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KEAM 2019 Physics and Chemistry Paper
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© examsnet.com
Question : 105
Total: 120
The edge length of a solid possessing cubic unit cell is
2
√
2
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
√
3
r
is obtained, where r is the radiusof the hard sphere. Which of the following statements is true?
Density of the structure II is lower than structure I
Density of structure II is higher than structure I
The pore volume in structure I is 1.2 times higher than that of structure II
The pore volume of both the structures are equal
The octahedral voids in structure I is transformed into tetrahedral voids in structure II
Validate
Solution:
Density of a unit cell
∝
1
a
3
(
∵
z
=
1
)
for structure
I
,
d
1
∝
1
(
2
√
2
r
)
3
....(i)
for structure II
d
2
∝
1
(
4
r
√
3
)
3
.......(ii)
Dividing Eqs. (i) and (ii)
d
1
d
2
=
1
(
2
√
2
)
3
r
3
1
(
4
√
3
)
3
×
r
3
⇒
d
1
d
2
=
1
16
(
√
2
)
×
√
3
×
√
3
×
√
3
4
=
3
√
3
64
√
2
d
1
d
2
⇒
5.19
90.5
d
1
=
d
2
×
5.19
90.5
⇒
d
1
=
0.056
×
d
2
Final result concludes that density of structure I is higher than structure II.
Hence, statement I is correct.
© examsnet.com
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