Question

What is the smallest Bragg angle for x rays of wavelength 30 pm to reflect from reflecting planes spaced 0.30 nm apart in a calcite crystal?

Short answer

The angle minimum will be $\theta =2.9°$.

Step-by-step solution

Introduction

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,

$$\begin{gathered} \mathrm{n\lambda }=2\mathrm{dsin\theta } \\ \mathrm{\lambda }=\mathrm{wavelength} \\ \mathrm{d}=\mathrm{spacing} \\ \mathrm{\theta }=\mathrm{braggangle} \\ \mathrm{n}=\mathrm{orderofdiffraction} \end{gathered}$$

Given

$$\begin{gathered} \lambda =30\text{pm} \\ d=0.30\text{nm} \end{gathered}$$

The smallest Bragg angle

For smallest angle value n will be 1 so putting all the values the angle minimum will be,

$$\begin{gathered} \theta ={\sin }^{-1}\frac{n\lambda }{2d} \\ \theta ={\sin }^{-1}\left(\frac{1\times 30\text{pm}}{2\times 0.30\times {10}^3\text{pm}}\right) \\ \theta =2.9° \end{gathered}$$