Answer:
[tex]5.1645\times 10^{-11}\ m[/tex]
Explanation:
n = Order = 1
c = Speed of light = [tex]3\times 10^8\ m/s[/tex]
f = Frequency = [tex]3\times 10^{18}\ Hz[/tex]
[tex]\theta[/tex] = Angle = [tex]75.5^{\circ}[/tex]
Lattice spacing is given by
[tex]d=\dfrac{n\lambda}{2\sin\theta}\\\Rightarrow d=\dfrac{n\times c}{f2\sin\theta}\\\Rightarrow d=\dfrac{1\times 3\times 10^{8}}{3\times 10^{18}\times 2\times \sin75.5^{\circ}}\\\Rightarrow d=5.1645\times 10^{-11}\ m[/tex]
The lattice spacing of the crystal is [tex]5.1645\times 10^{-11}\ m[/tex]
