Category: Maharashtra State Board Notes

By going through these Maharashtra State Board 12th Science Chemistry Notes Chapter 8 Transition and Inner Transition Elements students can recall all the concepts quickly.

Maharashtra State Board 12th Chemistry Notes Chapter 8 Transition and Inner Transition Elements

d – Series :

• 3d-Series : ₂₁Sc to ₃₀Zn
• 4d-Series: ₃₉Y to ₄₈Cd
• 5d-Series : ₅₇La to ₈₀Hg
• 5d-Series : ₈₉Ac to ₁₁₂Cn

Electronic Configuration :

• 3d-Series: [Ar] 3d^1-10 4s^1-2
• 4d-Series:[Kr] 4d^1-10 5s^1-2
• 5d-Series: [Xe] 4f¹⁴ 5d^1-10 6s^1-2
• 6d- Series: [Rn] 5f¹⁴ 6d^1-10 7s^1-2

For 3d-Series :

• Atomic radii decrease from Sc to Cu
• Ionic radii decrease from Sc to Ni
• First ionisation enthalpy increases from Sc to Zn.

Transition elements show variable oxidation states common being + 2.

1 Bohr Magneton (B.M) = \(\frac{e h}{4 \pi m_{\mathrm{e}} c}\)

Spin only formula : \(\mu=\sqrt{n(n+2)}\)

KMnO₄

Preparation from MnO₂

Strong oxidising agent

• in acidic medium
• in neutral or weakly alkaline medium

K₂Cr₂O₇ :

Preparation from chromite ore :

Metallurgy :

1. Metal extraction processes –

• Pyrometallurgy
• Hydrometallurgy
• Electrometallurgy

2. Steps involved in the extraction of pure metal-

• Concentration
• Conversion of an ore into oxides
• Reduction of an ore
• Refining of metals

3. Extraction of iron from haematite ore by Blast furnace

f-Block elements :

Lanthanoids : _{5 8}Ce to _{7 1}Lu
Actinoids : _{9 0}Th to _{1 0 3}Lr

Electronic configuration :

Lanthanoids : [Xe] 4f^1-14 5d^0-1 6s²
Actinoids : [Rn] 5f^1-14 6d^0-1 7s²

Position in periodic table :

Lanthanoid contraction, Actinoid contraction

By going through these Maharashtra State Board 12th Science Chemistry Notes Chapter 7 Elements of Groups 16, 17 and 18 students can recall all the concepts quickly.

Maharashtra State Board 12th Chemistry Notes Chapter 7 Elements of Groups 16, 17 and 18

Atomic, physical and chemical properties of group 16,17 and 18 elements-

Group 16 elements-

O to Po:

• Atomic size, M.P., B.P., Density increase
• Ionisation enthalpy, electronegativity decrease
• Hydrides (H₂X) : Bond angle, bond energy decrease Reducing power increases
• Oxides (EO₂, EO₃) (E = S, Se, Te, Po)
• Halides (EX₆, EX₄, EX2) (E = S, Se, Te)
• Reacts with metals to form compounds

Allotropes :

• O : O₂, O₃ (Ozone)
• S : Rhombic, monoclinic, cyclo-S6
• Se : red, grey
• Te : Crystalline, amorphous
• Po : α, β

Group 17 elements-

F to I (At):

• Atomic size, Density increase
• Ionisation enthalpy, electronegativity decrease
• (Haloacids, HX) : Acidity, reducing character increase Stability decrease
• Oxides of halogens (Most of them are unstable)
• Interhalogen compounds
• Metal halides

Group 18 elements-

He to Xe (Rn):

• Atomic size, density, M.P., B.P., increase
• Ionisation enthalpy, decreases
• Chemically inert towards hydrogen, oxygen
• krypton and Xenon form fluorides

Oxoacids of sulphur-

Oxoacids of halogens-

O₂ – Preparation –

O₂ –
2Ca + O₂ → 2CaO
C + O₂ → CO₂

Simple oxides-

Acidic (CO₂, SO₂, etc.)
Basic (CaO, BaO, etc.)
Amphoteric (Al₂O3, Zno, etc.)

Ozone –

Oxidising property: (i) PbS_(S) + 4O_3(g) → PbSO₄ + 4O_2(g)
(ii) 2KI + H₂O +O₃ →2KOH + I₂ + O₂
(iii) NO_(g) + O_3(g) → NO_2(g) + O_2(g)
Bleaching property O₃ → O + O₂
Reducing property : BaO₂ + O₃ → BaO + 2O₂
H₂O₂ + O₃ → H₂O + 2O₂

SO₂ – preparation

S_(S) + O_2(g) → SO_2(g)
Na₂SO₃ + H₂SO_4(aq) → Na₂SO₄ + H₂O_(I) + SO_2(g)

SO₂ –

2NaoH + SO₂ → Na₂SO₃ + H₂O
Na₂SO₃ + H₂O + SO₂ → 2NaSO₃
2Fe³⁺ + SO₂ + 2H₂O → 2Fe²⁺ + SO₄ ^2- + 4H⁺

H₂SO₄ (Manufacture)—Contact process—(Catalyst V₂O₅)

H₂SO₄ – 

C + 2H₂SO₄ → CO₂ + 2H₂O + 2SO₂
S + 2H₂SO₄ → 3SO₂ + 2H₂O
Cu + 2H₂SO₄ → CuSO₄ + SO₂ + 2H₂O

NaCl + H₂SO₄ → NaHSO₄ + HCl
KNO₃ + H₂SO₄ → KHSO₄ + HNO₃
CaF₂ + H₂SO₄ → CaSO₄ + 2HF

Chlorine Preparation –

MnO₂ + 4HCl → MnCl₂ + Cl₂ + 2H₂O
4NaCl + MnO₂ + 4H₂SO₄ → 4NaHSO₄ + MnCl₂ + 2H₂O + Cl₂

NaCl ⇌ Na⁺ + Cl^–

Cl₂ –

2Al + 3Cl₂ → 2AlCl₃
P₄ + 6Cl₂ → 4PCl₃
H₂ + Cl₂ → 2HCl
8NH₃ (Excess) + 3Cl₂ → 6NH₄Cl + N₂
2Ca(OH)₂ + 2Cl₂ → Ca(OCl)₂ + CaCl₂ + 2H₂O

2FeSO₄ + H₂SO₄ + Cl₂ → Fe₂(SO₄)₃ + 2HCl
Cl₂ + H₂O → HCl + HOCl

HCl : Preparation –

HCl –

HCl_(g) + H₂O_(l) → H₃O⁺ + Cl^–(aq)
NH₃ + HCl → NH₄Cl
Au + 4H⁺ + NO^–₃ + 4Cl^– → AuCl^–₄ + NO + 2H₂O

Interhalogen Compounds-

Compounds of Xenon-

By going through these Maharashtra State Board Class 11 Political Science Notes Chapter 10 The World Since 1945 – II students can recall all the concepts quickly.

Maharashtra State Board Class 11 Political Science Notes Chapter 10 The World Since 1945 – II

Introduction:

This chapter deals with international relations from 1959 to 1991. We will study the Non-Aligned Movement, efforts at detente, SAARC, the collapse of the Soviet Union, and the role played by Mikhail Gorbachev in the new world order.

Developments (1959 – 1991)

Phase 1959 – 1962 (Shifts in the Cold War) –
In spite of attempts to create goodwill between the two power blocs (such as at Camp David Summit), tensions continued to escalate. In 1961, USSR began erecting the Berlin Wall due to which people couldn’t travel between East and West Berlin. In 1962, the first direct confrontation of the Cold War took place. This was the Cuban Missile Crisis.

Cuba is a small nation off the coast of the USA. It had the support of the USSR. Due to its’ strategic location, then Soviet Premier, Khrushchev, decided to convert it into a Soviet base by placing missiles there. This was a serious, direct threat to the USA which retaliated with a naval blockade of Cuba. There was a real possibility of a nuclear war. But, both the superpowers realized the need to prevent such a situation and USSR withdrew it’s missiles from Cuba.

Non Alignment

A group of Third World countries (i.e., from Asia, Africa, South America), most of whom had recently gained sovereignty from colonial rule, refused to join any Cold War alliances. This laid the foundation for the Non- Aligned Movement. It was formally established at the Belgrade Conference (1961) with 25 members. Some of the founding member leaders were Marshall Tito (Yugoslavia), Jawaharlal Nehru, (India), Gamal Nasser (Egypt), Nkrumah (Ghana), Sukarno (Indonesia), etc.

The concept of Non-alignment is based on two main principles

• independent understanding of the world affairs
• peace approach. Thus it does not mean political passivity or neutrality. In fact, the idea was active participation in world affairs to promote peace and development.

The purpose of the NAM was

• not to ally with any power bloc
• opposition to any military alliance
• freedom to take independent policy decisions with regard to international affairs.

NAM has helped the Third World countries to gain economic and political rights. Today it has 120 members countries and 17 observer countries. It is headed by a Secretary General. The 17th NAM summit was held in Venezuela in September 2016 while 18th summit (2019) will be held in Azerbaijan.

Phase 1962 – 1972 (Foundations Of Detente)

After the Cuban Missile Crisis, both the USA and the USSR made several efforts at reducing bilateral tensions (detente). This included —

• a hot line was set up between main leaders of the two nations.
• signing of agreements such as N.N.P.T., L.T.B.T. to reduce nuclear weapons.
• In 1972 the Moscow Summit between President Nixon (USA) and Brezhnev (USSR).

USA had not recognized the Chinese government since 1949. But in 1972, President Nixon visited China and thus recognized the Communist regime of Mao Zedong.

Phase 1972 – 1979 (Detente)

Some of the initiatives taken by the superpowers to bring about detente included –

• Conference at Paris (1973) to bring the Vietnam crisis to an end.
• Helsinki conference on security in Europe (1975) was attended by 35 nations including USA and USSR. It aimed to reduce the tensions between Eastern and Western European countries.
• The first joint US-Soviet space flight was the Apollo Soyuz Test project (1975)
• The USA held a conference at Camp David in 1978 to resolve the long pending Arab-Israel dispute. The ‘Framework for Peace in the Middle East’ was signed between President Carter (USA), President Sadat (Egypt) and Prime Minister Begin (Israel).

Other Significant developments include in this period.

• Arab – Israel War (1973) and increase in the price of oil all over the world.
• Demand by non-aligned counties for New International Economic Order (NIEO)
• Growing importance of economic issues in international relations and increasing demands put forward by Third World nations.
• North-South world divide i.e. between rich nations of the Northern Hemisphere in Europe and North America and Southern Hemisphere nations of Asia, Africa, South America.
• Period of economic interdependence, signing of “Free Trade” agreements and establishing of ‘trade blocs’ such as NAFTA.

Phase 1979 – 1985 (New Cold War)

Two events that occurred in 1979 changed the course of detente

• Islamic Revolution in Iran under leader Ayatollah Khomeini overthrew the rule of M.R. Shah Pahlavi. The new government withdrew from the CENTO alliance.
• Soviet Union invaded Afghanistan in 1979 and installed Babrak Karmal as the President. The insurgent groups in Afghanistan (mujahideen) fought against this government (1979 – 1989).

New Cold War refers to the end of the period of detente and return of tensions between USA and USSR.

Phase 1985 – 1991 (Gorbachev Era)

There were significant changes in the Soviet policy under Mikhail Gorbachev (President of USSR). He introduced the policies of Glasnost and Perestroika.

His new foreign policy included (i) withdrawal of Soviet troops from Afghanistan, (ii) stopping of the arms race with US and focus on arms control (iii) opening up a dialogue with China.

Gorbachev also tried to reform Soviet domestic politics. The control of Communist Party ended and people were given the right to criticize the government. On 25th December, 1991, Gorbachev resigned and the next day the USSR as a country ceased to exist.

The Commonwealth of Independent States (CIS) came into existence and finally new countries were formed such as Ukraine, Belarus, Georgia, Armenia, etc.

Other changes due to the disintegration of Soviet Union include

• Reunification of Germany in 1990.
• Splitting of Czechoslovakia into Slovakia and Czech Republic
• Splitting of Yugoslavia into Serbia, Bosnia, Croatia, Slovenia, etc.

The disintegration of the USSR signified the end of the Cold War and USA emerged as the only superpower (unipolarity). New organisations like WTO,EU,G-20, SAARC. BRICS started to play a role in world affairs. This is called multi polarity.

By going through these Maharashtra State Board Class 11 Political Science Notes Chapter 9 The World Since 1945 – I students can recall all the concepts quickly.

Maharashtra State Board Class 11 Political Science Notes Chapter 9 The World Since 1945 – I

Introduction

This chapter provides a survey of major world events since the end of the Second World War (1945 – 1959). The focus is on the U.N.O. i.e., its purposes, organs, etc, the Cold War i.e., it’s dimensions and phases and the establishment of military alliances. We will also study about Regionalism.

League Of Nations

The League of Nations was created after the First World War (1914 – 1918) to establish peace and stability in the world. However, it could not succeed in it’s objectives. The Second World War (1939 – 1945) had several consequences that became the foundation of the world order post 1945. Some of these changes are –

1. End of the primacy of Europe – European imperialism and colonialism had led it to enjoy a dominant position in the 19th century and early 20th century. The Second World War had seen the defeat of Germany, Italy and devastation in France and England. USA and USSR emerged as major powers and hence the world ceased to be ‘eurocentric’.

2. Division of Europe – During the Second world War, Soviet forces occupied parts of Eastern Europe e.g., Poland while Western Europe was occupied by UK, France, USA. By the end of the war, Europe was divided into East Europe and West Europe.

3. Role of Ideology – The Bolshevik Revolution in October 1917 established Communism in Russia. Hence, East European countries that were under Soviet influence also adopted communist ideology while West European countries mainly adopted the Capitalist ideology.

4. Establishment of United Nations Organization (UNO) on 24,h October, 1945. It was to replace the League of Nations. The main purpose of the UNO was to maintain international peace and security. It had six main organs viz. General Assembly, Security Council, ECOSOC, Trusteeship Council (suspended operations in 1994), International Court of Justice, Secretariat (headed by a Secretary- General). The UNO has 193 members at present.

5. Rise of Asia – Asia and Africa witnessed many anti-colonial struggles for self-determination, leading to many sovereign nations being created e.g., Indonesia, India, etc.

Cold War

In the Second World War, the allied forces led by USA. USSR and UK had defeated the Axis Powers consisting of Germany, Italy and Japan. The end of the war led to the emergence of USA and USSR as “super powers” with superior military technology. The east-west division of Europe led to tensions between the USA and USSR. The hostile relations between the USA and its’ allies and the USSR and its’ allies along with ideological conflict between them is called the ‘Cold War’ or Bipolarity. The dimensions of the cold war included —

• Political dimension – Areas under U.S. influence included UK, France, Spain, Italy, Netherlands, West Germany, etc. while areas under Soviet influence were Poland, Czechoslovakia, Bulgaria, East Germany, etc.
• Ideological dimension – Allies of the US had democratic governments and adopted capitalist ideology while countries under Soviet influence lacked democracy and followed a socialist ideology.
• Economic dimension – In the capitalist countries, private sector and profit making were significant while in the socialist bloc, public sector and welfare state were considered significant.
• Security dimension – A number of military alliances were created by both groups such as NATO by the USA and Warsaw Pact by the USSR.

Phases Of The Cold War (1945 – 1959)

Phase I (1945 – 1950) .
In this formative phase of the Cold War, the focus was on the ideological, military, political and economic division of Europe (East – West division). NATO was created. In 1947, the first Asian Relations Conference (25 nations) was held in New Delhi.

Phase II (1950 – 1959)

• In 1949, China adopted communism under chairman Mao Zedong and in 1950 it signed a military alliance with USSR.
• The Korean War was the first proxy war of the Cold War. In 1945, Korea was divided along the 38th parallel into North and South Korea. In June 1950, North Korea invaded South Korea. The North was helped by China and USSR while UN sent in armed forces to defend South Korea. The war ended in 1953, restoring the borders.
• Many military alliances were created in Asia such as SEATO (1954), CENTO (1955), etc.
• Warsaw Pact (1955) created by USSR had Albania, Romania, Bulgaria, East Germany, etc. as its members.
• In 1953, Nikita Khrushchev became leader of USSR. He brought in the policy of ‘peaceful co-existence’ between the two blocs of the Cold War.
• Growth of regionalism in Asia and Africa e.g., Bandung Conference (1955) had 24 participating nations of Asia and Africa.
• Camp David Summit (1959) between President Eisenhower (USA) and Khrushchev (USSR) was the first attempt at seeking a dialogue. It is a turning point in the history of the Cold War.

By going through these Maharashtra State Board 12th Science Chemistry Notes Chapter 6 Chemical Kinetics students can recall all the concepts quickly.

Maharashtra State Board 12th Chemistry Notes Chapter 6 Chemical Kinetics

→ For a reaction, aA + bB → cC + dD
Average rate = \(-\frac{1}{a} \frac{\Delta[\mathrm{A}]}{\Delta t}=-\frac{1}{b} \frac{\Delta[\mathrm{B}]}{\Delta t}=-\frac{1}{c} \frac{\Delta[C]}{\Delta t}=-\frac{1}{d} \frac{\Delta[\mathrm{D}]}{\Delta t}\)

→ Rate law : Rate = k [A]^a x [B]^b

→ k = \(\frac{2.303}{t}\) log₁₀ \(\frac{[\mathrm{A}]_{0}}{[\mathrm{~A}]_{\mathrm{t}}}\) (For first order reaction)

→ t_1/2 = \(\frac{0.693}{k}\) (For first order reaction)

→ k = \(\frac{[\mathrm{A}]_{0}-[\mathrm{A}]_{t}}{t}\) (For zero order reaction)

→ t_1/2 = \(\frac{[\mathrm{A}]_{0}}{2 k}\)(For zero order reaction)

→ k = Ae^-Ea/RT (Arrhenius equation)

→ log₁₀k =log₁₀A – \(\frac{E_{a}}{2.303 R \mathrm{~T}}\)

→ log₁₀\(\frac{k_{2}}{k_{1}}=\frac{E_{a}\left(T_{2}-T_{1}\right)}{2.303 R \times T_{1} \times T_{2}}\)

By going through these Maharashtra State Board 12th Science Chemistry Notes Chapter 5 Electrochemistry students can recall all the concepts quickly.

Maharashtra State Board 12th Chemistry Notes Chapter 5 Electrochemistry

→ Electrical conductance (G) = \(\frac{1}{R}\)Ω^-1 2 or S

→ Cell constant = \(\frac{l}{a}\) cm^-1 (m^-1)

→ Conductivity(k) = \(\frac{\text { Cell constant }}{\text { Resistance }}\)

→ Molar Conductivity(∧_m) = \(\frac{\kappa}{C}\) (k in Ω^-1 m^-1 and C in mol^-3) OR
∧_m = \(\frac{\kappa \times 1000}{C}\) (k in Ω^-1 cm^-1 and C in mol dm^-3)

→ Kohlrausch’s law : ∧₀ = \(\lambda_{+}^{0}+\lambda_{-}^{0}\)

→ Degree of dissociation (α) = \(\frac{\Lambda_{\mathrm{m}}}{\Lambda_{0}}\)

→ Dissociation constant (Ka) = \(\frac{\bigwedge_{\mathrm{m}}^{2} C}{\Lambda_{0}\left(\Lambda_{0}-\Lambda_{\mathrm{m}}\right)}\)

→ 1 Faraday = 96500 C (Change on one mole of electrons)

→ E°_cell = E°_red (cathode) – E°_red (anode)

→ E_Mⁿ⁺/M = E°_Mⁿ⁺/M – \(\frac{0.0592}{n}\) log₁₀[Mⁿ⁺]

→ E_cell = E°_cell – \(\frac{0.0592}{n} \log _{10} \frac{[\text { Products }]}{[\text { Reactants }]}\)

→ ΔG° = – nFE°_cell

→ ΔG = -nFE_cell

→ ΔG°= -RTlnK

→ E°_cell = \(\frac{0.0592}{n}\) log₁₀K
For spontaneous cell reaction : E_cell > 0; ΔG < 0

By going through these Maharashtra State Board 12th Science Chemistry Notes Chapter 4 Chemical Thermodynamics students can recall all the concepts quickly.

Maharashtra State Board 12th Chemistry Notes Chapter 4 Chemical Thermodynamics

→ W = -P (V₂ – V₁) = -PΔV (For expansion)

→ W = P (V₂ – V₁) = PΔV (For compression)

→ W_max = -2.303 nRT log₁₀ \(\frac{V_{2}}{V_{1}}\)

→ W_max= -2.303 nRT log₁₀ \(\frac{P_{1}}{P_{2}}\)

→ ΔU = q + W

→ H = U + PV

→ ΔH = ΔU + PΔV

→ ΔH = ΔU + ΔnRT

→ Hess’s law : ΔH = ΔH₁ + ΔH₂ + ΔH₃

→ ΔS = \(\frac{q_{\mathrm{rev}}}{T}=\frac{\Delta H}{T}\)

→ G = H – TS

→ ΔG = ΔH – TΔS

→ ΔG°= – 2.303 RTlog₁₀K

→ (i) ΔG = 0, the system is at equilibrium
(ii) ΔG < 0, the process is spontaneous
(iii) ΔG > 0, the process is non-spontaneous.

By going through these Maharashtra State Board 12th Science Chemistry Notes Chapter 3 Ionic Equilibria students can recall all the concepts quickly.

Maharashtra State Board 12th Chemistry Notes Chapter 3 Ionic Equilibria

→ Formulae on Ostwald’s dilution law:

→ K_w = [H₃O⁺] × [OH^–], at 25°C K_w = 1 × 10^-14

→ pH = -log₁₀[H⁺]; pOH = -log₁₀[OH^–]

→ pH + pOH = 14

→ Acidic buffer solution: pH = PK_a + log₁₀ \(\frac { [salt] }{ [acid] }\)

→ Basic buffer solution: pOH = pK_b + log₁₀ \(\frac { [salt] }{ [acid] }\)

→ PK_a = – log₁₀ K_a; pK_b = – log₁₀ K_b

→ Solubility product:

k_sp = (xs)^x (ys)^y = x^xy^y x (S)^x+y

By going through these Maharashtra State Board 12th Science Chemistry Notes Chapter 2 Solutions students can recall all the concepts quickly.

Maharashtra State Board 12th Chemistry Notes Chapter 2 Solutions

→ Henry’s law : S = K_HP

→ Raoult’s law : P_soln = x₁P₀

→ Mole fractions, x₁ + x₂ = 1

→ P_soln = P°₁x₁ + P°₂x₂

→ P_soln = (P°₂ – P°₁)x₂ + P°₁

→ Mole fractions of components in vapour phase : y₁ = \(\frac{x_{1} P_{1}^{0}}{P}\) and y₂ = \(\frac{x_{2} P_{2}^{0}}{P}\)

→ For ideal solutions : ΔV_mix = 0; Δ_mixH = 0

→ Relative lowering of vapour pressure = \(\frac{P^{0}-P}{P^{0}}\), x₂ = \(\frac{P^{0}-P}{P^{0}}\)

→ \(\frac{P^{0}-P}{P^{0}}=\frac{W_{2} \times M_{1}}{W_{1} \times M_{2}}\)

→ Δ T_b = K_b x m and Δ T_f — K_f x m

→ ΔT_b = K_b x \(\frac{W_{2} \times 1000}{W_{1} \times M_{2}}\)

→ ΔT_f = K_f x \(\frac{W_{2} \times 1000}{W_{1} \times M_{2}}\)

→ π = cRT and π = \(\frac{W R T}{M \times V}\)

→ i = \(\frac{Colligative property of electrolyte solution}{Colligative property of nonelectrolyte solution of the same concentration}\)

→ Van’t Hoff factor (i) = \(\frac{\Delta T_{\mathrm{b}(\mathrm{ob})}}{\Delta T_{\mathrm{b}(\mathrm{th})}}=\frac{\Delta P_{(\mathrm{ob})}}{\Delta P_{(\mathrm{th})}}=\frac{\Delta T_{\mathrm{f}(\mathrm{ob})}}{\Delta T_{\mathrm{f}(\mathrm{th})}}=\frac{\pi_{\mathrm{ob}}}{\pi_{\mathrm{th}}}=\frac{M_{\mathrm{th}}}{M_{\mathrm{ob}}}\)

→ Colligative properties considering van’t Hoff factor :

→ α = \(\frac{i-1}{n-1}\) (for dissociation)

By going through these Maharashtra State Board 12th Science Chemistry Notes Chapter 1 Solid State students can recall all the concepts quickly.

Maharashtra State Board 12th Chemistry Notes Chapter 1 Solid State

Solids-

• Crystalline
• Amorphous

Crystalline solids-

• Ionic crystals
• Covalent network crystals
• Molecular crystals
• Metallic crystals

Crystal systems-

• Cubic
• Orthorhombic
• Tetragonal
• Monoclinic
• Rhombohedral
• Triclinic
• Hexagonal

Classification of crystal systems (Bravais lattices) :

Cubic lattice –

1. Simple cubic or primitive
2. Body centred cubic
3. Face centred cubic

Number of atoms in the unit cell :

Packing efficiency :

Number of tetrahedral voids = 2 Number of atoms
Number of octahedral voids = Number of atoms

Relation between radius (r) of an atom and edge length (a) of cubic unit cell

Density of the crystal: p = \(=\frac{n \times M}{a^{3} \times N_{\mathrm{A}}}\)

Defects in solids-

(1) Point defects-

1. Vacancy defects (Schottky defects)
2. Interstitial defects (Frenkel defects)
3. Impurity defects-
   • Substitutional impurity defects
   • Interstitial impurity defects

(2) Nonstoichiometric defects

• Metal deficiency defect
• Metal excess defect

Conducting solids-

• Conductors
• Semiconductors
• Insulators

Semiconductors –

• Intrinsic
• Extrinsic
• n-type
• p-type

Magnetic properties-

• Diamagnetic
• Paramagnetic
• Ferromagnetic

(1) Diamagnetism is due to the presence of all paired electrons in the substance.
(2) Paramagnetism is due to the presence of one or more unpaired electrons in the substance.