Question

If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change. because STATEMENT-2 When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy. (A) Statement- 1 is True, Statement- 2 is True; Statement- 2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True

Short answer

Both Statement-1 and Statement-2 are True, but Statement-2 is NOT a correct explanation for Statement-1. The answer is (B).

Step-by-step solution

Understanding the Statements

Assess each statement's veracity. Statement 1 claims that increasing the accelerating potential in an X-ray tube does not affect the wavelengths of characteristic X-rays. Statement 2 explains that when an electron beam hits the target inside the X-ray tube, the kinetic energy of the electrons is partly converted into X-ray energy.

Analyzing Statement 1

The wavelengths of characteristic X-rays depend on the energy levels of the electrons in the atoms of the target material. These levels are quantized and fixed. When the accelerating potential is increased, the kinetic energy of the electrons increases, but this does not change the energy levels in the atoms. Thus, the characteristic X-ray wavelengths, which depend on the differences between these fixed energy levels, stay the same.

Analyzing Statement 2

The statement is true because when high-speed electrons collide with the target material in an X-ray tube, some of their kinetic energy is indeed converted into X-ray energy. This is part of the process that generates X-rays.

Correlation between the Statements

Even though both statements are true, Statement 2 does not explain why the characteristic X-ray wavelengths remain unchanged when the accelerating potential is increased. Statement 2 is more about the conversion of kinetic energy into X-ray energy rather than the invariance of the X-ray wavelengths.

Key concepts

Characteristic X-rays

When exploring the intricacies of X-ray production, one cannot overstate the importance of characteristic X-rays. These are a distinct set of X-rays emitted by atoms when their inner-shell electrons are ejected and higher energy electrons fall into the lower energy vacancies. This process results in the emission of X-rays with very specific energies, unique to the element.

Consider this in the context of the textbook exercise where the students are informed that the wavelength of characteristic X-rays remains unchanged even when the accelerating potential of an X-ray tube is increased. It is crucial to grasp that the energy levels of electrons in an atom are quantized and stable. Each element on the periodic table has its own set of these levels, which define the 'characteristic' part of these X-rays. The transitions between these levels result in X-rays with energies—and consequently wavelengths—that are specific for each element. No matter how much you increase the accelerating potential, these unique energy levels don't change, hence the characteristic wavelengths stay the same.

In simpler terms, it is as if each element has its unique fingerprint. An increased accelerating potential does not alter these fingerprints, thus the characteristic X-rays serve as reliable identifiers for different elements, irrespective of changes in the external conditions.

Accelerating Potential

The concept of accelerating potential in X-ray tubes can be pictured as the throttle of a car, adjusting the speed at which electrons race towards their target. It is a measure of the voltage applied between the cathode and the anode in an X-ray tube; a higher accelerating potential means that the electrons gain more speed—and hence more kinetic energy—on their journey from cathode to anode.

As students might learn, increasing the accelerating potential boosts the kinetic energy of the electrons. Nevertheless, as perplexing as it might seem, this doesn't affect the wavelengths of characteristic X-rays for reasons already discussed.

However, the accelerating potential does have a direct influence on another aspect of the X-rays produced, often referred to as 'bremsstrahlung' or 'braking radiation'. This is the continuous spectrum of X-rays produced when electrons are decelerated in the electric field of the atoms in the target. In this case, a higher accelerating potential will lead to a higher energy bremsstrahlung radiation and thus a shift towards shorter wavelengths in the continuous spectrum. Understanding this dichotomy is essential for students to comprehend how different parameters affect the X-ray production process.

Kinetic Energy Conversion

The principle of kinetic energy conversion is pivotal in understanding how X-rays are generated within the tube. As electrons are hurled at great speeds towards the target by the accelerating potential, they collide with the target atoms with significant kinetic energy. The eureka moment for students is recognizing that not all of this kinetic energy is converted into X-ray energy—it's only a part of it.

On impact, several events can occur: some kinetic energy may be converted into heat, contributing to the considerable heating of the anode; some may be responsible for ejecting electrons from their atomic orbits, leading to the emission of characteristic X-rays; and the rest may be involved in producing the bremsstrahlung radiation mentioned earlier.

This energy conversion is highly inefficient; a large proportion of the energy is lost as heat, which is why only a small fraction of the electron's kinetic energy is transformed into X-ray energy. To help students visualize it, consider the metaphor of throwing a squash ball against a wall; not all the energy in the ball's motion (kinetic energy) will come back to you, some of it is converted into sound, heat, and deformation of the ball and the wall. Similarly, in an X-ray tube, not all of the electron’s kinetic energy comes back as useful X-ray energy.