Modern Physics Concept Page - 6

Definition

Matter wave

All matter can exhibit wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave. Matter waves are a central part of the theory of quantum mechanics, being an example of wave particle duality.

Definition

Davisson and Germer experiment

Davison and Germer observed the diffraction of electrons by crystals. The setup consists of an electron gun firing electron beam onto a nickel target inside a vaccum chamber. The diffracted electrons are observed by the galvanometer.The experiment was performed by varying the voltage from 44V to 68V. It was observed that a strong peak appeared when the voltage was 54V at a scattering angle of 500${50}^0$ due to constructive interference effects of the electrons. The wavelength of the matter waves was found to be 0.168 nm from diffraction measurements which matches that of de-Broglie wavelength at 54 V thus verifying the wave nature of electrons. 

Definition

Production of X rays

The device used to produce X-rays is called an X-ray tube. Figure shows a schematic diagram of such a device. A filament and a metallic target are fixed in an evacuated glass chamber. the filament is heated electrically and emits electrons by thermionic emission. A constant potential difference of several kilovolts is maintained between the filament and the target using a DC power supply so that the target is at a higher potential than the filament. The electrons emitted by the filament are, therefore, accelarated by the electric field set up between the filament and the target with a very high speed. These electrons are stopped by the target and in the process X-rays are emitted. These X-rays are brought out of the tube through a window made of thin mica or mylar or some such material which does not absorb X-rays appreciably.

Definition

Explain the properties of X rays

1.  They have a very short wavelength (about the same size as the diameter of an atom).
2.  They cause ionisation (adding or removing electrons in atoms and molecules).
3.  They affect photographic film in the same way as visible light (turning it black).
4.  They are absorbed (stopped) by metals and bones.

Definition

Maximum frequency of X-rays

X-ray frequency, ν=eVh$\nu ={\displaystyle \frac{eV}{h}}$
This shows that the maximum frequency is directly proportional to the accelerating voltage. 
The maximum frequency of X-rays produced in an
X-ray tube at an operating voltage of 25 kV$25kV$ is
(h=6.63×10−34 Js$=6.63\times {10}^{-34}Js$ and c=3×108$c=3\times {10}^8$ m/s)Operating voltage =hνe$Operatingvoltage={\displaystyle \frac{h\nu }{e}}$

operating voltage×eh=ν${\displaystyle \frac{operatingvoltage\times e}{h}}=\nu$

ν=25×103×1.6×10−196.63×10−34$\nu ={\displaystyle \frac{25\times {10}^3\times 1.6\times {10}^{-19}}{6.63\times {10}^{-34}}}$

=6.08×1018 Hz$6.08\times {10}^{18}Hz$

Diagram

Intensity of X-rays

Definition

Decay of X-Rays in a medium

X-rays travelling through a medium suffers decay with distance as they travel.
I=Ioe−αx$I=I_o{e}^{-\alpha x}$
where,
I:$I:$ Intensity after travelling a distance x$x$ in the medium.
Io:$I_o:$ Incident intensity.
α$\alpha$: Absorption coefficient.

Definition

Understand the difference between continuous and characteristic X-rays

At certain sharply defined wavelengths, the intensity of X-rays is very large as marked Kα,Kβ$K_{\alpha },K_{\beta }$ in figure. These X-rays are called characteristic X-rays.
At other wavelengths the intensity varies gradually and theses X-rays are called continuous X-rays.

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