Properties of Solids

ChemistrySolid StateFor JEE aspirants

The properties of solids covered here are electrical, magnetic and dielectric. Band theory explains why metals conduct, why insulators do not, and why semiconductors such as silicon conduct better when heated or doped (n-type and p-type). Unpaired electrons make solids diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic or ferrimagnetic, depending on how their moments line up. These properties of solids were part of the old NCERT Solid State chapter. They are no longer in the JEE Main, NEET or JEE Advanced syllabus, so this page is for boards and background reading.

On this page1Conductivity ranges2Band theory3Semiconductors4Doping: n and p5Semiconducting compounds6Magnetic moments7Five magnetic classes8Dielectric properties

Key Formulas - Quick Reference

★ Must learn Conductivity ( $Ω^{- 1} m^{- 1}$ ): conductors $1 0^{4}$ to $1 0^{7}$ ; semiconductors $1 0^{- 6}$ to $1 0^{4}$ ; insulators $1 0^{- 20}$ to $1 0^{- 10}$ .
★ Must learn Band gap $E_{g}$ : metals none (bands overlap or partly filled); semiconductors small (Si 1.1 eV, Ge 0.7 eV); insulators large (diamond about 5.5 eV).
★ Must learn Metals: $σ$ falls as $T$ rises. Semiconductors: $σ$ rises as $T$ rises.
★ Must learn n-type: group-15 dopant (P, As) in Si/Ge, electrons carry current. p-type: group-13 dopant (B, Al, Ga), holes carry current.
Spin-only magnetic moment $μ = n (n + 2)$ BM ( $n$ = unpaired electrons); $1 μ_{B} = 9.27 \times 1 0^{- 24}$ A m $^{2}$ .
Magnetic classes: dia (no unpaired e), para (random), ferro (parallel), antiferro (antiparallel, cancel), ferri (antiparallel, unequal).
Ferromagnet → paramagnet above the Curie temperature $T_{C}$ .

1. Electrical Conductivity of Solids

Solids show an enormous range of electrical conductivity, from about $1 0^{- 20}$ to $1 0^{7} Ω^{- 1} m^{- 1}$ . By this measure they fall into three classes.

Figure 1: Solids span about 27 orders of magnitude in conductivity. The ranges follow NCERT: insulators

1 0^{- 20}

1 0^{- 10}

, semiconductors

1 0^{- 6}

1 0^{4}

, metallic conductors

1 0^{4}

1 0^{7} Ω^{- 1} m^{- 1}

Conductors: $1 0^{4}$ to $1 0^{7} Ω^{- 1} m^{- 1}$ . Metals such as Cu, Ag, Al.
Insulators: $1 0^{- 20}$ to $1 0^{- 10} Ω^{- 1} m^{- 1}$ . Glass, wood, diamond, most ionic solids.
Semiconductors: $1 0^{- 6}$ to $1 0^{4} Ω^{- 1} m^{- 1}$ . Si, Ge, GaAs.

In metals the current is carried by electrons (electronic conduction). In ionic solids it is carried by ions, but only when the ions can move, that is in the molten state or in solution (ionic conduction).

2. Band Theory

In a solid, the atomic orbitals of a huge number of atoms combine to form bands of molecular orbitals so closely spaced that they form a continuum of energy. The highest band containing the valence electrons is the valence band (VB); the next higher band is the conduction band (CB). The energy between them is the forbidden gap $E_{g}$ .

Figure 2: Band theory explains conduction. Electrons move only in a band with empty levels. The size of the forbidden gap

E_{g}

between the valence band and the conduction band decides the class of solid.

Conductor: the valence band is only partly filled, or it overlaps the empty conduction band. Electrons flow into empty levels easily under a field.
Insulator: a large gap separates a completely filled VB from an empty CB. No electron can cross, so no current flows.
Semiconductor: the gap is small. At room temperature a few electrons jump to the CB; each leaves behind a hole in the VB. Both carry current.

Figure 3: Opposite trends. Heating a metal makes its ions vibrate more and scatter electrons, so

σ

falls. Heating a semiconductor lifts more electrons across the band gap, so

σ

rises steeply.

Metal

No gap. Many free electrons at all temperatures. Heating increases ion vibrations, which scatter electrons: conductivity decreases with temperature.

Semiconductor

Small gap. Few carriers at room temperature. Heating lifts more electrons across the gap: conductivity increases steeply with temperature.

Key idea

The size of the band gap sorts solids into conductors, semiconductors and insulators.

Quick Recall: tap to check

Why does the conductivity of a metal fall on heating?

Stronger lattice vibrations scatter the moving electrons more.

What is a hole?

The vacancy left in the valence band when an electron moves to the conduction band; it behaves as a positive carrier.

Why is diamond an insulator but graphite a conductor?

Diamond has a large band gap (about 5.5 eV); graphite has a delocalised electron in each layer and its bands touch.

3. Intrinsic and Extrinsic Semiconductors

Figure 4: In pure silicon, thermal energy breaks a few Si-Si bonds. Each break gives one mobile electron and one hole, so the numbers of both carriers are equal.

Pure silicon or germanium is an intrinsic semiconductor: its small conductivity comes only from electrons and holes produced thermally, in equal numbers. It is far too small for practical use. Adding a tiny amount of a suitable impurity (doping, about 1 atom in $1 0^{6}$ to $1 0^{8}$ ) raises the conductivity enormously. Doped silicon is an extrinsic semiconductor.

3.1 n-type semiconductors

Figure 5: n-type. A group-15 atom (P, As) uses 4 electrons in bonding; its 5th electron is loosely held and conducts. Charge carriers are mainly electrons (negative, hence n).

Silicon and germanium are in group 14 and have 4 valence electrons, each used in a bond to a neighbour. A group-15 atom (P, As) has 5 valence electrons. Four form bonds; the fifth is loosely bound and becomes free to conduct. The extra carriers are electrons, which are negative, so this is an n-type semiconductor.

3.2 p-type semiconductors

Figure 6: p-type. A group-13 atom (B, Al, Ga) has only 3 valence electrons, so one bond lacks an electron: a hole. Electrons from neighbouring bonds hop into it, so the hole moves like a positive charge (hence p).

A group-13 atom (B, Al, Ga) has only 3 valence electrons. One of its four bonds lacks an electron: an electron hole. An electron from a neighbouring bond can move into the hole, leaving a hole where it came from. The hole therefore moves through the crystal as if it were a positive charge; under a field, electrons move towards the positive plate through holes and the holes appear to move towards the negative plate. This is a p-type semiconductor.

Exam Trick Count to four. Silicon wants 4. Dopant with 5 (group 15): one electron too many, negative carriers, n-type. Dopant with 3 (group 13): one electron short, a hole, positive carriers, p-type.

Combining n-type and p-type layers gives the devices of modern electronics: diodes (p-n junctions, used as rectifiers), transistors (npn and pnp, used to amplify and switch), photodiodes and solar cells.

3.3 Semiconducting compounds

Compounds made from elements on either side of group 14 mimic its average of 4 valence electrons.

Type	Combination	Examples
13-15 compounds	group 13 + group 15	InSb, AlP, GaAs (fast electronics, LEDs)
12-16 compounds	group 12 + group 16	ZnS, CdS, CdSe, HgTe

The bonds in these compounds are not perfectly covalent: the difference in electronegativity gives them partial ionic character. Some transition-metal oxides also show striking electrical behaviour: TiO, CrO $_{2}$ and ReO $_{3}$ conduct like metals (ReO $_{3}$ looks like copper); VO, VO $_{2}$ , VO $_{3}$ and TiO $_{3}$ change from metallic to insulating with temperature.

JEE Advanced Why does a donor level sit just below the conduction band? The fifth electron of phosphorus is held only by the single extra positive charge of the P nucleus, screened by the silicon crystal around it, so its binding energy is tiny, about 0.045 eV in Si. At room temperature (

k T \approx 0.026

eV) almost every donor is ionised. Acceptor levels of B lie a similar small energy above the valence band. This is why doping at parts per million changes conductivity by factors of thousands.

Key idea

Doping creates carriers: group 15 → electrons (n-type), group 13 → holes (p-type).

Quick Recall: tap to check

Germanium is doped with gallium. What type of semiconductor forms?

p-type (Ga is in group 13).

Silicon is doped with arsenic. What are the majority carriers?

Electrons: n-type.

Why is an n-type semiconductor still electrically neutral?

Each extra electron is balanced by the extra proton in the donor nucleus.

4. Magnetic Properties

Every electron behaves like a tiny magnet, for two reasons: its orbital motion round the nucleus (a small current loop) and its spin about its own axis. The unit of magnetic moment is the Bohr magneton, $μ_{B} = 9.27 \times 1 0^{- 24}$ A m $^{2}$ . Paired electrons have opposite spins and cancel, so only unpaired electrons give a solid a net moment.

Figure 7: Each electron is a tiny magnet, from its orbital motion and its spin. Paired electrons cancel; unpaired electrons give a net moment, measured in Bohr magnetons

μ_{B}

μ_{spin only} = n (n + 2) μ_{B}

where $n$ is the number of unpaired electrons. Depending on the moments and how they are arranged, solids fall into five classes.

Figure 8: How the atomic magnets line up decides the class. Only ferromagnets and ferrimagnets keep a net moment without a field, and only ferromagnets have all moments parallel.

Class	Moments	Behaviour in a field	Examples
Diamagnetic	all electrons paired	weakly repelled	$H_{2} O$ , NaCl, $C_{6} H_{6}$ , $Ti O_{2}$
Paramagnetic	unpaired, random	weakly attracted; no permanent magnetism	$O_{2}$ , $C u^{2 +}$ , $F e^{3 +}$ , $C r^{3 +}$
Ferromagnetic	unpaired, all parallel in domains	strongly attracted; permanent magnets	Fe, Co, Ni, Gd, $Cr O_{2}$
Antiferromagnetic	antiparallel, equal	net moment zero	MnO
Ferrimagnetic	antiparallel, unequal	net moment; weaker than ferro	$F e_{3} O_{4}$ , $MgF e_{2} O_{4}$ , $ZnF e_{2} O_{4}$ (ferrites)

4.1 Domains and the effect of temperature

Figure 9: A ferromagnet is made of domains, regions in which all moments are already parallel. In a strong field the domains line up and stay aligned when the field is removed, making a permanent magnet.

In the solid state, the metal ions of a ferromagnet group into small regions called domains, each acting as a tiny magnet. In an unmagnetised piece the domains point randomly and cancel. In a strong magnetic field they all line up with the field, and they stay aligned when the field is removed: the substance becomes a permanent magnet. $Cr O_{2}$ is used in audio and video cassette tapes for this reason.

Figure 10: Heat fights alignment. A paramagnet's susceptibility falls as

1/ T

. A ferromagnet loses its spontaneous magnetisation at the Curie temperature

T_{C}

(Fe 1043 K) and becomes paramagnetic;

F e_{3} O_{4}

(ferrimagnetic) does so at about 850 K.

Ferromagnetic and ferrimagnetic solids become paramagnetic on heating, because thermal motion randomises the moments. For ferromagnets the transition occurs at the Curie temperature.
$F e_{3} O_{4}$ is ferrimagnetic at room temperature and becomes paramagnetic at about 850 K.
The susceptibility of a paramagnet falls with temperature ( $χ = C / T$ ).

Figure 11: Three questions classify any magnetic solid: are there unpaired electrons, are their moments ordered, and how are they lined up?

Exam Trick Ferri = ferro with a handicap. Both give a net moment, but in a ferrimagnet the antiparallel moments are unequal, so part of the magnetisation cancels. Antiferro is the full cancel: equal and opposite.

Key idea

Unpaired electrons + alignment decide the magnetic class; heating destroys alignment.

Quick Recall: tap to check

Why is MnO antiferromagnetic?

The moments of neighbouring

M n^{2 +}

ions point in opposite directions and are equal, so they cancel.

Spin-only moment of

F e^{3 +}

(

3 d^{5}

5 \times 7 = 5.92

BM.

What happens to a ferromagnet above its Curie temperature?

It becomes paramagnetic.

5. Dielectric Properties

In an insulator, electrons are held tightly and cannot flow, but an electric field can separate the centres of positive and negative charge, forming dipoles. How these dipoles are arranged gives special properties.

Piezoelectricity: in some crystals the dipoles cancel only partly, and pressure changes their net polarity, producing a voltage. Quartz and Rochelle salt are used in lighters, gas igniters, record-player pick-ups and sensors. Applying a voltage conversely makes the crystal change shape.
Pyroelectricity: some polar crystals produce a voltage when heated.
Ferroelectricity: the dipoles are permanently aligned in one direction even without a field, and the direction can be reversed by a field. Examples: $BaTi O_{3}$ , $K H_{2} P O_{4}$ , Rochelle salt.
Antiferroelectricity: neighbouring dipoles are aligned in opposite directions and cancel. Example: $PbZr O_{3}$ .

Key idea

Dielectric solids have no free charges, but their dipoles respond to pressure, heat and fields.

5.1 The whole concept at a glance

Figure 12: Electrical, magnetic and dielectric properties on one page.

6. Solved Examples

Solved Example 1

Classify each doped semiconductor as n-type or p-type: (a) Ge doped with In, (b) Si doped with B, (c) Si doped with P, (d) Ge doped with As.

Solution:

(a) p-type (In is group 13). (b) p-type. (c) n-type (P is group 15). (d) n-type.

Solved Example 2

Which of the following will become a p-type semiconductor when added to silicon?
(A) As
(B) Sb
(C) Ga
(D) P

Solution:

Answer: (C). Gallium has 3 valence electrons, one fewer than silicon, so it creates holes. As, Sb and P are group 15 and give n-type.

Solved Example 3

Explain why the conductivity of silicon increases while that of copper decreases on heating.

Solution:

In silicon, heating supplies energy to lift more electrons across the band gap into the conduction band, creating more electrons and holes, so conductivity rises. In copper the number of free electrons is already huge and does not change; heating only makes the ions vibrate more, which scatters electrons, so conductivity falls.

Solved Example 4

Calculate the spin-only magnetic moments of

F e^{3 +}

(

Z = 26

) and

C u^{2 +}

(

Z = 29

Solution:

$F e^{3 +}$ is $3 d^{5}$ : $n = 5$ , $μ = 5 \times 7 = 35 = 5.92$ BM.

$C u^{2 +}$ is $3 d^{9}$ : $n = 1$ , $μ = 1 \times 3 = 1.73$ BM.

Solved Example 5

Which of these is ferrimagnetic?
(A) MnO
(B)

F e_{3} O_{4}

(C)

Cr O_{2}

(D)

Ti O_{2}

Solution:

Answer: (B). In magnetite the antiparallel moments on tetrahedral and octahedral sites are unequal. MnO is antiferromagnetic, $Cr O_{2}$ ferromagnetic and $Ti O_{2}$ diamagnetic.

Solved Example 6

A magnetic solid has its domains aligned as ↑↓↑↓↑↓ with all moments equal. What type of magnetism does it show, and what is its net moment?

Solution:

Antiferromagnetism. Equal and opposite moments cancel, so the net moment is zero.

Solved Example 7

Why is a crystal of

BaTi O_{3}

called ferroelectric while

PbZr O_{3}

is antiferroelectric?

Solution:

In $BaTi O_{3}$ the $T i^{4 +}$ ions sit slightly off-centre in their oxide octahedra in the same direction throughout a region, so the dipoles are permanently aligned and the crystal is polarised even without a field. In $PbZr O_{3}$ neighbouring dipoles point in opposite directions and cancel.

Practice Questions

Name the charge carriers in (a) an n-type and (b) a p-type semiconductor.Answer: (a) electrons, (b) holes.
Silicon is doped with aluminium. What type of semiconductor results?Answer: p-type.
Give one 13-15 and one 12-16 semiconducting compound.Answer: GaAs (or InSb, AlP); CdS (or ZnS, CdSe).
Spin-only magnetic moment of $M n^{2 +}$ ( $3 d^{5}$ )?Answer: $5.92$ BM.
Which is used in audio cassette tapes and why?Answer: $Cr O_{2}$ ; it is ferromagnetic and retains magnetisation.
What happens to $F e_{3} O_{4}$ above about 850 K?Answer: It becomes paramagnetic.
Name the property used in gas lighters with quartz crystals.Answer: Piezoelectricity.

Common Mistakes to Avoid

Watch out

Saying metals conduct better when heated. Their conductivity falls; semiconductors conduct better.
Calling Si doped with B n-type. Group 13 dopants give p-type; group 15 dopants give n-type.
Thinking a doped semiconductor carries a net charge. It stays neutral.
Treating holes as real particles. A hole is the absence of an electron that behaves like a positive charge.
Confusing ferrimagnetic with antiferromagnetic. Ferri has unequal antiparallel moments and a net moment; antiferro cancels completely.
Saying a paramagnet stays magnetised after the field is removed. Only ferro- and ferrimagnets do.
Writing that ionic solids conduct in the solid state. They conduct only when molten or dissolved.
Assuming these topics are in the JEE Advanced syllabus. They were dropped with the NCERT rationalisation.

Frequently Asked Questions

What is band theory of solids?

Band theory says that the orbitals of many atoms in a solid merge into bands of closely spaced energy levels. The valence band holds the bonding electrons and the conduction band lies above it. The gap between them decides whether a solid is a conductor, a semiconductor or an insulator.

What is the difference between n-type and p-type semiconductors?

An n-type semiconductor is made by doping silicon or germanium with a group 15 element such as phosphorus; the extra electron carries current. A p-type semiconductor is made with a group 13 element such as boron; the missing electron creates a hole that carries current like a positive charge.

Why does the conductivity of a semiconductor increase with temperature?

Heating gives electrons in the valence band enough energy to jump across the small band gap into the conduction band. Each jump creates a free electron and a hole, so the number of charge carriers, and hence the conductivity, rises.

What are ferromagnetic and ferrimagnetic substances?

In ferromagnetic substances such as iron, cobalt, nickel and CrO2, all the magnetic moments in a domain point the same way, giving strong permanent magnetism. In ferrimagnetic substances such as Fe3O4 and ferrites, moments point in opposite directions but are unequal, so a smaller net moment remains.

What is antiferromagnetism?

In an antiferromagnetic solid such as MnO, the magnetic moments of neighbouring ions are equal and point in opposite directions. They cancel each other, so the solid has no net magnetic moment.

What is piezoelectricity?

Piezoelectricity is the production of an electric voltage when certain crystals, such as quartz and Rochelle salt, are pressed or stretched. It is used in gas lighters, sensors and ultrasonic devices.

Are electrical and magnetic properties of solids in the NEET or JEE syllabus?

No. They were removed from NCERT in the 2023 rationalisation, and the whole Solid State chapter left NEET and JEE Main from 2024. JEE Advanced 2026 covers only structure and point defects under Solid State, not electrical or magnetic properties.

Where are semiconductors used?

Semiconductors are used in diodes, transistors, integrated circuits, solar cells, light-emitting diodes and photodiodes. n-type and p-type layers joined together form the p-n junction on which most of these devices are built.

Previous year questions on Properties of Solids

1 question from past papers, each with a step-by-step solution.

JEE Main 2025 Jan 28 Shift 1, Chemistry Q9

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