CHEMISTRY 201X
September 1721, 2007
Practice Problems
(45)
Polonium adopts a “simple cubic” structure at room temperature and pressure.
The unit
cell is a cube, side is
a
= 336.8 pm, and contains Po atoms just at the corners.
Vertical direction is parallel to
a side of the cubic unit cell (
a
).
Vertical direction is parallel to
a diagonal of a square face of
the cubic unit cell (
2
a
).
Vertical direction is parallel to
the body diagonal of the cubic
unit cell (
3
a
).
For Cu Xradiation, calculate the angles 2
θ
where Bragg reflections would be observed
for each set of planes for
n
= 1, 2, and 3.
If the Xray diffractometer could only observe
reflections for 2
θ
≤
90
°
, which reflections would be observed?
λ
= 154.178 pm
Left:
d = a = 336.8 pm
sin
θ
= n
λ
/2d = 0.2289n
n = 1: sin
θ
= 0.2289
2
θ
= 26.46
°
n = 2:
sin
θ
= 0.4598
2
θ
= 54.49
°
ALL OBSERVED
n = 3:
sin
θ
= 0.6867
2
θ
= 86.74
°
Middle:
d = a/
√
2 = 238.2 pm sin
θ
= n
λ
/2d = 0.3237n
n = 1: sin
θ
= 0.3237
2
θ
= 37.77
°
n = 2:
sin
θ
= 0.6474
2
θ
= 80.69
°
JUST n=1 and n=2
n = 3:
sin
θ
= 0.9711
2
θ
= 152.38
°
Right:
d = a/
√
3 = 194.5 pm sin
θ
= n
λ
/2d = 0.3964n
n = 1: sin
θ
= 0.3964
2
θ
= 46.71
°
n = 2:
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 Fall '07
 Miller
 Chemistry, Atom, Sin, CHEMISTRY 201X Practice, 201X Practice Problems

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