Answer to Question #91431 in Quantum Mechanics for Innocent

Question

The Bragg plates or crystalline material are separated by 1.2Armstrong. Calculate highest order Bragg reflection for 2.1ev

Answer 1

Convert electron-volts to joules:

$$E=2.1\text{ eV}\cdot1.602\cdot10^{-19}\frac{\text{J}}{\text{eV}}=3.36\cdot10^{-19}\text{ J}.$$

Hence calculate the wavelength:

$$\lambda=\frac{hc}{E}=5.91\cdot10^{-7}\text{ m}.$$

Angstroms to meters:

$$d=1.2\cdot10^{-10}\text{ m}.$$

Apply Bragg's law:

$$2d\space\text{sin}\theta=n\lambda,$$

express the order, which is a positive integer:

$$n=\frac{2d\space\text{sin}\theta}{\lambda}=4.06\cdot10^{-4}\space\text{sin}\theta.$$

As we can see, with any value of the angle theta the order becomes close to 0 and by no means can become 1 for instance. Thus, we should choose a different wavelength for the experiment.