Answer:
0.15 nm
Explanation:
d = Distance between the atomic planes
m = Order
[tex]\theta_{m}[/tex] = First angle = [tex]45.6^{\circ}[/tex]
[tex]\theta_{m+1}[/tex] = Adjacent angle = [tex]21^{\circ}[/tex]
[tex]\lambda[/tex] = Wavelength = 0.07 nm
From Bragg's relation we know
[tex]2d\cos\theta_{m}=m\lambda[/tex]
[tex]2d\cos45.6^{\circ}=m0.07[/tex]
[tex]2d\cos\theta_{m+1}=(m+1)\lambda[/tex]
[tex]2d\cos21^{\circ}=(m+1)0.07\\\Rightarrow 2d\cos21^{\circ}=m(0.07)+0.07[/tex]
So
[tex]2d\cos21^{\circ}=2d\cos45.6^{\circ}+0.07\\\Rightarrow 2d(\cos21^{\circ}-\cos45.6^{\circ})=0.07\\\Rightarrow d=\dfrac{0.07}{2(\cos21^{\circ}-\cos45.6^{\circ})}\\\Rightarrow d=0.14962\ \text{nm}[/tex]
The distance between the atomic planes is 0.15 nm.
