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Continuous X-ray- Spectra, Its Origin, Shortest Wavelength, Practice Problems, FAQs

Continuous X-ray- Spectra, Its Origin, Shortest Wavelength, Practice Problems, FAQs

Electromagnetic waves have a wide range of uses in engineering, communication, and medicine, to name a few. Spectroscopy is used to examine the spectrum of electromagnetic radiation. The frequency range of X-rays is between to . Scientists may measure and detect photons with a frequency range in the X-ray spectrum of electromagnetic waves using X-ray spectroscopy techniques. This aids their comprehension of item chemical and elemental characteristics. Continuous X-rays and Characteristic X-rays are the two types of X-rays identified by X-ray spectra. We'll look at their origins and qualities in this post.

Table of Contents

  • Continuous X-rays
  • Origin of Continuous X-ray 
  • Shortest Wavelength
  • Intensity Vs Graph
  • Practice Problems
  • FAQs

Continuous X-rays

A range of photon energy produced in an X-ray tube as a result of the electron's retardation as it approaches an atomic nucleus. The spectrum is continuous and contains a wide variety of wavelengths. They're termed Continuous X-rays because of this.


Origin of Continuous X-ray 

The above diagram can be used to demonstrate the mechanism that produces continuous X-rays. It depicts an atom of a high-atomic-weight anode material with its electrical arrangement. With an accelerating voltage V, an electron is projected toward the anode in a Coolidge tube. As a result, the projectile electron's kinetic energy will be eV. When the projectile electron enters the extremely high electric field of the nucleus of the atom of the anode material, as illustrated in the figure, It is attracted to the nucleus of the atom by a strong electric force, and as a result of this strong attraction, the velocity of this electron as it emerges from the atom is greatly diminished and insignificant when compared to the original velocity of the projectile electron. This electron suffers a very high acceleration under the effect of the highly positive nucleus, and according to classical theory, every accelerated charge particle generates electromagnetic radiation, thus this electron will release electromagnetic radiation as well. X-rays are the name for these electromagnetic radiations. The energy of these electromagnetic radiations will be equal to the reduction in the kinetic energy of the projectile electron, according to the equation of conservation of energy. This is a figure that can be computed.

If the initial velocity of the projectile electron is , then as the velocity is gained due to the accelerating voltage , we have

Where, ,

When this electron leaves the atom of anode material, its speed will be significantly reduced compared to its starting speed. As a result, the anode atom emits an X-ray photon as a result of the difference in kinetic energy of this electron.

Shortest Wavelength ()

In comparison to electrons passing through the atom at a relatively great distance from the nucleus, electrons passing through the atom extremely near to the nucleus will be accelerated and have a higher energy corresponding to them. An X-ray photon's maximal energy corresponds to the electron that loses practically all of its energy while travelling through the atom. Among all the photons emitted by other electrons, the photon corresponding to this electron will have the shortest wavelength. If this shortest wavelength is , then we have

The shortest wavelength of X-rays emitted by an X-ray tube is this. Thus, the maximum energy or minimum wavelength of X-rays released is solely dependent on the potential difference applied across the discharge tube, as shown by the preceding equation.

Thus, we can obtain X-rays in any range from by applying an appropriate voltage across the discharge tube, which will fix , and other photons emitted from the tube will have wavelengths more than , and ranging up to . That is why these X-rays are called continuous X-rays.

Intensity Vs Graph

For various accelerating voltages, we plotted the intensity of released X-rays vs photon wavelengths. The intensity of emitted X-rays will be greatest for a given wavelength at a certain accelerating voltage across the discharge tube, as shown in the graph. Because the intensity of X-rays is proportional to the number of electrons hitting the anode, the intensity of X-rays may be adjusted by altering the current in the circuit at a certain voltage. "Bremsstrahlung" refers to the broad continuous spectrum that extends beyond the peak intensity.


Practice Problems

Q 1. The potential difference applied to an X-ray tube is and the current through it is . Then the number of electrons striking the target per second is?

A. As we know,

Number of electrons striking the target per second,

Q 2. An X-ray tube operates at . A particular electron loses of its kinetic energy to emit an X-ray photon at the first collision. Find the wavelength corresponding to this collision?

A. Kinetic energy acquired by the electron is

The energy of the photon is =

Thus,

Q 3. The voltage applied to an X-ray tube being increased times, the shortest wavelength of an X-ray continuous spectrum shifts by . Find the initial voltage applied to the tube?

A. Given,

Q 4. An X-ray tube operates at . Find the maximum speed of the electrons striking the anode?

A. When an electron of charge e is accelerated through a potential difference V, it acquires energy eV. If m be the mass of the electron and the maximum speed of electron, then

FAQs

Q 1. What is the distinction between a continuous X-ray and a characteristic X-ray? 
A. When free moving electrons interact electromagnetically with nuclei, continuous X-rays are produced, whereas characteristic X-rays are produced during the electron transition processes that occur when an inner shell electron is liberated from an atom.

Q 2. How are the Continuous X-rays Produced? 
A. Continuous x-rays are produced when high-velocity electrons collide with a high-atomic-number target atom.

Q 3. Which of the following properties is/are not shown by X-rays?

a. Polarisation
b. Diffraction
c. Interference
d. refraction

A. (d) X-rays do not show Refraction.

Q 4. How cutoff wavelength of continuous X-rays change if potential across the tube is doubled?
A. Cutoff wavelength is inversely proportional to voltage across X-ray tube, . So if we double the voltage cutoff wavelength will become half of the initial wavelength.

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