Calculations Involving Unit Cell Dimensions
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CHXII01:THE SOLID STATE

318654 An element \(X\) (atomic weight \(=24 \mathrm{~g} / \mathrm{mol}\) ) forms a face centered cubic lattice. If the edge length of the lattice is \(4 \times 10^{-8} \mathrm{~cm}\) and the observed density is \(2.40 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\), then the percentage occupancy of lattice points by element \(\mathrm{X}\) is (use \(\left.N_{A}=6 \times 10^{23}\right)\)

1 96
2 98
3 99.9
4 none of these
CHXII01:THE SOLID STATE

318655 The edge length of a solid possessing cubic unit cell is \(22 \mathrm{r}\) (structure I), based on hard sphere model, which upon subjecting to a phase transition, a new cubic structure (structure II) having an edge length of \(4 r / 3\) is obtained, where ' \(r\) ' is the radius of the hard sphere. Which of the following statements is true?

1 Density of the structure II is lower than structure I
2 Density of the structure II is higher than strugture I
3 The pore volume in structure I is 1.2 times higher than that of structure II
4 The octahedral voids in structure I is transformed into tetrahedrar voids in structure II
CHXII01:THE SOLID STATE

318656 The formula for determination of density of unit cell is

1 \(\frac{{{\rm{M \times N}}}}{{{{\rm{a}}^{\rm{3}}}{\rm{ \times Z}}}}{\rm{g}}\,{\rm{c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
2 \(\frac{{{{\rm{a}}^{\rm{3}}}{\rm{ \times }}{{\rm{N}}_{\rm{A}}}}}{{{\rm{Z \times M}}}}{\rm{g\;c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
3 \(\frac{{{{\rm{a}}^{\rm{3}}}{\rm{ \times M}}}}{{{\rm{Z \times }}{{\rm{N}}_{\rm{A}}}}}{\rm{g\;c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
4 \(\frac{{{\rm{Z \times M}}}}{{{{\rm{a}}^{\rm{3}}}{\rm{ \times }}{{\rm{N}}_{\rm{A}}}}}{\rm{g\;c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
CHXII01:THE SOLID STATE

318657 Edge length of a cube is \({\text{400 pm}}\), its body diagonal would be

1 \({\text{566}}\,{\text{pm}}\)
2 \({\text{600}}\,{\text{pm}}\)
3 \({\text{500}}\,{\text{pm}}\)
4 \({\text{693}}\,{\text{pm}}\)
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CHXII01:THE SOLID STATE

318654 An element \(X\) (atomic weight \(=24 \mathrm{~g} / \mathrm{mol}\) ) forms a face centered cubic lattice. If the edge length of the lattice is \(4 \times 10^{-8} \mathrm{~cm}\) and the observed density is \(2.40 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\), then the percentage occupancy of lattice points by element \(\mathrm{X}\) is (use \(\left.N_{A}=6 \times 10^{23}\right)\)

1 96
2 98
3 99.9
4 none of these
CHXII01:THE SOLID STATE

318655 The edge length of a solid possessing cubic unit cell is \(22 \mathrm{r}\) (structure I), based on hard sphere model, which upon subjecting to a phase transition, a new cubic structure (structure II) having an edge length of \(4 r / 3\) is obtained, where ' \(r\) ' is the radius of the hard sphere. Which of the following statements is true?

1 Density of the structure II is lower than structure I
2 Density of the structure II is higher than strugture I
3 The pore volume in structure I is 1.2 times higher than that of structure II
4 The octahedral voids in structure I is transformed into tetrahedrar voids in structure II
CHXII01:THE SOLID STATE

318656 The formula for determination of density of unit cell is

1 \(\frac{{{\rm{M \times N}}}}{{{{\rm{a}}^{\rm{3}}}{\rm{ \times Z}}}}{\rm{g}}\,{\rm{c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
2 \(\frac{{{{\rm{a}}^{\rm{3}}}{\rm{ \times }}{{\rm{N}}_{\rm{A}}}}}{{{\rm{Z \times M}}}}{\rm{g\;c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
3 \(\frac{{{{\rm{a}}^{\rm{3}}}{\rm{ \times M}}}}{{{\rm{Z \times }}{{\rm{N}}_{\rm{A}}}}}{\rm{g\;c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
4 \(\frac{{{\rm{Z \times M}}}}{{{{\rm{a}}^{\rm{3}}}{\rm{ \times }}{{\rm{N}}_{\rm{A}}}}}{\rm{g\;c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
CHXII01:THE SOLID STATE

318657 Edge length of a cube is \({\text{400 pm}}\), its body diagonal would be

1 \({\text{566}}\,{\text{pm}}\)
2 \({\text{600}}\,{\text{pm}}\)
3 \({\text{500}}\,{\text{pm}}\)
4 \({\text{693}}\,{\text{pm}}\)
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CHXII01:THE SOLID STATE

318654 An element \(X\) (atomic weight \(=24 \mathrm{~g} / \mathrm{mol}\) ) forms a face centered cubic lattice. If the edge length of the lattice is \(4 \times 10^{-8} \mathrm{~cm}\) and the observed density is \(2.40 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\), then the percentage occupancy of lattice points by element \(\mathrm{X}\) is (use \(\left.N_{A}=6 \times 10^{23}\right)\)

1 96
2 98
3 99.9
4 none of these
CHXII01:THE SOLID STATE

318655 The edge length of a solid possessing cubic unit cell is \(22 \mathrm{r}\) (structure I), based on hard sphere model, which upon subjecting to a phase transition, a new cubic structure (structure II) having an edge length of \(4 r / 3\) is obtained, where ' \(r\) ' is the radius of the hard sphere. Which of the following statements is true?

1 Density of the structure II is lower than structure I
2 Density of the structure II is higher than strugture I
3 The pore volume in structure I is 1.2 times higher than that of structure II
4 The octahedral voids in structure I is transformed into tetrahedrar voids in structure II
CHXII01:THE SOLID STATE

318656 The formula for determination of density of unit cell is

1 \(\frac{{{\rm{M \times N}}}}{{{{\rm{a}}^{\rm{3}}}{\rm{ \times Z}}}}{\rm{g}}\,{\rm{c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
2 \(\frac{{{{\rm{a}}^{\rm{3}}}{\rm{ \times }}{{\rm{N}}_{\rm{A}}}}}{{{\rm{Z \times M}}}}{\rm{g\;c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
3 \(\frac{{{{\rm{a}}^{\rm{3}}}{\rm{ \times M}}}}{{{\rm{Z \times }}{{\rm{N}}_{\rm{A}}}}}{\rm{g\;c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
4 \(\frac{{{\rm{Z \times M}}}}{{{{\rm{a}}^{\rm{3}}}{\rm{ \times }}{{\rm{N}}_{\rm{A}}}}}{\rm{g\;c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
CHXII01:THE SOLID STATE

318657 Edge length of a cube is \({\text{400 pm}}\), its body diagonal would be

1 \({\text{566}}\,{\text{pm}}\)
2 \({\text{600}}\,{\text{pm}}\)
3 \({\text{500}}\,{\text{pm}}\)
4 \({\text{693}}\,{\text{pm}}\)
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CHXII01:THE SOLID STATE

318654 An element \(X\) (atomic weight \(=24 \mathrm{~g} / \mathrm{mol}\) ) forms a face centered cubic lattice. If the edge length of the lattice is \(4 \times 10^{-8} \mathrm{~cm}\) and the observed density is \(2.40 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\), then the percentage occupancy of lattice points by element \(\mathrm{X}\) is (use \(\left.N_{A}=6 \times 10^{23}\right)\)

1 96
2 98
3 99.9
4 none of these
CHXII01:THE SOLID STATE

318655 The edge length of a solid possessing cubic unit cell is \(22 \mathrm{r}\) (structure I), based on hard sphere model, which upon subjecting to a phase transition, a new cubic structure (structure II) having an edge length of \(4 r / 3\) is obtained, where ' \(r\) ' is the radius of the hard sphere. Which of the following statements is true?

1 Density of the structure II is lower than structure I
2 Density of the structure II is higher than strugture I
3 The pore volume in structure I is 1.2 times higher than that of structure II
4 The octahedral voids in structure I is transformed into tetrahedrar voids in structure II
CHXII01:THE SOLID STATE

318656 The formula for determination of density of unit cell is

1 \(\frac{{{\rm{M \times N}}}}{{{{\rm{a}}^{\rm{3}}}{\rm{ \times Z}}}}{\rm{g}}\,{\rm{c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
2 \(\frac{{{{\rm{a}}^{\rm{3}}}{\rm{ \times }}{{\rm{N}}_{\rm{A}}}}}{{{\rm{Z \times M}}}}{\rm{g\;c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
3 \(\frac{{{{\rm{a}}^{\rm{3}}}{\rm{ \times M}}}}{{{\rm{Z \times }}{{\rm{N}}_{\rm{A}}}}}{\rm{g\;c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
4 \(\frac{{{\rm{Z \times M}}}}{{{{\rm{a}}^{\rm{3}}}{\rm{ \times }}{{\rm{N}}_{\rm{A}}}}}{\rm{g\;c}}{{\rm{m}}^{{\rm{ - 3}}}}\)
CHXII01:THE SOLID STATE

318657 Edge length of a cube is \({\text{400 pm}}\), its body diagonal would be

1 \({\text{566}}\,{\text{pm}}\)
2 \({\text{600}}\,{\text{pm}}\)
3 \({\text{500}}\,{\text{pm}}\)
4 \({\text{693}}\,{\text{pm}}\)
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