Solution: Given: k K a
ð Þ of W = 210 ˚
A ; At. No. (W) = 74, At. No. (Cu) = 29, for
K-series of X-ray b = 1, k K ðaÞ of copper = ?
We know that the characteristic frequency emitted by an element and its atomic
number is related through
m = [a(Z À b)]
2
where a, b are constants.
Thus, for tungsten, this equation can be written as
m W ¼
c
k W
¼ a 74 À 1
ð
Þ
½
Š
2 ¼ a  73
ð
Þ
2
ðiÞ
Similarly, for copper
m Cu ¼
c
k Cu
¼ a  28
ð
Þ
2
ðiiÞ
From these two equations, we can obtain
k Cu ¼
73
28
2
Â210 ¼ 1427 ˚
A
Example 9 The wavelengths of K a (X-ray lines) of iron and platinum are 1.93 Å
and 0.19 Å, respectively. Determine the wavelengths of K a lines for tin and barium.
Solution: Given: k Fe ¼ 1:93 ˚
A; k Pt ¼ 0:19 ˚
A; k Sn ¼ ?; k Ba ¼ ?
We know that the atomic number Z Fe ¼ 26; Z Pt ¼ 78; Z Sn ¼ 50
and Z Ba ¼ 56; also for K a line b ¼ 1
Now, for K a line; the Moseley’s law is given by
m / Z À 1
ð
Þ
2 ; or
c
k
/ Z À 1
ð
Þ
2 ; or k /
1
Z À 1
ð
Þ
2
So that
k Fe /
1
25
ð Þ
2
and k Sn /
1
49
ð Þ
2
and
k Sn
k Fe
¼
25
ð Þ
2
49
ð Þ
2
270
7 Diffraction of Waves and Particles by Crystal