Direction for: In each of the following questions a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements mark the correct answer as
Assertion: Standard optical diffraction cannot be used for discriminating between different X-ray wavelengths. Reason: The grating spacing is not of the order of X-ray wavelengths.A) If both assertion and reason are true and the reason is the correct explanation of assertion.
B) If both assertion and reason are true but the reason is not the correct explanation of the assertion.
C) If assertion is true statement but reason is false.
D) If both assertion and reason are false.
Correct Answer: A
Solution :
X-rays are electromagnetic radiations whose wavelengths are of the order of \[1\overset{\text{o}}{\mathop{\text{A}}}\,\] \[\left( ={{10}^{-10}}m \right)\]. A standard optical diffraction grating cannot be used to discriminate between different wavelengths in the X-ray wavelength range. For \[\lambda =1\overset{\text{o}}{\mathop{\text{A}}}\,(=0.1\,nm)\] and d = 3000 nm, for example, the first order maximum occurs at, \[\theta ={{\sin }^{-1}}\left( \frac{m\lambda }{d} \right)={{\sin }^{-1}}\frac{(1)(0.1)}{3000}={{0.0019}^{o}}\] This is too close to the central maximum to be practical. A grating with \[d\approx \lambda \] is desirable, but, since X-ray wavelengths are about equal to atomic diameter, such gratings cannot be constructed directly. Hence, option (a) is true.
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