Question
An X-ray tube with $$Cu$$ target is operated at $$25\,kV.$$ The glancing angle for a $$NaCl.$$ Crystal for the $$Cu{k_\alpha }$$ line is $${15.8^ \circ }.$$ Find the wavelength of this line. ($$d$$ for $$NaCl = 2.82\,\mathop {\text{A}}\limits^ \circ ,h = 6.62 \times {10^{ - 27}}erg - \sec $$ )
A.
$$3.06\,\mathop {\text{A}}\limits^ \circ $$
B.
$$1.53\,\mathop {\text{A}}\limits^ \circ $$
C.
$$0.75\,\mathop {\text{A}}\limits^ \circ $$
D.
None of these
Answer :
$$1.53\,\mathop {\text{A}}\limits^ \circ $$
Solution :
According to Bragg’s law,
$$ \Rightarrow 2d\sin \theta = n\lambda ,$$
$$n = 1$$ for first order
$$\eqalign{
& \Rightarrow 2 \times 2.82\sin 15.8 = \lambda \cr
& \Rightarrow \lambda = 5.64 \times 0.2723 = 1.53\,\mathop {\text{A}}\limits^ \circ \cr} $$