Question

An X-rays tube with Cu target is operated at 25 kV. The glancing angle for a NaCl. Crystal for the Cu \[{{K}_{\alpha }}\]line is \[{{15.8}^{0}}\]. Find the wavelength of this lime.
(d for NaCl=\[2.82{{A}^{0}}\],h=\[6.62\times {{10}^{-27}}erg\sec \])
(A) 3.06
(B) 1.53
(C) 0.75
(D) none of the above

Answer 1

Hint:This problem is about X-ray diffraction and this can be solved easily by using Bragg’s law for diffraction of X-rays which is used to determine the internal structure of the solids. It is a special case of Laue diffraction. The given solid is NaCl.

Complete step by step answer:
The given potential difference is 25kV
Glancing angle let us show it by \[\theta \]= \[{{15.8}^{0}}\]
D for NaCl is given as, d=\[2.82{{A}^{0}}\]
Using Bragg’s law, \[2d\sin \theta =\lambda \]
d is given in Angstrom, so our wavelength will also come in the same units. Substituting the values and using a scientific calculator to find out the value of Sine,
\[\begin{align}
  & 2\times 2.82\sin 15.8=\lambda \\
 & \lambda =1.53{{A}^{0}} \\
\end{align}\]
The wavelength comes out to be 1.53\[{{A}^{0}}\]and which matches with the option (B). So, the correct option is (B)

Additional Information: Bragg's law helps us to calculate details about the crystal structure, or if the crystal structure is known, to determine the wavelength of the x-rays incident upon the crystal. We have used it here to find the unknown wavelength.

Note:In this problem, we are also given with the potential difference by which the x rays are generated but that is misleading as it is not used in Bragg’s law. Also, a scientific calculator was used to calculate the sine of the given angle.