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Page 1 JEE Advanced Previous Year Questions (2021-2023): Solid State 2023 Multiple Correct Type JEE Advanced 2023 Paper 2 Online Q3. Atoms of metals ?? , ?? , and ?? form face-centred cubic ( ?????? ) unit cell of edge length ?? ?? , body-centred cubic (bcc) unit cell of edge length ?? ?? , and simple cubic unit cell of edge length ?? ?? , respectively. If ?? ?? = v?? ?? ?? ?? ; ?? ?? = ?? v?? ?? ?? ; ?? ?? = ?? ?? ?? ?? and ?? ?? = ?? ?? ?? , then the correct statement(s) is(are): [Given: ?? ?? , ?? ?? , and ?? ?? are molar masses of metals ?? , ?? , and ?? , respectively. ?? ?? , ?? ?? , and ?? ?? are atomic radii of metals ?? , ?? , and ?? , respectively.] A. Packing efficiency of unit cell of ?? > Packing efficiency of unit cell of ?? > Packing efficiency of unit cell of ?? B. ?? ?? > ?? ?? C. ?? ?? > ?? ?? D. Density of ?? > Density of ?? Ans: (A,B,D) Atomic radii relations : Given, ?? ?? = 8 v3 ?? ?? . … (1) ?? ?? = v3 2 ?? ?? . … (2) Substituting Eq. (1) into Eq. (2), we get : ?? ?? = v3 2 × 8 v3 ?? ?? = 4?? ?? … . (3) Edge lengths of the unit cells: The edge lengths (?? ) of the unit cells for ?? , ?? , and ?? are given by : ?? ?? = 2v2?? ?? … (4) (for FCC) Page 2 JEE Advanced Previous Year Questions (2021-2023): Solid State 2023 Multiple Correct Type JEE Advanced 2023 Paper 2 Online Q3. Atoms of metals ?? , ?? , and ?? form face-centred cubic ( ?????? ) unit cell of edge length ?? ?? , body-centred cubic (bcc) unit cell of edge length ?? ?? , and simple cubic unit cell of edge length ?? ?? , respectively. If ?? ?? = v?? ?? ?? ?? ; ?? ?? = ?? v?? ?? ?? ; ?? ?? = ?? ?? ?? ?? and ?? ?? = ?? ?? ?? , then the correct statement(s) is(are): [Given: ?? ?? , ?? ?? , and ?? ?? are molar masses of metals ?? , ?? , and ?? , respectively. ?? ?? , ?? ?? , and ?? ?? are atomic radii of metals ?? , ?? , and ?? , respectively.] A. Packing efficiency of unit cell of ?? > Packing efficiency of unit cell of ?? > Packing efficiency of unit cell of ?? B. ?? ?? > ?? ?? C. ?? ?? > ?? ?? D. Density of ?? > Density of ?? Ans: (A,B,D) Atomic radii relations : Given, ?? ?? = 8 v3 ?? ?? . … (1) ?? ?? = v3 2 ?? ?? . … (2) Substituting Eq. (1) into Eq. (2), we get : ?? ?? = v3 2 × 8 v3 ?? ?? = 4?? ?? … . (3) Edge lengths of the unit cells: The edge lengths (?? ) of the unit cells for ?? , ?? , and ?? are given by : ?? ?? = 2v2?? ?? … (4) (for FCC) ?? ?? = 4?? ?? = 32 v3 ?? ?? … . (5) (for BCC, using Eq. (1)) ?? ?? = 2?? ?? = 8?? ?? … . (6) (for simple cubic, using Eq. (3)) Comparing the edge lengths : From Eq. (4), (5) and (6), we find : ?? ?? > ?? ?? > ?? ?? This means Option B: ?? ?? > ?? ?? is correct. Packing Efficiencies: The packing efficiencies for FCC, BCC, and simple cubic are calculated as follows: ? FCC : ?? ?? ?????? = 4 × 4 3 ?? ?? ?? 3 (?? ?? ) 3 = ?? v2 ? BCC: ?? ?? ?????? = 2 × 4 3 ?? ?? ?? 3 (?? ?? ) 3 = 3?? v3 32 ? Simple Cubic : ?? ?? ???? = 1 × 4 3 ?? ?? ?? 3 (?? ?? ) 3 = ?? 6 Comparing these packing efficiencies, we find: ?? ?? ?????? > ?? ?? ?????? > ?? ?? ???? This means Option A : Packing efficiency of unit cell of ?? > ?? > ?? is correct. 5 Calculating Densities : The densities of x and y are given by the formula ?? = ?? ·?? ?? ?? ·?? 3 , where ?? is the number of atoms in the unit cell, ?? is the molar mass of the metal, ?? ?? is Avogadro's number, and ?? is the edge length of the unit cell. ? For ?? (FCC), ?? = 4 : ?? ?? = 4?? ?? ?? ?? (?? ?? ) 3 ? For y (BCC), ?? = 2 : Page 3 JEE Advanced Previous Year Questions (2021-2023): Solid State 2023 Multiple Correct Type JEE Advanced 2023 Paper 2 Online Q3. Atoms of metals ?? , ?? , and ?? form face-centred cubic ( ?????? ) unit cell of edge length ?? ?? , body-centred cubic (bcc) unit cell of edge length ?? ?? , and simple cubic unit cell of edge length ?? ?? , respectively. If ?? ?? = v?? ?? ?? ?? ; ?? ?? = ?? v?? ?? ?? ; ?? ?? = ?? ?? ?? ?? and ?? ?? = ?? ?? ?? , then the correct statement(s) is(are): [Given: ?? ?? , ?? ?? , and ?? ?? are molar masses of metals ?? , ?? , and ?? , respectively. ?? ?? , ?? ?? , and ?? ?? are atomic radii of metals ?? , ?? , and ?? , respectively.] A. Packing efficiency of unit cell of ?? > Packing efficiency of unit cell of ?? > Packing efficiency of unit cell of ?? B. ?? ?? > ?? ?? C. ?? ?? > ?? ?? D. Density of ?? > Density of ?? Ans: (A,B,D) Atomic radii relations : Given, ?? ?? = 8 v3 ?? ?? . … (1) ?? ?? = v3 2 ?? ?? . … (2) Substituting Eq. (1) into Eq. (2), we get : ?? ?? = v3 2 × 8 v3 ?? ?? = 4?? ?? … . (3) Edge lengths of the unit cells: The edge lengths (?? ) of the unit cells for ?? , ?? , and ?? are given by : ?? ?? = 2v2?? ?? … (4) (for FCC) ?? ?? = 4?? ?? = 32 v3 ?? ?? … . (5) (for BCC, using Eq. (1)) ?? ?? = 2?? ?? = 8?? ?? … . (6) (for simple cubic, using Eq. (3)) Comparing the edge lengths : From Eq. (4), (5) and (6), we find : ?? ?? > ?? ?? > ?? ?? This means Option B: ?? ?? > ?? ?? is correct. Packing Efficiencies: The packing efficiencies for FCC, BCC, and simple cubic are calculated as follows: ? FCC : ?? ?? ?????? = 4 × 4 3 ?? ?? ?? 3 (?? ?? ) 3 = ?? v2 ? BCC: ?? ?? ?????? = 2 × 4 3 ?? ?? ?? 3 (?? ?? ) 3 = 3?? v3 32 ? Simple Cubic : ?? ?? ???? = 1 × 4 3 ?? ?? ?? 3 (?? ?? ) 3 = ?? 6 Comparing these packing efficiencies, we find: ?? ?? ?????? > ?? ?? ?????? > ?? ?? ???? This means Option A : Packing efficiency of unit cell of ?? > ?? > ?? is correct. 5 Calculating Densities : The densities of x and y are given by the formula ?? = ?? ·?? ?? ?? ·?? 3 , where ?? is the number of atoms in the unit cell, ?? is the molar mass of the metal, ?? ?? is Avogadro's number, and ?? is the edge length of the unit cell. ? For ?? (FCC), ?? = 4 : ?? ?? = 4?? ?? ?? ?? (?? ?? ) 3 ? For y (BCC), ?? = 2 : ?? ?? = 2?? ?? ?? ?? (?? ?? ) 3 ?? ?? = 3 2 ?? ?? and ?? ?? = 3?? ?? . This implies that ?? ?? = ?? ?? 2 . Thus, 2?? ?? = ?? ?? , we can write : ?? ?? ?? ?? = 2?? ?? ?? ?? × ( ?? ?? ?? ?? ) 3 Substituting the given relation 2?? ?? = ?? ?? into Eq. (7), we get : ?? ?? ?? ?? = 2 × 1 × ( 32/3 2v2 ) 3 . After simplifying Eq. (8), we find ?? ?? > ?? ?? . This means Option D : Density of ?? > ?? is correct. So, the correct answers are Options A, B, and D. Page 4 JEE Advanced Previous Year Questions (2021-2023): Solid State 2023 Multiple Correct Type JEE Advanced 2023 Paper 2 Online Q3. Atoms of metals ?? , ?? , and ?? form face-centred cubic ( ?????? ) unit cell of edge length ?? ?? , body-centred cubic (bcc) unit cell of edge length ?? ?? , and simple cubic unit cell of edge length ?? ?? , respectively. If ?? ?? = v?? ?? ?? ?? ; ?? ?? = ?? v?? ?? ?? ; ?? ?? = ?? ?? ?? ?? and ?? ?? = ?? ?? ?? , then the correct statement(s) is(are): [Given: ?? ?? , ?? ?? , and ?? ?? are molar masses of metals ?? , ?? , and ?? , respectively. ?? ?? , ?? ?? , and ?? ?? are atomic radii of metals ?? , ?? , and ?? , respectively.] A. Packing efficiency of unit cell of ?? > Packing efficiency of unit cell of ?? > Packing efficiency of unit cell of ?? B. ?? ?? > ?? ?? C. ?? ?? > ?? ?? D. Density of ?? > Density of ?? Ans: (A,B,D) Atomic radii relations : Given, ?? ?? = 8 v3 ?? ?? . … (1) ?? ?? = v3 2 ?? ?? . … (2) Substituting Eq. (1) into Eq. (2), we get : ?? ?? = v3 2 × 8 v3 ?? ?? = 4?? ?? … . (3) Edge lengths of the unit cells: The edge lengths (?? ) of the unit cells for ?? , ?? , and ?? are given by : ?? ?? = 2v2?? ?? … (4) (for FCC) ?? ?? = 4?? ?? = 32 v3 ?? ?? … . (5) (for BCC, using Eq. (1)) ?? ?? = 2?? ?? = 8?? ?? … . (6) (for simple cubic, using Eq. (3)) Comparing the edge lengths : From Eq. (4), (5) and (6), we find : ?? ?? > ?? ?? > ?? ?? This means Option B: ?? ?? > ?? ?? is correct. Packing Efficiencies: The packing efficiencies for FCC, BCC, and simple cubic are calculated as follows: ? FCC : ?? ?? ?????? = 4 × 4 3 ?? ?? ?? 3 (?? ?? ) 3 = ?? v2 ? BCC: ?? ?? ?????? = 2 × 4 3 ?? ?? ?? 3 (?? ?? ) 3 = 3?? v3 32 ? Simple Cubic : ?? ?? ???? = 1 × 4 3 ?? ?? ?? 3 (?? ?? ) 3 = ?? 6 Comparing these packing efficiencies, we find: ?? ?? ?????? > ?? ?? ?????? > ?? ?? ???? This means Option A : Packing efficiency of unit cell of ?? > ?? > ?? is correct. 5 Calculating Densities : The densities of x and y are given by the formula ?? = ?? ·?? ?? ?? ·?? 3 , where ?? is the number of atoms in the unit cell, ?? is the molar mass of the metal, ?? ?? is Avogadro's number, and ?? is the edge length of the unit cell. ? For ?? (FCC), ?? = 4 : ?? ?? = 4?? ?? ?? ?? (?? ?? ) 3 ? For y (BCC), ?? = 2 : ?? ?? = 2?? ?? ?? ?? (?? ?? ) 3 ?? ?? = 3 2 ?? ?? and ?? ?? = 3?? ?? . This implies that ?? ?? = ?? ?? 2 . Thus, 2?? ?? = ?? ?? , we can write : ?? ?? ?? ?? = 2?? ?? ?? ?? × ( ?? ?? ?? ?? ) 3 Substituting the given relation 2?? ?? = ?? ?? into Eq. (7), we get : ?? ?? ?? ?? = 2 × 1 × ( 32/3 2v2 ) 3 . After simplifying Eq. (8), we find ?? ?? > ?? ?? . This means Option D : Density of ?? > ?? is correct. So, the correct answers are Options A, B, and D. 2022 Single Correct Type JEE Advanced 2022 Paper 2 Online Q1. Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closest to A. 25 B. 35 C. 55 D. 75 Ans: (B) Atom ?? occupies FCC lattice sites as well as alternate tetrahedral voids of FCC. In FCC, tetrahedral voids are 8 (in a unit cell) Hence Atom ?? in a unit cell (FCC lattice sites) = 8 × 1 8 + 6 × 1 2 = 4 Atom ?? in a unit cell (in T.V.) = 1 2 × 8 = 4 Total atom X in one unit cell = 8 For relation between a and ?? , since T.V. forms at 1 4 th of body diagonal, ?? v3 4 = 2?? ? ?? = 8?? v3 Packing efficiency = 8 × 4 3 ?? ?? 3 ?? 3 × 100 = 8 × 4 3 ?? ?? 3 ( 8?? v3 ) 3 × 100 ? 35% Page 5 JEE Advanced Previous Year Questions (2021-2023): Solid State 2023 Multiple Correct Type JEE Advanced 2023 Paper 2 Online Q3. Atoms of metals ?? , ?? , and ?? form face-centred cubic ( ?????? ) unit cell of edge length ?? ?? , body-centred cubic (bcc) unit cell of edge length ?? ?? , and simple cubic unit cell of edge length ?? ?? , respectively. If ?? ?? = v?? ?? ?? ?? ; ?? ?? = ?? v?? ?? ?? ; ?? ?? = ?? ?? ?? ?? and ?? ?? = ?? ?? ?? , then the correct statement(s) is(are): [Given: ?? ?? , ?? ?? , and ?? ?? are molar masses of metals ?? , ?? , and ?? , respectively. ?? ?? , ?? ?? , and ?? ?? are atomic radii of metals ?? , ?? , and ?? , respectively.] A. Packing efficiency of unit cell of ?? > Packing efficiency of unit cell of ?? > Packing efficiency of unit cell of ?? B. ?? ?? > ?? ?? C. ?? ?? > ?? ?? D. Density of ?? > Density of ?? Ans: (A,B,D) Atomic radii relations : Given, ?? ?? = 8 v3 ?? ?? . … (1) ?? ?? = v3 2 ?? ?? . … (2) Substituting Eq. (1) into Eq. (2), we get : ?? ?? = v3 2 × 8 v3 ?? ?? = 4?? ?? … . (3) Edge lengths of the unit cells: The edge lengths (?? ) of the unit cells for ?? , ?? , and ?? are given by : ?? ?? = 2v2?? ?? … (4) (for FCC) ?? ?? = 4?? ?? = 32 v3 ?? ?? … . (5) (for BCC, using Eq. (1)) ?? ?? = 2?? ?? = 8?? ?? … . (6) (for simple cubic, using Eq. (3)) Comparing the edge lengths : From Eq. (4), (5) and (6), we find : ?? ?? > ?? ?? > ?? ?? This means Option B: ?? ?? > ?? ?? is correct. Packing Efficiencies: The packing efficiencies for FCC, BCC, and simple cubic are calculated as follows: ? FCC : ?? ?? ?????? = 4 × 4 3 ?? ?? ?? 3 (?? ?? ) 3 = ?? v2 ? BCC: ?? ?? ?????? = 2 × 4 3 ?? ?? ?? 3 (?? ?? ) 3 = 3?? v3 32 ? Simple Cubic : ?? ?? ???? = 1 × 4 3 ?? ?? ?? 3 (?? ?? ) 3 = ?? 6 Comparing these packing efficiencies, we find: ?? ?? ?????? > ?? ?? ?????? > ?? ?? ???? This means Option A : Packing efficiency of unit cell of ?? > ?? > ?? is correct. 5 Calculating Densities : The densities of x and y are given by the formula ?? = ?? ·?? ?? ?? ·?? 3 , where ?? is the number of atoms in the unit cell, ?? is the molar mass of the metal, ?? ?? is Avogadro's number, and ?? is the edge length of the unit cell. ? For ?? (FCC), ?? = 4 : ?? ?? = 4?? ?? ?? ?? (?? ?? ) 3 ? For y (BCC), ?? = 2 : ?? ?? = 2?? ?? ?? ?? (?? ?? ) 3 ?? ?? = 3 2 ?? ?? and ?? ?? = 3?? ?? . This implies that ?? ?? = ?? ?? 2 . Thus, 2?? ?? = ?? ?? , we can write : ?? ?? ?? ?? = 2?? ?? ?? ?? × ( ?? ?? ?? ?? ) 3 Substituting the given relation 2?? ?? = ?? ?? into Eq. (7), we get : ?? ?? ?? ?? = 2 × 1 × ( 32/3 2v2 ) 3 . After simplifying Eq. (8), we find ?? ?? > ?? ?? . This means Option D : Density of ?? > ?? is correct. So, the correct answers are Options A, B, and D. 2022 Single Correct Type JEE Advanced 2022 Paper 2 Online Q1. Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closest to A. 25 B. 35 C. 55 D. 75 Ans: (B) Atom ?? occupies FCC lattice sites as well as alternate tetrahedral voids of FCC. In FCC, tetrahedral voids are 8 (in a unit cell) Hence Atom ?? in a unit cell (FCC lattice sites) = 8 × 1 8 + 6 × 1 2 = 4 Atom ?? in a unit cell (in T.V.) = 1 2 × 8 = 4 Total atom X in one unit cell = 8 For relation between a and ?? , since T.V. forms at 1 4 th of body diagonal, ?? v3 4 = 2?? ? ?? = 8?? v3 Packing efficiency = 8 × 4 3 ?? ?? 3 ?? 3 × 100 = 8 × 4 3 ?? ?? 3 ( 8?? v3 ) 3 × 100 ? 35% 2021 JEE Advanced 2021 Paper 1 Online Q2. For the given close packed structure of a salt made of cation ?? and anion ?? shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction = packing efficiency ?????? ) A. 0.74 B. 0.63 C. 0.52 D. 0.48 Ans: (B) Radius of cation X = r + Number of cation ?? present = 6 × 1 2 = 3 Radius of anion ?? = ?? -Read More
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