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

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,

& 2\times 2.82\sin 15.8=\lambda \\\ & \lambda =1.53{{A}^{0}} \\\ \end{aligned}$$ The wavelength comes out to be 1.53$${{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.