X-rays were discovered nearly one hundred years ago by Wilhelm Konrad Roentgen who was horified at the first sight of x-rays, an image of his skeletal hand. Roentgen was later awarded the first Noble Prize for his discovery in 1901. The production of x-rays is extremely simple. Electrons bombard a metal target anode at high energy (greater than 20eV), the target anode is orientated at about 45 degrees to the electron beam, and x-rays are emitted about 90 degrees to the electron beam. The appuratus we will use to study x-rays is a Telexometer which consists of 1) the X-ray tube, 2) the crystal holder, 3) a G-M tube detector mounted on an arm that can be set at any angle, and 4) collimators at the source and at the detector so the detected X-rays are scattered from the crystal rather than short-cutted.

###### Figure created by Don Collins for lab handout.

X-rays are electromagnetic radiation. Electric and magnetic fields oscillate together but perpendicular to each other and the electromagnetic wave moves in a direction perpendicular to both of the fields.

###### Animated GIF from Physics 2000.
This means that they have a wavelength, and they should also be quantized as photons according to the Planck radiation law.
Eample: The wavelength of a X-ray photon according to Planck's Radiation law is:

# Bragg Diffraction

The wavelength spectrum was first studied by William Henery Bragg and his son using single crystals as diffraction gratings. Bragg diffraction differs from ordinary optical diffraction from a grating in that the crystal "grating" is three dimensional and the grating consists of successive layers of crystal planes separated by the interatomic spacing d.
The X-rays penetrate several atomic layers of the crystal, are specularly reflected (scattered) from each layer, and only at certain angles, where the path-difference is a multiple of the wavelength, there is constructive interference. The resulting Bragg condition is:

###### Figure by Don Collins for lab handout.

We will examine three different crystals: Sodium Chloride- NaCl, Lithium Floride- LiF, and Rubidium Chloride- RbCl. Using the telexometer we will gather intensity vs detector angle for each crystal. When the copper anode is bombarded with the high energy electrons the copper will emit characteristic photons: kalpha, kbeta, and Bremsstrahlung. The different crystal act as optical gratings that will produce characteristic grating patterns.

## NaCl Crystal

LiF Crystal

RbCl Crystal

###### Graphs created in Graphical Analysis.

The data collected suggest that these crystals do indeed act as a grating. We can examine the difference in the spacing d for each crystal and relate that to the difference in the peak frequency. As the spacing of the crystal changes the effect of the crystals diffraction will change as well. These changes will follow the difinition of gratings. As the spacing between the gaps (or crystals) increases the light approaches point source and the frequence of the peaks increases.

## Calculation of Wavelength using Bragg Condition

Kalpha = 0.154nm
Kbeta = 0.138nm

### Sodium Chloride- NaCl

Kalpah = 0.155nm
Kbeta = 0.138nm

### Lithium Floride- LiF

Kalpah = 0.151nm
Kbeta = 0.138nm

### Rubidium Chloride- RbCl

Kalpah = 0.150nm
Kbeta = 0.133nm