hi prof,

this is a good reference:

the following are texts curated by teachers to teach this topic.

X-ray Spectra
explain the origins of the features of a typical X-ray spectrum using quantum theory

X-rays was discovered accidentally by Wilhelm Rontgen in 1895 while conducting experiments on the cathode rays. For his achievements, he became the first recipient of the Nobel Prize in Physics in 1901. He had noticed that a distant screen coated with barium salt glowed whenever the cathode gun was activated. A new invisible penetrating radiation was emitted from the discharge tube. Rontgen called it X-rays because x in mathematics represents an unknown and it was later revealed that X-rays is another kind of electromagnetic radiation except it has an even smaller wavelength than visible light. Its wavelength ranges between 10[sup]-9[/sup] m and 10[sup]-11[/sup] m.

The process of X-rays production can be perceived as the reverse of photoelectric effect, that is electrons go in and electromagnetic radiant energy comes out.

Producing X-rays
X-rays are generated when high-speed electrons crash into a material target and rapidly decelerate, thereupon emitting electromagnetic radiation.

When the cathode is heated, electrons are emitted in a process called thermionic emission with a very small (near zero) initial velocity. To achieve high energy (i.e. fast moving) electrons, they are accelerated through a large applied electric potential difference, V (typically about 100kV) across the cathode and the anode which is maintained at a higher potential. The metal target is usually an material eg tungsten with very high melting point.  

By conservation of energy, and assuming the electrons initially have zero velocity at the cathode,

   Gain in K.E. = Loss in Electric P. E.
0.5m[sub]e[/sub]v[sup]^2[/sup] = eV where V is the accelerating potential difference.

Hence, just before the electron strikes the metal surface it would have gained a kinetic energy of e V and a velocity of v. The electron may carry energy as high as thousands of electronvolts. When it strikes the target material, it decelerates at a very high rate and loses its kinetic energy which converts into electromagnetic waves (or photons).

But the production of X-ray is not one that is power efficient. The efficiency of an X-ray tube is usually less than 1% and so much heat is generated that the tungsten is set in a copper plate which is attached to a cooling system ventilated by the passage of cooling oil.  

Efficiency of X-ray tube =  (X-ray energy produced per sec)/(Electrical power supplied)×100%

If the power supply is 3000 W and the efficiency is 1%, the X-ray energy produced per second is only 30 W. So 2970 W must be removed by the cooling system.

X-rays production

The X-rays spread out from the angled target, penetrate through the glass tube walls and onto a photographic plate to capture X-ray images of things that is hidden from the human eyes.

Application of X-ray
1. The main use of X-rays is in medicine.  A common application is taking X-ray photos of a patient’s body to check for injury to the bones. The rays go through the skin and flesh easily, showing up as dark areas on the film, but with more difficulty through the bones or teeth.  

2. X-rays is also used for industrial purposes eg to check for structural defects in machines,  building material or to check if the welding made on the aircraft wings is complete and able to withstand stress.  

3. Lower energy X-ray is used in airport to check for bombs or weapons hidden in luggage

Experimental Observation ; X-ray spectra
The intensity of an X-ray beam varies with its wavelength. This spread is called an X-ray spectrum.

The X-ray spectrum typically consists of two superimposed parts:

(1) a broad continuous spectrum (with a minimum wavelength ?min which decreases with larger applied potential difference) and

(2) a line spectrum which consists of a series of characteristic sharp peaks (or spikes) which remains unchanged even when the applied potential difference is altered.

X-ray spectra of same target material but using two separate tube voltages
taken from http://www.schoolphysics.co.uk/age16-19/Atomic%20physics/X%20rays/text/X_ray_spectra/index.html

Features of X-rays spectra and Quantum Theory
(A) Continuous Spectrum

When a high energy electron approaches the target atom, it is deflected from its original path because of the electrostatic attraction between itself and the positively charged nucleus.

The deflection due to the interaction between the incident electron and target atom, results in an ‘acceleration’ of the electron.

The term ’acceleration’ is used rather loosely here to mean either a change in magnitude or direction of velocity or both. In this interaction, there is a change in direction coupled with a reduction in the speed. So, the KE of the exiting electron is less than the original KE before it enters the target atom.  

From the classical Electromagnetic Theory point of view, it has been shown that any charged particle when it is ‘accelerated’ will emit a quantum of electromagnetic radiation or photon. Because the radiated photon carries energy, the electron must lose kinetic energy in the inelastic collision in accordance to the conservation of energy.

taken from http://ie.lbl.gov/xray/xrf.htm
Energy of emitted photon depends on the initial KE, proximity of the travelling electron to the target nucleus and the charge of the nucleus.  

Initial KE – Final KE of electron =  Energy of an emitted photon
?KE=hf= hc/?
Thus the wavelength lambda of the photon emitted = hc/?KE

This type of emission due to the rapid deceleration of electrons is referred to as Bremsstrahlung radiation (German for ‘braking radiation’). Since in this type of interaction, the electron loses only a portion of its kinetic energy, it may take one or more interactions with other atoms before expending all of its kinetic energy. In this manner, it could produce several photons with various energies ranging from zero up to the entire kinetic energy of the electron (ie a continuous spectrum of wavelengths).

taken from http://armymedical.tpub.com/md0950/md09500023.htm
Two different electrons might interact with more than one atom to produce photons with a wide range of energies.

The extreme example whereby the electron loses ALL of its kinetic energy (Emax) in a single encounter and converting it into a single photon is as follows.

Loss of Max. KE of electron = Energy carried by the most energetic photon

The electron cannot emit more energy than it already has, and that maximum amount corresponds to the minimum wavelength end of the continuous spectrum. Thus, the continuous spectrum of the emitted photons exist from a minimum wavelength onwards.

As ?_min?1/V   , when a larger voltage is applied, the minimum wavelength (or lower limit) of the X-ray spectrum decreases. Also the area under the graph expands indicating greater intensity for the X-ray emitted as shown in Fig. 18b.3.  ?_min   is independent of the material used for the target.

The great majority of the electrons after impact, however, lose their kinetic energies gradually such that heat, instead of X-rays is emitted thus raising the temperature of the target rapidly. In fact, usually less than 1% of the electron kinetic energy is converted to X-rays. The other 99% of the electron kinetic energy is converted into heat through low-energy collision with target atoms.

(B) Line Spectrum

It is observed that there are series of intensity peaks or ‘spikes’ at specific wavelengths which remain unchanged in their positions even when the applied tube voltages were changed. The sharp spikes in the X-ray have a different origin from the continuous spectrum and they are usually called line spectrum.

taken from http://ie.lbl.gov/xray/xrf.htm
Inner  electron energy levels and the transitions that give rise to characteristic X-ray emission

These discrete series of lines of wavelengths where the intensity peaks occur are characteristic of the target material because each atom has a unique set of atomic energy levels. Thus, the line spectrum is also called ‘characteristic X-rays spectrum’ and it can be used to identify the material used for the target.

The intensity peaks were successfully explained by the quantum theory in which Bohr relate them to the discrete energy levels or shells that exit in an atom. The sets of peaks were labeled as K, L, M … and so forth series which corresponded to the end transition for the respective shells K, L, M etc.    

When the high-energy electron collides with a target atom, the incoming electron may have sufficient energy to remove an inner shell electron (or electron in a low energy state) from the atom.

The vacancy created in the shell is filled when an electron in a higher energy level drops to fill the ‘vacancy’, accompanied by the emission of a X-ray photon whose energy corresponds to the difference in energies between the two levels (change E). As such, the X-ray emitted has a specific wavelength.

?= hc/?E
Note that the larger the energy transition, the shorter the wavelength. So, to obtain wavelengths in the X-rays range, the energy transition must be of that of heavy atoms
Typically, such transitions occur over a short time, less than 10-9 s, and the energy of photon emission is greater than 10,000 eV and the emitted X-ray photons have wavelengths in the range 0.01 nm to 1.0 nm.

The K-series of X-rays lines is produced when an electron is knocked out of the K-shell, the lowest energy state of the atom. If the vacancy is filled by an electron dropping from the next higher shell, the L shell, the photon emitted has an energy corresponding to the K? characteristic X-ray line on the curve. If the vacancy the K-shell is filled by an electron dropping from the M-shell, the K? line is produced and so on.

Other characteristic X-ray lines are formed when electrons drop from upper levels to vacancies other than those in the K-shell. For example, the L lines are produced when vacancies in the L-shell are filled by electrons dropping from higher shells. An L? line is produced as an electron drops from the M-shell to the L-shell, and an L? line is produced as an electron drops from the N-shell to the L-shell.

So superimposed onto the continuous spectrum are a number of sharp intensity peaks that constitute the line spectrum. The quantum theory explains the overall X-ray spectrum.

extracted is notes from a Singapore teacher lecture notes.
this is shared to give the context of the request of a simulation to aid learning of this topic, difficult for students to understand without the ability to inquiry on.

thanks prof hwang!
for your consideration.