Unit 1 The Solid State

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Cleopatra Chapman
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1 Points to Remember Amorphous and Crystalline Solids Unit 1 The Solid State Amorphous- short range order, Irregular shape eg-glass Crystalline Solids- long range order, regular shape eg : NaCl Molecular solids Ar, CCl 4, H 2 O (ice) Covalent or Network solid SiO 2 diamond No of lattice points per Simple cubic -4, BCC- 9, FCC 14, End-Centred- 10 unit cell No of atoms per unit cell Simple cubic -1, BCC- 2, FCC 4, End-Centred- 2 (z ) Coordination Number FCC- 6:6 BCC- 8:8 Calculation of number of voids Let the number of close packed spheres be N, then: The number of octahedral voids generated = N The number of tetrahedral voids generated = 2N Relation between r and a Simple Cubic a = 2r, BCC 4r = a 3 FCC 4r = a 2 Packing Efficiency ( ) = Calculations Involving Unit Cell Dimensions Frenkel Defect: Schottky Defect Metal excess defect due to anionic vacancies (Fcentres ) Simple Cubic 52.4%, BCC 68%, FCC 74% M=molar mass (g/mol) a = edge length in cm, N A = cation is dislocated to an interstitial site. It does not change the density of the solid. Frenkel defect is shown by ionic substance in which there is a large difference in the size of ions, for example, ZnS, AgCl, AgBr and AgI due to small size of Zn 2+ and Ag + ions. A vacancy defect. The number of missing cations and anions are equal. Density decreases. For example, NaCl, KCl, CsCl and AgBr. When NaCl heated in an atmosphere of Na vapour, the Na atoms deposited on the surface of the crystal. The Cl ions diffuse to the surface of the crystal and combine with Na atoms to give NaCl. The released electrons diffuse into the crystal and occupy anionic sites The anionic sites occupied by unpaired electrons are called F - centres They impart yellow colour to the crystals of NaCl. Similarly, excess of lithium makes LiCl crystals pink and excess of potassium makes KCl crystals violet (or lilac). Doping The conductivity of intrinsic semiconductors is increased by adding an appropriate amount of suitable impurity. This process is called doping

2 n / p -type semiconductors n- type : Si + As or Sb or Bi p-type: Si + B or Ga or In or Tl compounds &12 16 compounds compounds: InSb, AlP and GaAs compounds :ZnS, CdS, CdSe and HgTe Paramagnetic substances Weakly attracted by a magnetic field. Examples: O 2, Cu 2+, Fe 3+, Cr 3+ Diamagnetic substances Weakly repelled by a magnetic field. Example: H 2 O, NaCl and C 6 H 6 Ferromagnetism: A few substances like iron, cobalt, nickel, gadolinium and CrO 2 are attracted very strongly by a magnetic field. Antiferromagnetism MnO. Domains oppositely oriented and cancel out magnetic moment Ferrimagnetism: domains aligned in parallel and anti-parallel directions in unequal numbers. Example: Fe 3 O 4 (magnetite) Very Short Answer Type Questions (1mark) 1. How may the conductivity of an intrinsic semiconductor be increased? By increasing its temperature conductivity can be increased. 2. Which stoichiometric defect increases the density of a solid? Schottky defect in a crystal lowers its density. 3. What are n-type semiconductors? Doping of silicon or germanium with electron rich impurities like P, As, Sb results in formation of n-type semiconductors 4. What type of semiconductor is obtained when Si is doped with As n-type semiconductors 5. Which point defect decreases the density of a solid Schottky defect 6. What is the No. of atoms in a unit cell of fcc crystal? 4 7. Define forbidden zone of an insulator? The energy gap between conduction band and valence band is called forbidden zone. 8. What is the No. of atoms in a unit cell of simple cubic crystal? 1 9. State a feature to distinguish a metallic solid from an ionic solid. Metallic solids are conductors in solid as well as in molten state but ionic solids are electric conductor only in molten state 10. Crystalline solids are anisotropic in nature. What does this statement mean? These solids are anisotropic, i.e. their physical properties such as electrical conductivity, refractive index, thermal expansion etc. have different values in different directions. 11. Which point in crystal does not change the density of a solid? Frankel defect does not change the density of the crystal. 12. What type of interaction hold the molecule together in a polar molecule? Dipole dipole attraction force 13. Wrire a distinguishing feature of metallic solid.

3 Metallic solids are conductors in solid as well as in molten state, hard,malleable. 14. What is meant by intrinsic semiconductor? An insulator capable of conducting electric current at higher temperature or when irradiated with electromagnetic radiations, are known as intrinsic semiconductor. 15. What is the No. of atoms in a unit cell of bcc crystal? Why LiCl acquire pink colour when heated in Li vapour? Its due to presence of F-centre in the crystal. 17.Why is the window glass of the old building thick at the bottom? (Ans) Glass is a pseudo solid, that is, it is a super-cooled liquid of high viscosity. It flows down very slowly and makes the bottom portion of window glass of old building slightly thicker. 18. What causes the conduction of electricity by semiconductors? (Ans) Electrons and holes produced by defects cause the conduction of electricityby semiconductors. 19. Name the salt which can be added to AgCl so as to produce cationic vacancies. Ans SrCl 2 orcdcl 2 is added to AgCl to produce cationic vacancies. 20. What is a diode? (Ans) Diode is a combination of n- type and p- type semiconductors. It is used as a rectifier. 21. Name a transition metal oxide which has appreance and conductivity like that of Cu? (Ans) Rhenium oxide (ReO 3 ) 21.What is the co-ordination number of an atom present in octahedral void? (Ans) The co-ordination number of atom present in octahedral void is Write one property which is caused due to the presence of F-center in a solid. The colours and paramagnetic behaviour of the solid is due to the presence of F-center in a solid. Short Answer Type Questions (2 Marks) 1. Silver crystallises in fcc structure. Each side of the unit cell has a length of 409 pm.what is the radius of Ag atom? Given, a= 409 pm For fcc, a= 2 2 x r r = a/2 2 = 409/ 2x1.41 = pm 2. Calculate the packing efficiency of a metal crystal for simple cubic lattice. 3. Define the following terms w.r.t. crystalline solid (a) Unit cell (b) Coordination No. Give example in each case.

4 (a) Unit cell- An unit cell is the smallest portion of the crystal lattice. When it is moved repeatedly a distance equal to its own dimension along each direction, a three dimensional crystal lattice is generated. (b) Coordination No. - It is the number of atoms or spheres that surrounds the single sphere / atom in a crystal. C.N of tetragonal arrangement = 3 C.N of tetrahedral arrangement = 4 C.N of octahedral arrangement = 6 C.N of body centered cubic arrangement = 8 Any close ( tight ) packing having C.N = 12 i.e. hcp and ccp i.e. fcc having C.N = Aluminium crystallises in an fcc structure. Atomic radius of the metal is 125 pm. What is the length of the side of the unit cell of the metal? 5. Classify each of the following as being either a p- type or a n-type semiconductor. Give reason. (a) Si doped with In (b) Si doped with P. (a) Si is group 14 element and In is group13 element. Therefore, an electron deficit hole is created. Thus semi conductor is p type. (b) Since P is group15 element and Si is group 14 element, there will be an free electron, Thus it is n type semi conductor. 6. Explain the following with one example each: (i)ferrimagnetism (ii)antiferromagnetic substances Ans (i) When magnetic moments are aligned in parallel and anti parallel directions in unequal numbers itresults in net moment. It is called ferrimagnetism. These substances are weakly attracted by magnetic field as compared to ferromagnetic substances.e.g:magnetite (Fe 3 O 4 ) (ii) Antiferromagnetic substances are expected to possesparamagnetism or ferromagnetism but actually they possess zero net magnetic moment. It is due to the presence of equal number of domains in opposite direction. E.g: MnO. 7. A solid is made of two elements A and B. Atoms of element A ocupy all the tetrahedral sites while atoms of element B are in ccp arrangement.from this data find the formula of the compound. There are 2 tetrahedral sites per atom of B because atoms of element B have ccp arrangement.there are 2 atoms of element A for each atom of element B because all tetrahedral sites are occupied by atoms of element A. Therefore, the formula of the compound is A 2 B.

5 8. A solid A + B has NaCl closed packed structure. The radius of anion is 245 pm. Find radius of anion. (2 Marks) The co-ordination number of A + B = 6 ( It has NaCl type structure.) For this, Short Answer Type Questions (3 Marks) 1. Copper crystallises with fcc unit cell. if the radius of Copper atom is pm, calculate the density of copper metal. (Atomic Mass of Cu = & Avagadro No. = 6.02x mol -1 ) 2. Iron has a bcc unit cell with the cell dimension of pm. Density of iron is 7.87 g/cc. use this information to calculate & Avagadro s No. (At. Mass of Fe = 56). 3. The density of copper metal is 8.95 g/cc, if the radius of Cu atom is pm, is the Cu unit cell simple Cubic, bcc or fcc?

6 4. Silver crystallizes in fcc structure if the edge length of the unit cell is 4.07 x 10-8 cm & density of the crystal is 10.5 g/cc, calculate the atomic mass of Silver. 5. Copper crystallises into a fcc lattice with edge length cm. Show that the calculated density is in agreement with its measured value of 8.92 g cm 3 9atomic mass of Cu = 63.5 g mol For face-centered cubic structure, no. of atoms per unit cell z =4 Density, d = z.m/a 3.N A = 4 x 63.5 g mol -1 /( cm) 3 x 6.02x10 23 mol -1 = 8.97 g cm -3, which is close to the measured value of 8.92 g cm 3 6.An element with molar mass kg mol -1 forms a cubic unit cell with edge length 405 pm. If its density is kg -3, what is the nature of the cubic unit cell? Density, d = z.m/a 3.N A Therefore Z= d a 3.N A /M = kg -3 x (405 x10-12 m ) 3 x 6.02x10 23 / kg -3 = , hence face-centered cubic or ccp structure

7 7.Niobium crystallises in body-centered cubic structure. If density is 8.55 g cm 3, calculate atomic radius of niobium using its atomic mass 93 u. For body-centered cubic structure, no. of atoms per unit cell z =2 Density, d = Z.M/a 3.N A a =( Z.M/d.N A ) 1/3 = (2 x 93g mol -1 / 8.55g cm 3 x 6.02x10 23 mol -1 ) 1/3 = 330.4pm For body-centred cubic structure r= 3 a/4 = 3 x 330.4/4 = pm 8.Aluminium crystallises in a cubic close-packed structure. Its metallic radius is 125 pm.(i) What is the length of the side of the unit cell? (ii) How many unit cells are there in 1.00 cm3 of aluminium? For a ccp or face-centered unit cell. a= 2 2r =2 x x 125 pm = 354 pm Volume one unit cell, a 3 = (354 x cm) 3 No. of unit cells in 1.00 cm 3 of aluminium = 1/ a 3 = 1/(354 x cm) 3 =2.25x If NaCl is doped with 10 3 mol % of SrCl 2, what is the concentration of cation vacancies? 10 3 mol % of SrCl 2 = 10 3 x 6.02x10 23 /100 (as 1 mol =6.02x10 23, % =1/100) = 6.02x10 18 mol An element has a body-centred cubic (bcc) structure with a cell edge of288 pm. The density of the element is 7.2 g/cm 3. How many atoms are present in 208 g of the element?

8 HOTS QUESTIONS 1. If the radius of the octahedral void is r and radius of the atoms in close packing is R, derive relation between r and R. let the length of unit cell=a Radius of octahedral void = r Radius of sphere = R In right angled ABC AC AC 2a AB a Also AB 2R Sub in equation (1) r R AB 2 BC 2R 2r 2 2r r R a 2 b ( 1) 2 2a AC R 2r R 2R 2r 2. Analysis shows that nickel oxide has the formula Ni 0.98 O What fractions of nickel exist as Ni 2+ and Ni 3+ ions? Let the total no. of oxygen atoms be 100. Then the no. of nickel atoms as per the formula of nickel oxide is =98 Let the no. of Ni 2+ ions =x Then no. of Ni 3+ ions = 100 x Total Charge on Ni 2+ ions Total Charge on Ni 3+ ions = 2x (since Ni 2+ is dipositive) =3(100 x) (since Ni 3+ is tripositive) Total positive Charge = 2x + 3(100 x) Total negative Charge on 100 oxide ions = 2x100 since oxygen is O 2- As the nickel oxide is neutral, Total positive Charge = Total negative Charge i.e. 2x + 3(98 x) =200 Hence x = 88

9 Total no. of Ni 2+ ions = x = 88 Then no. of Ni 3+ ions = 100 x = =12 % of Ni 2+ = 88x100/96 = 91.7% % of Ni 3+ = = 8.3% 3. Calcium crystallizes in a face centred cubic unit cell with a=0.556nm. Calculate the density if i. It contains 0.1% Frenkel defects. ii. It contains 0.1% Schottky defects. Hint: Frenkel defect does not affect density. d=zm/a 3 N A Schottky defect reduces the density by 0.1%, assuming that volume remains constant. d =d( 1-0.1/100) d =0.999d 4.Ferric oxide crystallises in a hexagonal close-packed array of oxide ions with two out of every three octahedral holes occupied by ferric ions. Derive the formula of the ferric oxide. Oxide forms the hexagonal close packed structure. Total number of O 2- in the unit cell = 12 x 1/6 + 1x3 + 2x 1/2 = = 6 Therefore number of Octahedral voids = 6 Number of Octahedral voids occupied = 6 x 2/3 = 4 Number of Fe 3+ =4 Formulae of Ferric Oxide = Fe 4 O 6 = Fe 2 O 3 VALUE BASED QUESTIONS 1. Solids have fixed shape and volume but experimentally it has been observed that solids are also defective. Two types of defects are found in solids, namely, point defect and line defect. After reading the above passage, answer the following questions- (i) What type of defect can arise when a solid is heated? (ii) How many types of point defects are there in ionic solids? (iii) Mention the values associated with the above information. Ans: (i) Vacancy defect. (ii) 2 types Schottky and Frenkel defect. (iii) self-analysis and critical thinking or any related answer. 2. Rajendra and Manoj went to market to buy study lamp. Shopkeeper showed them one electric rechargeable lamp and one solar lamp. Rajendra wanted to buy electric rechargeable lamp but Manoj advised him to buy the solar lamp. (a) What is the application of solar cell? (b) What is the role of semiconductors in solar cells? (c) What are the values associated with preference of solar cells? Ans: (a) Solar cells convert solar energy into electrical energy. It helps us in saving nonrenewable sources of energy. (b) The n-type semiconductors is used in making solar cells which stores solar energy in the cell.

Unit-1 THE SOLID STATE QUESTIONS VSA QUESTIONS (1 - MARK QUESTIONS)

Unit-1 THE SOLID STATE QUESTIONS VSA QUESTIONS (1 - MARK QUESTIONS) 1. What are anistropic substances. 2. Why are amorphous solids isotropic in nature?. Why glass is regarded as an amorphous solid? 4.