Chapter 12, Problem 1SAQ

Interpretation Introduction

Introduction: The distance between the atomic layers in a crystal can be calculated by using Bragg’s law.

Answer to Problem 1SAQ

Correct answer: The separation between atomic layers is $158\text{ pm}$. There fore, option (d) is correct.

Explanation of Solution

Justify reasons for the correct answer:

Calculate the separation between the atomic layers in the crystal by using the rearranged equation of Bragg’s law as follows:

$d=\frac{n\lambda }{2\sin \theta }$

Here, n is the order of diffraction (an integral number), $\lambda$ is the wavelength, d is the separation between layers, and $\theta$ is the reflection angle.

Substituting the known values:

$\begin{array}{c}d=\frac{\left(1\right)\times \left(154\text{pm}\right)}{2\times \sin \left(29.1º\right)}\\ =158\text{ pm}\end{array}$

There fore, option (d) is correct.

Justify reasons for the incorrect answer:

Option (a) results by using the wrong equation of Bragg’s law as follows:

$\begin{array}{c}d=\frac{\left(2\right)\times \left(154\text{pm}\right)}{2\times \sin \left(29.1º\right)}\\ =316\text{ pm}\end{array}$

Or:

$\begin{array}{c}d=\frac{\left(1\right)\times \left(154\text{pm}\right)}{\sin \left(29.1º\right)}\\ =316\text{ pm}\end{array}$

So, it is an incorrect answer.

Option (b) has the wrong value. So, it is an incorrect answer.

Option (c) has the same value as the wavelength of the incident light. No equation is used. So, it is an incorrect answer.

Hence, options (a), (b), and (c) are incorrect.

Conclusion

The separation between the atomic layers is $158\text{ pm}$.