# Learning Exercise

## Bragg's Law Worksheet

How waves reveal the atomic structure of crystals see more

#### Exercise

# Bragg's Law Worksheet

Introduction

The simulation can be found at the link http://www.journey.sunysb.edu/ProjectJava/Bragg/home.html

.

Since the simulation has only two rows of "atoms", there are only two

reflected waves interfering. The applet shows the relative phase

of the incident and reflected waves. Users can vary the interatomic

spacing

*d,*the wavelength

*l*, and

the grazing angle

*q*. Only angles between

5 deg and 50 deg are permitted. Clicking on the "Details" button

brings up a meter that shows the intensity of the combined waves. Since

only two waves are combined, the intensity varies smoothly from a maximum

at the angles satisfying Bragg's Law:

*2d*sin*q* = *ml(m=1,2,3...)*

.

Procedure

Complete the following tables using the given values for each parameter.

In each case, calculate the value of

*m*from the values for

*d*,

*l*,

and

*q*.

Lambda (angstroms) | Distance (angstroms) | Theta (degrees) | Order (m ) |

2.7 | 3.6 | ||

2.5 | 25 | ||

3.2 | 35 | ||

3.3 | 3.3 | ||

3.0 | 4.5 | ||

3.6 | 11 |

For some combinations of *d *and *l *in

the table above, there is more than one angle that satisfies Bragg's Law.

Identify these case by determining the other angle(s) that work and calculate

the corresponding value of *m *in each case. List your answers in

the table below. **Note: The number of rows in the table is not equalto the number of cases.**

< br/>

Lambda (angstroms) | Distance (angstroms) | Theta (degress) | Order (m) |