91影视

The angle of constructive interference${\text{胃}}_{\text{1}}=\text{23.0}掳$.

The angle of constructive interference${\text{胃}}_{\text{2}}=\text{51.4}掳$.

The wavelength of X-rays is$位=\text{0.26}脳{\text{10}}^{\text{-9}}\text{鈥�}m$ .

When there is constructive interference, Bragg's equation can be used to describe the relationship between the quantities.

$\text{2诲蝉颈苍胃=尘位鈥︹赌︹赌︹赌�(1)}$

Constructive interference occurs from two perspectives. Using the equation ,

$\begin{array}{c}{\text{2诲蝉颈苍胃}}_{\text{1}}\text{=尘位鈥︹赌︹赌︹赌�(2)}\\ {\text{2诲蝉颈苍胃}}_{\text{2}}\text{=(尘+1)位鈥︹赌︹赌︹赌�(3)}\end{array}$

From equation

$\begin{array}{c}{\text{2诲蝉颈苍胃}}_{\text{1}}\text{=尘位}\\ \text{m=}\frac{{\text{2诲蝉颈苍胃}}_{\text{1}}}{位}\end{array}$

Substitute$\text{m}$ value in the equation.

$\begin{array}{l}{\text{2诲蝉颈苍胃}}_{\text{2}}\text{=(m+1)}位\\ {\text{2诲蝉颈苍胃}}_{\text{2}}\text{=}\left(\frac{{\text{2诲蝉颈苍胃}}_{\text{1}}}{\text{位}}\text{+1}\right)位\\ {\text{2诲蝉颈苍胃}}_{\text{2}}{\text{=2诲蝉颈苍胃}}_{\text{1}}\text{+}位\\ \text{2d}\left({\text{蝉颈苍胃}}_{\text{2}}{\text{-蝉颈苍胃}}_{\text{1}}\right)\text{=}位\end{array}$

$\text{d=}\frac{位}{\text{2}\left({\text{蝉颈苍胃}}_{\text{2}}{\text{-蝉颈苍胃}}_{\text{1}}\right)}$鈥︹赌︹赌︹赌︹赌︹赌�(4)

Therefore, using equation (4), we get the interplanar spacing such that,

$\begin{array}{c}\text{d}=\frac{\text{0.26}脳{\text{10}}^{\text{-9}}\text{鈥�}m}{\text{2}(\text{sin}(\text{51.4}掳)鈭�\text{sin}(\text{23.0}掳))}\\ =\text{3.33}脳{\text{10}}^{\text{-10}}\text{鈥尘}\end{array}$

Therefore the atomic plane spacing is $\text{d}=\text{3.33}脳{\text{10}}^{\text{-10}}\text{鈥�}m$.