318919
A body centered cubic lattice is made up of hollow spheres of B. Spheres of solid A are present in hollow spheres of B. Radius A is half of the radius of \(B\). What is the ratio of total volume of spheres of B unoccupied by A in a unit cell and volume of unit cell?
Effective number of atoms of B present in a unit cell \(=2\) Total volume of \(\mathrm{B}\) unoccupied by \(\mathrm{A}\) in a unit \({\rm{cell = 2 \times }}\frac{{\rm{4}}}{{\rm{3}}}\left( {{{\rm{R}}^{\rm{3}}}{\rm{ - }}{{\rm{r}}^{\rm{3}}}} \right){\rm{ \times \pi }}\) \({\rm{ = }}\frac{{{\rm{7\pi }}{{\rm{R}}^{\rm{3}}}}}{{\rm{3}}}\) \(\left( {\because r = \frac{R}{2}} \right)\) Volume of unit cell \(=a^{3}\) \( \Rightarrow {\left( {\frac{{{\rm{4R}}}}{{\sqrt {\rm{3}} }}} \right)^3}{\rm{ = }}\frac{{{\rm{64}}}}{{{\rm{3}}\sqrt {\rm{3}} }}{{\rm{R}}^{\rm{3}}}\) \((\because \sqrt 3 a = 4R)\) Desired ratio \(=\dfrac{3}{\dfrac{64}{3 \sqrt{3}} R^{3}}=\dfrac{7 \pi}{64 \sqrt{3}}\)
CHXII01:THE SOLID STATE
318920
In which of following packing, \(74 \%\) space is occupied by the atoms with \(\mathrm{ABAB} . .\). packing of atoms?
1 Simple cubic
2 \(\mathrm{BCC}\)
3 \(\mathrm{CCP}\)
4 \(\mathrm{HCP}\)
Explanation:
\(\mathrm{ABAB}\)... pattern packing is known as HCP and has packing efficiency value as \(74 \%\)
CHXII01:THE SOLID STATE
318921
Statement A : Both hcp and ccp are equally efficient. Statement B : Packing efficiency of hcp is \(74 \%\).
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Both hcp and ccp are equally efficient. Packing efficiency of hcp and ccp is, \[ \begin{gathered} \text { PE }=\dfrac{4 \times(4 / 3) \pi r^{3} \times 100}{(2 \sqrt{2} r)^{3}} \% \\ =\dfrac{(16 / 3) \pi r^{3} \times 100}{16 \sqrt{2} r^{3}} \%=74 \% \end{gathered} \]
CHXII01:THE SOLID STATE
318922
The maximum proportion of available volume that can be filled by hard spheres in diamond is
1 0.52
2 0.34
3 0.32
4 0.68
Explanation:
The maximum packing or the maximum proportion of volume filled by hard spheres in various arrangements are as follows: (a) Simple cubic \(=\dfrac{\pi}{6}=0.52\) (b) Body - centered cubic \(=\dfrac{\pi \sqrt{3}}{8}=0.68\) (c) Face - centered cubic and hexagonal close \(\operatorname{packing}=\dfrac{\pi \sqrt{2}}{6}=0.74\) (d) Diamond \(=\dfrac{\pi \sqrt{3}}{6}=0.34\)
NEET Test Series from KOTA - 10 Papers In MS WORD
WhatsApp Here
CHXII01:THE SOLID STATE
318919
A body centered cubic lattice is made up of hollow spheres of B. Spheres of solid A are present in hollow spheres of B. Radius A is half of the radius of \(B\). What is the ratio of total volume of spheres of B unoccupied by A in a unit cell and volume of unit cell?
Effective number of atoms of B present in a unit cell \(=2\) Total volume of \(\mathrm{B}\) unoccupied by \(\mathrm{A}\) in a unit \({\rm{cell = 2 \times }}\frac{{\rm{4}}}{{\rm{3}}}\left( {{{\rm{R}}^{\rm{3}}}{\rm{ - }}{{\rm{r}}^{\rm{3}}}} \right){\rm{ \times \pi }}\) \({\rm{ = }}\frac{{{\rm{7\pi }}{{\rm{R}}^{\rm{3}}}}}{{\rm{3}}}\) \(\left( {\because r = \frac{R}{2}} \right)\) Volume of unit cell \(=a^{3}\) \( \Rightarrow {\left( {\frac{{{\rm{4R}}}}{{\sqrt {\rm{3}} }}} \right)^3}{\rm{ = }}\frac{{{\rm{64}}}}{{{\rm{3}}\sqrt {\rm{3}} }}{{\rm{R}}^{\rm{3}}}\) \((\because \sqrt 3 a = 4R)\) Desired ratio \(=\dfrac{3}{\dfrac{64}{3 \sqrt{3}} R^{3}}=\dfrac{7 \pi}{64 \sqrt{3}}\)
CHXII01:THE SOLID STATE
318920
In which of following packing, \(74 \%\) space is occupied by the atoms with \(\mathrm{ABAB} . .\). packing of atoms?
1 Simple cubic
2 \(\mathrm{BCC}\)
3 \(\mathrm{CCP}\)
4 \(\mathrm{HCP}\)
Explanation:
\(\mathrm{ABAB}\)... pattern packing is known as HCP and has packing efficiency value as \(74 \%\)
CHXII01:THE SOLID STATE
318921
Statement A : Both hcp and ccp are equally efficient. Statement B : Packing efficiency of hcp is \(74 \%\).
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Both hcp and ccp are equally efficient. Packing efficiency of hcp and ccp is, \[ \begin{gathered} \text { PE }=\dfrac{4 \times(4 / 3) \pi r^{3} \times 100}{(2 \sqrt{2} r)^{3}} \% \\ =\dfrac{(16 / 3) \pi r^{3} \times 100}{16 \sqrt{2} r^{3}} \%=74 \% \end{gathered} \]
CHXII01:THE SOLID STATE
318922
The maximum proportion of available volume that can be filled by hard spheres in diamond is
1 0.52
2 0.34
3 0.32
4 0.68
Explanation:
The maximum packing or the maximum proportion of volume filled by hard spheres in various arrangements are as follows: (a) Simple cubic \(=\dfrac{\pi}{6}=0.52\) (b) Body - centered cubic \(=\dfrac{\pi \sqrt{3}}{8}=0.68\) (c) Face - centered cubic and hexagonal close \(\operatorname{packing}=\dfrac{\pi \sqrt{2}}{6}=0.74\) (d) Diamond \(=\dfrac{\pi \sqrt{3}}{6}=0.34\)
318919
A body centered cubic lattice is made up of hollow spheres of B. Spheres of solid A are present in hollow spheres of B. Radius A is half of the radius of \(B\). What is the ratio of total volume of spheres of B unoccupied by A in a unit cell and volume of unit cell?
Effective number of atoms of B present in a unit cell \(=2\) Total volume of \(\mathrm{B}\) unoccupied by \(\mathrm{A}\) in a unit \({\rm{cell = 2 \times }}\frac{{\rm{4}}}{{\rm{3}}}\left( {{{\rm{R}}^{\rm{3}}}{\rm{ - }}{{\rm{r}}^{\rm{3}}}} \right){\rm{ \times \pi }}\) \({\rm{ = }}\frac{{{\rm{7\pi }}{{\rm{R}}^{\rm{3}}}}}{{\rm{3}}}\) \(\left( {\because r = \frac{R}{2}} \right)\) Volume of unit cell \(=a^{3}\) \( \Rightarrow {\left( {\frac{{{\rm{4R}}}}{{\sqrt {\rm{3}} }}} \right)^3}{\rm{ = }}\frac{{{\rm{64}}}}{{{\rm{3}}\sqrt {\rm{3}} }}{{\rm{R}}^{\rm{3}}}\) \((\because \sqrt 3 a = 4R)\) Desired ratio \(=\dfrac{3}{\dfrac{64}{3 \sqrt{3}} R^{3}}=\dfrac{7 \pi}{64 \sqrt{3}}\)
CHXII01:THE SOLID STATE
318920
In which of following packing, \(74 \%\) space is occupied by the atoms with \(\mathrm{ABAB} . .\). packing of atoms?
1 Simple cubic
2 \(\mathrm{BCC}\)
3 \(\mathrm{CCP}\)
4 \(\mathrm{HCP}\)
Explanation:
\(\mathrm{ABAB}\)... pattern packing is known as HCP and has packing efficiency value as \(74 \%\)
CHXII01:THE SOLID STATE
318921
Statement A : Both hcp and ccp are equally efficient. Statement B : Packing efficiency of hcp is \(74 \%\).
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Both hcp and ccp are equally efficient. Packing efficiency of hcp and ccp is, \[ \begin{gathered} \text { PE }=\dfrac{4 \times(4 / 3) \pi r^{3} \times 100}{(2 \sqrt{2} r)^{3}} \% \\ =\dfrac{(16 / 3) \pi r^{3} \times 100}{16 \sqrt{2} r^{3}} \%=74 \% \end{gathered} \]
CHXII01:THE SOLID STATE
318922
The maximum proportion of available volume that can be filled by hard spheres in diamond is
1 0.52
2 0.34
3 0.32
4 0.68
Explanation:
The maximum packing or the maximum proportion of volume filled by hard spheres in various arrangements are as follows: (a) Simple cubic \(=\dfrac{\pi}{6}=0.52\) (b) Body - centered cubic \(=\dfrac{\pi \sqrt{3}}{8}=0.68\) (c) Face - centered cubic and hexagonal close \(\operatorname{packing}=\dfrac{\pi \sqrt{2}}{6}=0.74\) (d) Diamond \(=\dfrac{\pi \sqrt{3}}{6}=0.34\)
318919
A body centered cubic lattice is made up of hollow spheres of B. Spheres of solid A are present in hollow spheres of B. Radius A is half of the radius of \(B\). What is the ratio of total volume of spheres of B unoccupied by A in a unit cell and volume of unit cell?
Effective number of atoms of B present in a unit cell \(=2\) Total volume of \(\mathrm{B}\) unoccupied by \(\mathrm{A}\) in a unit \({\rm{cell = 2 \times }}\frac{{\rm{4}}}{{\rm{3}}}\left( {{{\rm{R}}^{\rm{3}}}{\rm{ - }}{{\rm{r}}^{\rm{3}}}} \right){\rm{ \times \pi }}\) \({\rm{ = }}\frac{{{\rm{7\pi }}{{\rm{R}}^{\rm{3}}}}}{{\rm{3}}}\) \(\left( {\because r = \frac{R}{2}} \right)\) Volume of unit cell \(=a^{3}\) \( \Rightarrow {\left( {\frac{{{\rm{4R}}}}{{\sqrt {\rm{3}} }}} \right)^3}{\rm{ = }}\frac{{{\rm{64}}}}{{{\rm{3}}\sqrt {\rm{3}} }}{{\rm{R}}^{\rm{3}}}\) \((\because \sqrt 3 a = 4R)\) Desired ratio \(=\dfrac{3}{\dfrac{64}{3 \sqrt{3}} R^{3}}=\dfrac{7 \pi}{64 \sqrt{3}}\)
CHXII01:THE SOLID STATE
318920
In which of following packing, \(74 \%\) space is occupied by the atoms with \(\mathrm{ABAB} . .\). packing of atoms?
1 Simple cubic
2 \(\mathrm{BCC}\)
3 \(\mathrm{CCP}\)
4 \(\mathrm{HCP}\)
Explanation:
\(\mathrm{ABAB}\)... pattern packing is known as HCP and has packing efficiency value as \(74 \%\)
CHXII01:THE SOLID STATE
318921
Statement A : Both hcp and ccp are equally efficient. Statement B : Packing efficiency of hcp is \(74 \%\).
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Both hcp and ccp are equally efficient. Packing efficiency of hcp and ccp is, \[ \begin{gathered} \text { PE }=\dfrac{4 \times(4 / 3) \pi r^{3} \times 100}{(2 \sqrt{2} r)^{3}} \% \\ =\dfrac{(16 / 3) \pi r^{3} \times 100}{16 \sqrt{2} r^{3}} \%=74 \% \end{gathered} \]
CHXII01:THE SOLID STATE
318922
The maximum proportion of available volume that can be filled by hard spheres in diamond is
1 0.52
2 0.34
3 0.32
4 0.68
Explanation:
The maximum packing or the maximum proportion of volume filled by hard spheres in various arrangements are as follows: (a) Simple cubic \(=\dfrac{\pi}{6}=0.52\) (b) Body - centered cubic \(=\dfrac{\pi \sqrt{3}}{8}=0.68\) (c) Face - centered cubic and hexagonal close \(\operatorname{packing}=\dfrac{\pi \sqrt{2}}{6}=0.74\) (d) Diamond \(=\dfrac{\pi \sqrt{3}}{6}=0.34\)
