91Ó°ÊÓ

Diffraction is a phenomena in which the interference or the bending of waves occurs around the corners of the opening or obstacle through or on which it strikes.

The diffraction formula is following,

$$\begin{gathered} \mathrm{²Ôλ}=2\mathrm{»å²õ¾\pm ²Ôθ} \\ \mathrm{λ}=\mathrm{wavelength} \\ \mathrm{d}=\mathrm{spacing} \\ \mathrm{θ}=\mathrm{bragg}\mathrm{angle} \\ \mathrm{n}=\mathrm{order}\mathrm{of}\mathrm{diffraction} \end{gathered}$$

$$\begin{gathered} wavelengthforthirdorderreflection{\mathrm{λ}}_B=97\text{pm}\backslash \\ braggangleforfirstorderreflection{\mathrm{θ}}_1=23° \\ braggangleforthirdorderreflection{\mathrm{θ}}_2=60° \end{gathered}$$

From the bragg’s formula of diffraction as given above, the interplane spacing will be by using given data,

Here for 3rd order diffraction the wavelength will be 3 times.

$$\begin{gathered} d=\frac{3{\mathrm{λ}}_B}{2\sin {\mathrm{θ}}_2} \\ d=\frac{3\left(97\text{pm}\right)}{2\sin 60°} \\ d=1.7×{10}^2\text{pm} \end{gathered}$$

The wavelength A from the given and achieve data,

$$\begin{gathered} {\mathrm{λ}}_A=2d\sin {\mathrm{θ}}_1 \\ {\mathrm{λ}}_A=2\left(1.7×{10}^2\text{pm}\right)\sin 23° \\ {\mathrm{λ}}_A=1.3×{10}^2\text{pm} \end{gathered}$$