X ray and Compton scattering

X-ray production

The x-ray which is an example of electromagnetic, is produced when a rapid moving electron that have been accelerated through a potential difference of 103v to 106v strike a metal target.  The electron are produced by thermionic emission from the heated cathode and accelerated toward the anode (target) by large potential difference between the cathode where electrons are emitted and anode which is the target. The bulb where x-rays are produced should be evacuated tube so that the emitted electron from cathode will travel direct to target (anode) without colliding with air molecules.

 

x-ray
x-ray machine
x-ray
x-ray machine

When the potential difference between the cathode and anode is of the order of 103v or more, the electron strike the target (Tungsten anode) and x-ray is produced.

With a cold cathode the voltage required is 105v, this kind of tube produces, x-ray that has its wavelength in a range of 10-9 to 10-13

The energy of x-ray is related to it frequency and wavelength.

X-ray is opposite of photo electric effect. This is true because in photo electric effect, electrons are produced by photons, while in X-ray, electrons emitted by thermionic method produce photons.

The intensity of X-ray depends on the number of electron striking the target, per a second, which is controlled by heater current in hot cathodes. The wavelength of X-ray depends on the voltage across the tube, while the penetrating power depends on accelerating voltage and intensity of the beam.

The energy of X-ray can be give as

Ex-ray = hf = hc/λ =eV

where h = Plank constant, f=frequency, eV = potential difference measured in volts.  C = speed of light, and λ = the wavelength

Compton Scattering in x-ray

A phenomenon called Compton scattering provides a direct confirmation of the quantum (particle) nature of x-ray. When X-rays strike a matter, some of the radiation is scattered.  Compton discovered that the some of the scattered radiation have longer wavelength than the incident radiation.

The change in the wavelength of scattered radiation depends on the angle through which it scatter. If the scattered radiation is at angle ϕ with respect to the direction of incident radiation, and λ 1 and λ are wavelength of incident and scattered radiation respectively, then we can say that;

λ 1 –λ =h/mc (1-cosϕ) (Compton scattering)

Properties of X-ray

  1. It pass through many material without changing
  2. It causes fluorescence, in material
  3. It effect photographic plate
  4. it  cannot be refracted
  5. It is not affected by electric or magnetic field.
  6. It discharge electric field bodies by ionizing the surrounding air
  7. It can cause photoelectric emission

 

Use of X-ray

  1. It is used in detention of broken bone or tooth cavity
  2. It is used in treatment of tumor or cancer
  3. X-ray can be used to determine the atomic spacing in crystal.

 

x-ray
x-ray machine

Read also photo electric effect, 

Note that X-ray for medical treatment should be controlled as they can damage living tissues.

Example. Calculate the minimum wavelength of X-rays when a voltage of 45kv is applied to an X-ray tube. ( Take c=3 x 108, h = 6.63 x 10-34 and e =1.6 x 10-19)

Solution using E = hf =hc/λ =eV

Therefore   eV = hc/ λ ,   λ  =hc/eV ,

hc = 3 x 108 x 6.63 x 10-34 =  19.89 x 108-34 = 19.89 x 10-26 and

eV =  1.6 x 10-19 x 45 x 103 = 72 x 10-16

Therefore λ = 19.89 x 10-26/72 x 10-16 = 0.28 x 10-10

λ =2.8 x 10-11m

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