Problem 91 - Master Resource Book in JEE Main Physics

Question

Assertion (A) If an accelerating potential in a X-ray tube is increased, the wavelength of the characteristic X-ray do not change. Reason (R) When an electric beam strikes the target in an X-ray tube, part of KE is converted into X-ray equation. (a) A is true, \(\mathrm{R}\) is true, \(\mathrm{R}\) is correct explanation of \(\mathrm{A}\) (b) A is true, \(R\) is true, but \(R\) is not correct explanation of \(A\) (c) \(\mathrm{A}\) is true, \(\mathrm{R}\) is false (d) \(\mathrm{A}\) is false, \(\mathrm{R}\) is true

Step-by-Step Solution

Answer

(b) A is true, R is true, but R is not the correct explanation of A.

Step 1: Understand Assertion

The assertion (A) states that if the accelerating potential in an X-ray tube is increased, the wavelength of the characteristic X-ray does not change. The characteristic X-ray wavelength is determined by the target material and is independent of the accelerating potential, thus making the assertion true.

Step 2: Understand Reason

The reason (R) states that when an electric beam strikes the target in an X-ray tube, part of the kinetic energy (KE) is converted into X-ray radiation. This is true because the energy of the electrons is converted into X-ray photons and other forms of energy upon impact.

Step 3: Evaluate the Relationship

The relationship proposed is that (R) is the correct explanation for (A). However, while (R) is true, it does not explain why the wavelength of the characteristic X-ray remains unchanged with increased accelerating potential. The characteristics are determined by the target material and not by the accelerating potential, breaking the causal explanation link.

Step 4: Choose the Correct Option

Based on the evaluation, ('A is true, R is true, but R is not the correct explanation of A') fits correctly, leading us to select option (b).

Key Concepts

Accelerating Potential

In an X-ray tube, the accelerating potential plays a crucial role in the generation of X-rays. It refers to the high voltage applied between the anode and cathode, which accelerates the electrons towards the target material.

• Increasing the accelerating potential increases the speed and energy of the electrons striking the target.
• This results in the production of X-rays with higher frequency and lower wavelength, known as the Bremsstrahlung or continuous spectrum.
• However, for characteristic X-rays, the accelerating potential does not directly change their wavelength, as these are determined by the atomic structure of the target material.

It is essential to understand that while increasing the voltage can enhance the overall X-ray output, it does not affect the intrinsic properties of the characteristic lines, which are specific to the material being used.

Characteristic X-Ray

The term 'Characteristic X-Ray' refers to the X-rays that are emitted with specific, fixed wavelengths unique to each element.

• These X-rays are produced when the high-energy electrons displace inner-shell electrons of the target atom, causing a higher energy electron transition to fill the vacancy.
• The energy difference between the higher shell and the inner shell is released as X-ray photons with a distinct energy and corresponding wavelength.
• This process results in a spectrum of well-defined lines, characteristic to the target material used in the X-ray tube.

Hence, regardless of changes in accelerating potential, the wavelengths of characteristic X-rays remain constant, as they are solely a factor of the electron transitions within the atom.

Kinetic Energy Conversion

In the operation of an X-ray tube, converting kinetic energy forms the basis of generating X-rays.

• Electrons accelerated by the high voltage collide with the target material.
• Their kinetic energy is transferred to the atoms in the target, leading to two main outcomes: emission of X-rays and increase in temperature of the target.
• Part of the energy is used to displace inner-shell electrons, creating vacancies filled by other electrons, thus emitting characteristic X-rays.

Most of the initial kinetic energy is converted to heat, while only a fraction is transformed into X-ray photons, which is why the target material must be able to withstand high temperatures to prevent damage or melting.

Target Material

The choice of target material in an X-ray tube is critical as it determines the nature of the X-rays produced.

• Common materials include tungsten, molybdenum, and copper, each chosen for their high melting points and specific characteristic X-ray emissions.
• The target's atomic number affects the energy and wavelength of the emitted characteristic X-rays: higher atomic numbers lead to higher-energy X-rays.
• For example, tungsten is widely used because it generates high-intensity X-rays and can endure extreme thermal conditions due to its high melting point.

Thus, the target material is carefully selected to match the intended application of the X-ray tube, ensuring both efficiency and durability of the device.