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Standard XII
Chemistry
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The diameter ...
Question
The diameter of atoms forming a closed packed structure in the given figure is
4
×
10
−
8
cm.
The maximum radius of the atom occupying the space in between is
×
10
−
8
cm.
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Solution
When we talk about the maximum possible radius of an atom that can be accommodated in the empty space, we come up with a figure as follows.
Here, we can use Pythagoras theorem.
(
2
R
)
2
+
(
2
R
)
2
=
(
2
R
+
2
r
)
2
2
√
2
R
=
2
R
+
2
r
2
R
(
√
2
−
1
=
2
r
)
When we substitute
√
2
=
1.414
a
n
d
R
=
2
×
10
−
8
c
m
, we get:
r
=
0.828
×
10
−
8
c
m
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