Minimum wavelength of the X-ray produced at the given electrode potential is
given by
k min ¼
hc
eV
¼
6:626 Â 10
À34
 3  10
8
1:6 Â 10 À19 Â 3 Â 10 4
¼ 4:14 Â 10
À11 m ¼ 0:414 ˚
A
Case I: Calculations for (110) plane
d 110 ¼
a
h
2 + k
2 + l
2
À
Á 1=2 ¼
a
1 2 þ 1
2
þ 0
2
À
Á 1=2 ¼
2:86
ffiffi ffi
2
p ¼ 2:02 ˚
A
Further, from Bragg’s equation, we have
sin h 110 ¼
k min
2d 110
¼
0:414
2 Â 2:02
or h 110 ¼ sin
À1
0:414
2 Â 2:02
¼ 5:88
Now, from the Laue geometry, we obtain
tan 2h ¼
r
D
or r ¼ D tan 2h ¼ 5 tan 11:76 ¼ 1:04 cm
Case II: Calculations for (200) plane
d 200 ¼
a
h
2 + k
2 + l
2
À
Á 1=2 ¼
a
2 2 þ 0
2
þ 0
2
À
Á 1=2 ¼
2:86
2
¼ 1:43 ˚
A
Further, from Bragg’s equation, we have
sin h 200 ¼
k min
2d 200
¼
0:414
2 Â 2:86
or h 200 ¼ sin
À1
0:414
2 Â 2:86
¼ 8:32
Again, from the Laue geometry, we obtain
tan 2h ¼
r
D
or r ¼ D tan 2h ¼ 5 tan 16:64 ¼ 1:49 cm
358
9 Determination of Crystal Structure Parameters