The Solid State Quiz-12
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Q1.Statement 1: bcc arrangement is less closely packed than ccp arrangement.
Statement 2: In ccp 74% of the available space is occupied by spheres bcc in bcc only 68% of the space is occupied by spheres.
Solution
(d) Both statement and explanation are correct but the reason is different
(d) Both statement and explanation are correct but the reason is different
Q2.Statement 1: In NaCl crystal each Na+ ion is touching 6Cl- ions but these Cl- ions do not touch each other.
Statement 2: The radius ratio r Na /r Cl- is greater than 0.414 required for exact fitting.
:
Solution
(a) Nacl has fcc structure in which each Na^+ is surrounded by six ions and vic versa.In this octahedral arrangement, coordination, number of bothNa^+ and Cl^- is six for which radius ratio lies between 0.414 and 0.732. The radius ratio does not allow Cl^- ions to touch each other.
(a) Nacl has fcc structure in which each Na^+ is surrounded by six ions and vic versa.In this octahedral arrangement, coordination, number of bothNa^+ and Cl^- is six for which radius ratio lies between 0.414 and 0.732. The radius ratio does not allow Cl^- ions to touch each other.
Q3. Statement 1: 8 : 8 co-ordination of CsCl at low temperature changes to 6:6 co-ordination at 760K.
Statement 2: Temperature also influence the structure of solids.
Solution
(c) Explanation is correct reason for statement.
(c) Explanation is correct reason for statement.
Q4. Statement 1: A crystal having fcc structure is more closely packed than a crystal having bcc structure. Statement 2: Packing fraction for fcc structure is double that of bcc structure.
Solution
(a) Packing fraction in fcc = 74% Packing fraction in bcc = 67.9%
(a) Packing fraction in fcc = 74% Packing fraction in bcc = 67.9%
Q5.Statement 1: In rock salt structure, all the octahedral voids in the close packing of anions are occupied by cations.
Statement 2: In rock salt structure, the distance of closest approach between two anions equal to half the face diagonal of unit cell.
Solution
(d) Both statement and explanation are correct but reason for the statement is different
(d) Both statement and explanation are correct but reason for the statement is different
The "OLIVINE" series of minerals consists ofcrystals in which Fe^(2+) and Mg^(2+)ions may substitute for each other causing substitutional impurity defects without changing the volume of unit cell. In "OLIVINE" series of minerals,O^(2-)ions exist as fcc with Si^(4+) occupying one-fourth of OVs and divalent metal ions occupying one-fourth of TVs. The density of “forsterite" (magnesium silicate) is 3.21 g cm^(-3) and that of "fayalite” (ferrous silicate) is 4.34 g cm^(-3)
Q6.The formula of "fayalite mineral” is:
Solution
(a) For fcc, Number of O^(2-) ions =8(corners)×1/8per corner share +6 (faces)×1/2per face share=4 Number of Si^(4+) ions =1/4×OV=1/4×4=1/unit cell Number Fe^(2+) ions =1/4×TV=1/4×8=2/unit cell ⇒Fe_2 SiO_4
(a) For fcc, Number of O^(2-) ions =8(corners)×1/8per corner share +6 (faces)×1/2per face share=4 Number of Si^(4+) ions =1/4×OV=1/4×4=1/unit cell Number Fe^(2+) ions =1/4×TV=1/4×8=2/unit cell ⇒Fe_2 SiO_4
AX, AY, BX, and BY have rock salt type structure with following internuclear distances:
Salt Anion-anion
distance in Ã… Cation-anion
distance in Ã…
AX 2.40 1.70
AY 1.63 1.15
BX 2.66 1.88
BY 2.09 1.48
Q7.Ionic radii of A^⨁ and B^⨁, respectively, are
Solution
(a) a. Y^⊖ is smaller than X^⊖ The difference in internucleardistance between AX and BX indicates that the cation must not be touching all the anions in AX (smaller cation, larger anion.
Radius of A^⊕andB^⊕, respectively, are =0.35 and 0.68 Ã…
(a) a. Y^⊖ is smaller than X^⊖ The difference in internucleardistance between AX and BX indicates that the cation must not be touching all the anions in AX (smaller cation, larger anion.
Radius of A^⊕andB^⊕, respectively, are =0.35 and 0.68 Ã…
The length of a unit (a) in the Ni crystal is 0.352 nm. The diffraction of X-rays of 0.154 nm wavelength (λ) from a Ni crystal occurs at 22.2°,25.9°, and 38.2°. By using Bragg’s law, nλ=2d sin〖θ)〗, and assuming that the diffractions are first order (n=1), the distances are calculated to be 0.204 nm, 0.176 nm, and 0.124 nm
The various structures for the Ni crystal are represented as:
Q8.The distance (d) of 0.204 nm represent which structure?
Q8.The distance (d) of 0.204 nm represent which structure?
Solution
(c) The distance 0.204 nm comes out to be " a⁄√3 " which corresponds to the perpendicular distance between a corner of unit cell and the plane of the three adjacent corners (Fig. III)
(c) The distance 0.204 nm comes out to be " a⁄√3 " which corresponds to the perpendicular distance between a corner of unit cell and the plane of the three adjacent corners (Fig. III)
In crystalline solids atoms or molecules are arranged in a regular and long range order fashion in a three dimensional pattern. These have sharp melting point, flat faces, sharp edges, bounded by well defined planes. A large number of unit cells, each of which possess a definite geometry bounded by plane faces give rise to the formation of a crystal. A point at the corner of unit cell contributes for 1/8 of each such point to unit cell. A point along an edge contributes for 1/4 of each such point to unit cell. A body centred point contributes for 1 each such points to unit cell. Coordination number is the number of nearest neighbours that each ion is surrounded by an oppositely charged ions. Radius of unit cell in sc, fcc and bcc is a/2,a/(2√2) and (√3 a)/4 where a is edge length of cell.
Q9.A mineral having the formula AB_2 crystallises in the cubic closed packed lattice, with A^(2+) atoms occupying the lattice points and B^- tetrahedral voids. The co-ordination number of A,B and fraction of the tetrahedral sites occupied by B atom respectively are:
Solution
(a) AB_2 has bcc structure, A^(2+) possess face centred cubic lattice. B^- ions occupy all the (100%) tetrahedral voids. Thus each A^(2+) is in contact with B^- and each B^- with 4A^(2+) ions.
(a) AB_2 has bcc structure, A^(2+) possess face centred cubic lattice. B^- ions occupy all the (100%) tetrahedral voids. Thus each A^(2+) is in contact with B^- and each B^- with 4A^(2+) ions.
Q10.Which is/are not amorphous solid(s
Solution
(b) All factual statements
(b) All factual statements
