ChemistryICSE Class 9 · The Periodic Table

Dobereiner's Triads, Newlands' Octaves, Mendeleev's Table and the Modern Periodic Law (ICSE Class 9)

Updated 17 October 2026 · Fact-checked

Dobereiner (triads): the middle element's atomic mass is about the mean of the other two. Newlands (octaves): every eighth element has similar properties. Mendeleev: properties are periodic functions of atomic masses; he left gaps and predicted elements. Moseley: properties are periodic functions of atomic numbers (modern law), which removes the problems of isotopes and anomalous pairs such as Ar and K.

Understand Dobereiner's Triads, Newlands' Octaves, Mendeleev's Table and the Modern Periodic Law

Dobereiner’s triads (1817–1829). Similar elements occur in threes; in order of atomic mass, the middle one has an atomic mass close to the mean of the other two, and properties in between.

Triad	Check
Li 7, Na 23, K 39	$(7 + 39) /2 = 23$
Ca 40, Sr 88, Ba 137	$(40 + 137) /2 = 88.5$
Cl 35.5, Br 80, I 127	$(35.5 + 127) /2 = 81.25$

*Limitation:* only a few triads exist; many sets (for example N, P, As) do not obey the rule.

Newlands’ law of octaves (1865). In increasing atomic mass, every eighth element resembles the first (like the eighth note in a musical scale): Li → Na → K; F → Cl.
*Limitations:* worked only up to calcium; put two elements in one slot (Co and Ni); placed unlike elements together; left no room for new elements; the noble gases, discovered later, spoilt the pattern (inserting Ne after F makes the 8th element from F sulphur, not chlorine).

Mendeleev’s periodic law (1869). The physical and chemical properties of elements are periodic functions of their atomic masses. He arranged the 63 known elements in vertical groups and horizontal periods.
*Merits:* left gaps for undiscovered elements and predicted their properties (eka-aluminium = gallium, eka-silicon = germanium, eka-boron = scandium); corrected doubtful atomic masses; noble gases fitted in as a new group.
*Limitations:* no fixed position for hydrogen; isotopes would need separate places; anomalous pairs (Ar 39.9 before K 39.1; Co 58.9 before Ni 58.7; Te 127.6 before I 126.9); some unlike elements grouped together.

Modern periodic law (Moseley, 1913). The properties of elements are periodic functions of their atomic numbers. Atomic number (the nuclear charge) rises by one from one element to the next and is the fundamental property. This removes Mendeleev’s problems: isotopes (same Z) share one place; Ar (18) precedes K (19), Co (27) precedes Ni (28), and Te (52) precedes I (53). Properties repeat because the arrangement of valence electrons repeats.

Using the triad rule. Find the mean of the outer two and compare with the middle: a close match (within about a unit or two) supports a triad.

Dobereiner's Triads, Newlands' Octaves, Mendeleev's Table and the Modern Periodic Law: formulas and key facts

Dobereiner's triad: $A_{mi dd l e} \approx \frac{A _{1} + A _{3}}{2}$; Atomic masses in increasing order.
Newlands' octave: $element n resembles the eighth element counting n as 1, i.e. element (n + 7)$; In order of atomic mass. For example, Li is 1 and Na is 8 in the list.
Mendeleev's law: $properties = f (atomic mass)$; Modern law uses atomic number.
Modern periodic law: $properties = f (atomic number)$; Moseley, 1913.

How to solve Dobereiner's Triads, Newlands' Octaves, Mendeleev's Table and the Modern Periodic Law questions

Match each scheme with its principle, merit and limitation.

1For triads compute the mean of the first and third masses and compare with the middle.
2For octaves count eight elements forward (the first counts as 1).
3For Mendeleev name one merit (gaps and predictions) and one limitation (hydrogen, isotopes, anomalous pairs).
4For the modern law, argue from atomic number, not mass.
5Use specific numbers from the elements when asked for examples.

Dobereiner's Triads, Newlands' Octaves, Mendeleev's Table and the Modern Periodic Law in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

A missing piece

Suppose a quiz asks why a scientist would leave a gap in a table.

Which scientist did this, and what did later discoveries show?

Try it first, then show the solutionSolution

Mendeleev left gaps for elements not yet discovered and predicted their properties.
Gallium, germanium and scandium were later found to match his predictions for eka-aluminium, eka-silicon and eka-boron.

Answer: Mendeleev; the predictions were confirmed.

Memory hook: Gaps and predictions are his best merit.

Tricks to remember Dobereiner's Triads, Newlands' Octaves, Mendeleev's Table and the Modern Periodic Law

Short memory aids. Say each one aloud once, then use it on a question the same day.

Three, eight, sixty-three
Triads: 3; Newlands: 8; Mendeleev: 63 elements.
Use it when: Recalling numbers.
Mass led, number fixed
Mass-based tables had anomalies; atomic number removed them.
Use it when: Modern law.
Ar before K
Argon 18, potassium 19: order by number.
Use it when: Anomalous pairs.

Dobereiner's Triads, Newlands' Octaves, Mendeleev's Table and the Modern Periodic Law: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Newlands’ law · 1 mark · MCQBoard level

According to Newlands’ law of octaves, the element showing properties similar to lithium is the:
(a) second element after it
(b) fifth element after it
(c) eighth element from it
(d) tenth element from it

Try it first, then show the solutionSolution

Every eighth element, counting lithium as the first, resembles the first: Li to Na.

Answer: (c) eighth element from it

Example 2: A triad check · 2 marks · Short answerBoard level

Sulphur, selenium and tellurium have atomic masses 32, 79 and 127.6. Do they form a Dobereiner triad?

Try it first, then show the solutionSolution

Mean of the outer two $= \frac{32 + 127.6}{2} = 79.8$ . (1)
This is close to 79, the atomic mass of selenium, so they form a triad. (1)

Answer: Yes (mean 79.8 against 79)

Example 3: Three sets · 3 marks · Short answerHarder board level

Which of these sets obey Dobereiner’s rule? (a) Li 7, Na 23, K 39 (b) Be 9, Mg 24, Ca 40 (c) F 19, Cl 35.5, Br 80.

Try it first, then show the solutionSolution

(a) $\frac{7 + 39}{2} = 23$ : obeys. (1)
(b) $\frac{9 + 40}{2} = 24.5 \approx 24$ : obeys. (1)
(c) $\frac{19 + 80}{2} = 49.5$ , not 35.5: does not obey. (1)

Answer: (a) and (b) obey; (c) does not

Example 4: Anomalous pairs · 3 marks · Short answerHarder board level

In Mendeleev’s table tellurium (127.6) came before iodine (126.9) and argon (39.9) before potassium (39.1). (a) Find the mass differences. (b) Explain with atomic numbers (Te 52, I 53, Ar 18, K 19) how the modern law fixes the order.

Try it first, then show the solutionSolution

(a) $127.6 - 126.9 = 0.7$ ; $39.9 - 39.1 = 0.8$ . (1)
(b) Arranging by atomic number puts Te (52) before I (53) and Ar (18) before K (19). (1)
The modern law is based on atomic number, so the order matches the properties and no exception is needed. (1)

Answer: 0.7; 0.8; order by atomic number

Example 5: Noble gases and octaves · 4 marks · Case-basedHOTS / competency

Newlands’ order (without noble gases) runs: Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, Cl, K, Ca.
(a) Which is the eighth element from Li, from Be and from F?
(b) Name the pairs that are similar.
(c) Neon is now placed between F and Na. Which element is now the eighth from F?
(d) State two other limitations of the law.

Try it first, then show the solutionSolution

(a) Na, Mg and Cl respectively. (1)
(b) Li–Na, Be–Mg and F–Cl (similar properties). (1)
(c) With Ne inserted the order is F, Ne, Na, Mg, Al, Si, P, S: the eighth is S, so the pattern breaks. (1)
(d) It worked only up to calcium; it put unlike elements together or two elements in one slot (Co and Ni). (1)

Answer: (a) Na, Mg, Cl (b) Li–Na, Be–Mg, F–Cl (c) S (d) works up to Ca only; misplaced elements

Where students lose marks in Dobereiner's Triads, Newlands' Octaves, Mendeleev's Table and the Modern Periodic Law

The slips examiners see most often, and what to write instead.

Mistake: Octave counted from the wrong element
The first element counts as 1.
Wrong working
Li, Be, B, C, N, O, F, Na: ninth is Na.
Right working
Na is the eighth counting Li as 1.
Do this: Count Li as the first.
Usually costs: 1 mark.
Mistake: Mendeleev’s law stated with atomic number
His law used atomic mass.
Wrong working
Properties are periodic functions of atomic number (Mendeleev).
Right working
Atomic mass (Mendeleev); atomic number (modern law).
Do this: Pair name with property.
Usually costs: 1 mark.
Mistake: Argon–potassium exception omitted
Examiners ask for an example.
Wrong working
Mendeleev’s table had no limitation.
Right working
Ar before K, hydrogen’s position, isotopes.
Do this: Learn three limitations.
Usually costs: 1 mark.

Exam tips

Give two numerical examples when asked for the triad rule.
Write the merits and limitations of each scheme in two short bullet lists.
Use atomic numbers when explaining anomalous pairs.
Name the scientists with the years where possible.

Practice questions on Dobereiner's Triads, Newlands' Octaves, Mendeleev's Table and the Modern Periodic Law

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
The modern periodic law states that the properties of elements are periodic functions of their:
(a) atomic masses
(b) atomic numbers
(c) mass numbers
(d) densities
Hint
Moseley.
Answer
(b) atomic numbers
Q2 · 1 mark · Very short answerBoard level
Who proposed the idea of triads?
Hint
1817–1829.
Answer
Johann Dobereiner.
Q3 · 2 marks · Short answerHarder board level
Potassium (39) and caesium (133) are two members of a triad with rubidium. Estimate the atomic mass of rubidium by the triad rule.
Hint
Mean of the outer two.
Answer
$\frac{39 + 133}{2} = 86$ .
Q4 · 3 marks · Short answerHarder board level
Explain why isotopes did not fit in Mendeleev’s table but pose no problem in the modern table, using the isotopes of chlorine (atomic mass 35 and 37, Z = 17) as an example.
Hint
Same atomic number.
Answer
Mendeleev arranged by atomic mass, so ³⁵Cl and ³⁷Cl would need different places though they are the same element. In the modern table the position depends on atomic number (17), which is the same for both, so they occupy one place.
Q5 · 2 marks · Assertion-reasonHarder board level
Assertion (A): Argon is placed before potassium in the modern periodic table although its atomic mass is higher.
Reason (R): The modern periodic law is based on atomic number.
(a) Both true, R explains A.
(b) Both true, R does not explain A.
(c) A true, R false.
(d) A false, R true.
Hint
Ar 18, K 19.
Answer
(a)
Q6 · 3 marks · Long answerHOTS / competency
Discuss in three points whether Newlands’ law of octaves was a useful step in classifying elements, mentioning one merit and two limitations.
Hint
Merit: periodicity.
Answer
Merit: the first to show periodicity and to arrange all known elements by atomic mass, with every eighth element similar. Limitations: it worked only up to calcium; it put two elements (Co, Ni) in one slot and placed unlike elements together; it left no room for new elements, and the noble gases spoilt the octave pattern.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Dobereiner's triad rule?Show answer
The middle element’s atomic mass is about the mean of the other two.
2.Newlands' law?Show answer
Every eighth element resembles the first.
3.Mendeleev's law?Show answer
Properties are periodic functions of atomic masses.
4.Modern periodic law?Show answer
Properties are periodic functions of atomic numbers.
5.Elements Mendeleev predicted?Show answer
Gallium, germanium and scandium (eka-aluminium, eka-silicon, eka-boron).

Dobereiner's Triads, Newlands' Octaves, Mendeleev's Table and the Modern Periodic Law: frequently asked questions

What is Dobereiner's triad?

A group of three similar elements in which the atomic mass of the middle element is about the average of the other two.

What is the modern periodic law?

The properties of elements are periodic functions of their atomic numbers.

What were the limitations of Mendeleev's table?

No fixed place for hydrogen, no separate place for isotopes, anomalous pairs like Ar and K, and some unlike elements placed together.