atomic radius, name the most electronegative element, or match a historical law to its limitation. Biology needs the table too — the essential mineral elements of Mineral Nutrition and the ions of Transport in Plants are read off it.
What the questions look like. For board work, expect state the law of triads and verify a given set, state the law of octaves with an example and its limitations, give three merits and three limitations of Mendeleev's table, state the Modern Periodic Law, and explain how atomic number removed the anomalies. Definitions must name the correct ordering quantity. For JEE Main and NEET, expect block identification, trend rankings, assertion-reason items on periodicity, and the eka-element pairings.
How board and competitive emphasis differ. A board paper rewards the stated law with its reason and a named example. A competitive paper assumes the history and asks you to rank four elements on a trend or locate one from its configuration.
The single trap that costs the most marks. Writing the Modern Periodic Law with atomic mass in it. The whole point of the modern law is that it uses atomic number, and a definition with the wrong quantity contradicts everything the anomalous pairs establish. The defence is to recite the two laws as a pair — mass for the older, number for the modern — so that the contrast is what you remember rather than the wording of either one alone.
Key takeaways
Triads, octaves and the two periodic laws: quick revision
- Law of triads: for three chemically similar elements in increasing order of atomic mass, the middle mass is approximately the arithmetic mean of the other two.
- Triads: Li , Na , K with ; Ca , Sr , Ba with ; Cl , Br , I with ; S , Se , Te with .
- Both conditions are needed. C, N, O give exactly and are not a triad — they are chemically unlike. Na, K, Rb are similar but give .
- Limitation of triads: very few sets satisfy both conditions, so most elements were left unclassified.
- Law of octaves: arranged by increasing atomic mass, every eighth element resembles the first. Li to Na; Na to K.
- Limitations of octaves: valid only up to calcium; assumed no further elements would be found; dissimilar elements shared a slot (cobalt and nickel with the halogens); iron was separated from cobalt and nickel.
- Mendeleev's periodic law: properties are a periodic function of atomic masses. Groups and periods, guided by the formulae of the oxide and the hydride.
- Merits: gaps left for unknown elements with predicted properties, later filled by scandium, gallium and germanium; doubtful atomic masses corrected (beryllium from about to about ); noble gases accommodated in a new zero group with nothing rearranged.
- Limitations: hydrogen had no fixed position (resembles group I and group VII); isotopes had no place; anomalous pairs where a heavier element came first — argon before potassium, cobalt before nickel, tellurium before iodine; some dissimilar elements grouped together; and the law explained why properties repeat.
- Modern Periodic Law: properties are a periodic function of atomic numbers.
- Why atomic number is better: it is a whole number, unique to the element, and not an average over isotopes.
- The anomalies vanish: Ar before K ; Co before Ni ; Te before I — all now in the required order.
- Isotopes share one place, because they share the atomic number.
- Repetition is explained: atomic number fixes the electronic configuration, and the outermost shell decides the chemistry.
- Hydrogen's position is still unsettled — a limitation of the modern table as well.
Take any three similar elements from a group, look up their atomic masses and run the mean test yourself — then try it on carbon, nitrogen and oxygen and see why the chemical condition exists.
- Triads: Li , Na , K with ; Ca , Sr , Ba with ; Cl , Br , I with ; S , Se , Te with .
- Both conditions are needed. C, N, O give exactly and are not a triad — they are chemically unlike. Na, K, Rb are similar but give .
- Limitation of triads: very few sets satisfy both conditions, so most elements were left unclassified.
- Law of octaves: arranged by increasing atomic mass, every eighth element resembles the first. Li to Na; Na to K.
- Limitations of octaves: valid only up to calcium; assumed no further elements would be found; dissimilar elements shared a slot (cobalt and nickel with the halogens); iron was separated from cobalt and nickel.
- Mendeleev's periodic law: properties are a periodic function of atomic masses. Groups and periods, guided by the formulae of the oxide and the hydride.
- Merits: gaps left for unknown elements with predicted properties, later filled by scandium, gallium and germanium; doubtful atomic masses corrected (beryllium from about to about ); noble gases accommodated in a new zero group with nothing rearranged.
- Limitations: hydrogen had no fixed position (resembles group I and group VII); isotopes had no place; anomalous pairs where a heavier element came first — argon before potassium, cobalt before nickel, tellurium before iodine; some dissimilar elements grouped together; and the law explained why properties repeat.
- Modern Periodic Law: properties are a periodic function of atomic numbers.
- Why atomic number is better: it is a whole number, unique to the element, and not an average over isotopes.
- The anomalies vanish: Ar before K ; Co before Ni ; Te before I — all now in the required order.
- Isotopes share one place, because they share the atomic number.
- Repetition is explained: atomic number fixes the electronic configuration, and the outermost shell decides the chemistry.
- Hydrogen's position is still unsettled — a limitation of the modern table as well.
Take any three similar elements from a group, look up their atomic masses and run the mean test yourself — then try it on carbon, nitrogen and oxygen and see why the chemical condition exists.