JEE Mains Chemistry · Classification of Elements and Periodicity

Atomic and Ionic Radii

Atoms shrink across a period as the nuclear charge grows on the same shell and swell down a group as shells are added; a cation is smaller than its atom and an anion larger.

All Classification of Elements and Periodicity notes JEE Mains Chemistry strategy

Why this matters

Twenty-one PYQs, nineteen of them multiple choice, and two from 2026. Seven rank atomic radii or ask what a covalent radius is; nine rank ions, most often an isoelectronic series; five count electrons and neutrons to decide which species are isoelectronic.

Concept 1 of 3: Atomic radius across a period and down a group

Across a period each step adds one proton and one electron to the same shell. The extra pull wins, so the atom gets smaller. Down a group each step adds a whole shell, and the atom gets bigger even though the nuclear charge rises.

Definition

Covalent radius = half the bond length in $\mathrm{X_2}$ : the Cl–Cl bond is 198 pm, so $r_{\mathrm{Cl}} = 99$ pm.
A bond between two different atoms is about $r_A + r_B$ long.
Metallic radius = half the distance between neighbouring nuclei in the metal crystal.
Across a period the radius falls; down a group it rises.
In period 4, K is the largest and Br the smallest; noble gases are left out, because their van der Waals radius is not comparable with a covalent radius.

Series	Atomic radius (pm)	Trend
Period 2	Li 152, Be 111, B 88, C 77, N 74, O 66, F 64	Falls steadily across
Period 3	Na 186, Mg 160, Al 143, Si 117, P 110, S 104, Cl 99	Falls steadily across
Group 1	Li 152, Na 186, K 231, Rb 244, Cs 262	Rises down the group
Group 17	F 64, Cl 99, Br 114, I 133, At 140	Rises down the group
Period 4 ends	K 231, Br 114	Largest and smallest in period 4, noble gas excluded

Compare the columns: Be (111) is smaller than Mg (160) and Mg is larger than Al (143).

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2025 · 28 January 2025 · Q26Moderate

Example 1 · Classification of Elements and Periodicity · Atomic and Ionic Radii

The incorrect decreasing order of atomic radii is :

Half the bond, not double

The covalent radius is half the distance between the two nuclei in

\mathrm{Cl_2}

. A statement that it is double the atomic radius has the relation upside down.

Down a group beats across a period

Be is at the left of period 2 but still smaller than Mg, which has one more shell. When an order mixes groups and periods, compare the shells first.

Drill 6 more on atomic radius across a period and down a group

Concept 2 of 3: Ionic radius and isoelectronic series

Removing electrons leaves the same nucleus pulling fewer electrons, so a cation is smaller than its atom. Adding electrons adds repulsion with no extra pull, so an anion is larger. In an isoelectronic series every ion has the same electrons, and the one with more protons pulls them in tighter.

Definition

Cation < parent atom: Na 186 pm, $\mathrm{Na^+}$ 102 pm.
Anion > parent atom: Cl 99 pm, $\mathrm{Cl^-}$ 184 pm.
Isoelectronic species: same number of electrons; the radius falls as $Z$ rises.
10 electrons: $\mathrm{N^{3-} > O^{2-} > F^- > Na^+ > Mg^{2+} > Al^{3+}}$ .
18 electrons: $\mathrm{P^{3-} > S^{2-} > Cl^- > K^+ > Ca^{2+}}$ .
Down a group, ions of the same charge grow: $\mathrm{Li^+ < Na^+ < K^+}$ .

Species	Protons	Electrons	Radius (pm)
Na atom	11	11	186
$\mathrm{Na^+}$	11	10	102
Cl atom	17	17	99
$\mathrm{Cl^-}$	17	18	184
$\mathrm{O^{2-}}$	8	10	140 Isoelectronic with $\mathrm{Mg^{2+}}$ (72 pm), yet about twice as large: the same electrons do not mean the same size.
$\mathrm{F^-}$	9	10	133
$\mathrm{Mg^{2+}}$	12	10	72
$\mathrm{Al^{3+}}$	13	10	53.5
$\mathrm{K^+}$	19	18	138

Within the 10-electron rows, every extra proton makes the ion smaller.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2022 · 27 June 2022 · Q125Moderate

Example 2 · Classification of Elements and Periodicity · Atomic and Ionic Radii

The correct order of increasing ionic radii is

Isoelectronic does not mean the same size

\mathrm{O^{2-}}

and

\mathrm{Mg^{2+}}

both have 10 electrons, but Mg has 12 protons against oxygen's 8. The claim that their radii are equal is false even though the reason (both are isoelectronic) is true.

Isoelectronic ions have different nuclear charges

The whole point of the series is that Z changes while the electron count does not. A statement that

\mathrm{O^{2-}}

\mathrm{F^-}

\mathrm{Na^+}

and

\mathrm{Mg^{2+}}

have the same nuclear charge is false.

Drill 8 more on ionic radius and isoelectronic series

Concept 3 of 3: Counting electrons to find isoelectronic species

Two species are isoelectronic when they carry the same number of electrons, whatever their nuclei. Count each one from Z and the charge, and the groups sort themselves out. Neutrons come from the mass number and play no part in being isoelectronic.

Definition

Electrons = $Z - q$ : subtract a positive charge, add a negative one.
Neutrons = $A - Z$ .
Common 10-electron set: $\mathrm{N^{3-}}$ , $\mathrm{O^{2-}}$ , $\mathrm{F^-}$ , Ne, $\mathrm{Na^+}$ , $\mathrm{Mg^{2+}}$ , $\mathrm{Al^{3+}}$ .
Common 18-electron set: $\mathrm{P^{3-}}$ , $\mathrm{S^{2-}}$ , $\mathrm{Cl^-}$ , Ar, $\mathrm{K^+}$ , $\mathrm{Ca^{2+}}$ , $\mathrm{Sc^{3+}}$ .
Hydrogen isotopes: protium (0 neutrons), deuterium (1) and tritium (2); only tritium is radioactive.

Counting particles

e^{-} = Z - q \qquad n = A - Z

qcharge on the species, with its sign
Amass number

Worked example

For the ion

^{31}_{15}\mathrm{P^{3-}}

, find the protons, neutrons and electrons. Which of Ne,

\mathrm{Na^+}

, Ar and

\mathrm{S^{2-}}

are isoelectronic with it?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2023 · 1 February 2023 · Q139Moderate

Example 3 · Classification of Elements and Periodicity · Atomic and Ionic Radii

Which one of the following sets of ions represents a collection of isoelectronic species? (Given: Atomic Number : F: 9, Cl: 17,

Na = 11,Mg = 12,Al = 13,\text{ }K = 19,Ca = 20,Sc = 21

)

A neutral atom is not its ion

Na has 11 electrons and

\mathrm{Na^+}

has 10. In a list that mixes atoms and ions, count each one separately: Al and Mg are not in the 10-electron set, while

\mathrm{Al^{3+}}

and

\mathrm{Mg^{2+}}

are.

Drill 4 more on counting electrons to find isoelectronic species

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Counting electrons to find isoelectronic species
Counting particles
$e^{-} = Z - q \qquad n = A - Z$

Reference tables (2)

Atomic radius across a period and down a group5 rows

Series	Atomic radius (pm)	Trend
Period 2	Li 152, Be 111, B 88, C 77, N 74, O 66, F 64	Falls steadily across
Period 3	Na 186, Mg 160, Al 143, Si 117, P 110, S 104, Cl 99	Falls steadily across
Group 1	Li 152, Na 186, K 231, Rb 244, Cs 262	Rises down the group
Group 17	F 64, Cl 99, Br 114, I 133, At 140	Rises down the group
Period 4 ends	K 231, Br 114	Largest and smallest in period 4, noble gas excluded

Compare the columns: Be (111) is smaller than Mg (160) and Mg is larger than Al (143).

Ionic radius and isoelectronic series9 rows

Species	Protons	Electrons	Radius (pm)
Na atom	11	11	186
$\mathrm{Na^+}$	11	10	102
Cl atom	17	17	99
$\mathrm{Cl^-}$	17	18	184
$\mathrm{O^{2-}}$	8	10	140 Isoelectronic with $\mathrm{Mg^{2+}}$ (72 pm), yet about twice as large: the same electrons do not mean the same size.
$\mathrm{F^-}$	9	10	133
$\mathrm{Mg^{2+}}$	12	10	72
$\mathrm{Al^{3+}}$	13	10	53.5
$\mathrm{K^+}$	19	18	138

Within the 10-electron rows, every extra proton makes the ion smaller.

Watch out for (5)

Half the bond, not double
→ Atomic radius across a period and down a group
Down a group beats across a period
→ Atomic radius across a period and down a group
Isoelectronic does not mean the same size
→ Ionic radius and isoelectronic series
Isoelectronic ions have different nuclear charges
→ Ionic radius and isoelectronic series
A neutral atom is not its ion
→ Counting electrons to find isoelectronic species

Test yourself on Classification of Elements and Periodicity

20 past JEE Mains questions from this chapter, timed at 48 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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