Question

Choose the INCORRECT statement. (1) Cut-off wavelength of X-rays is independent of filament voltage. (2) Presence of \(\mathrm{K}_{\mathrm{a}}\)-line in \(\mathrm{X}\)-ray spectrum means that L-series will also be present. (3) Increase in filament current increases intensity of X-ray. (4) Presence of L-series in X-ray spectrum means that K-series will also be present.

Short answer

Statement 2 is incorrect.

Step-by-step solution

- Understanding Each Statement

Review each of the statements to understand what they are asserting about X-rays and their properties.

- Analyze Statement 1

Cut-off wavelength of X-rays is independent of filament voltage. This statement is correct because the cut-off wavelength is determined by the accelerating voltage of the electrons, not the filament voltage.

- Analyze Statement 2

Presence of \( \mathrm{K}_{\mathrm{a}} \)-line in \( \mathrm{X} \)-ray spectrum means that L-series will also be present. This statement is incorrect because the \( \mathrm{K}_{\mathrm{a}} \)-line indicates electron transitions to the K-shell, and it does not necessarily mean there will be transitions that produce L-series lines.

- Analyze Statement 3

Increase in filament current increases intensity of X-ray. This is correct because a higher filament current produces more electrons, which in turn increases the intensity of the emitted X-rays.

- Analyze Statement 4

Presence of L-series in X-ray spectrum means that K-series will also be present. This can be correct because if L-series transitions are observed, K-shell transitions are also likely occurring, producing K-series lines.

Key concepts

X-ray spectrum

The X-ray spectrum illustrates the range of different wavelengths of X-rays emitted by a source. X-rays are produced when high-energy electrons collide with a target material, causing the emission of both continuous and characteristic X-rays.

• Continuous X-rays (Bremsstrahlung): These form a continuous spectrum and are generated when electrons lose energy during deceleration near the target's nuclei.
• Characteristic X-rays: These specific X-rays arise when electrons in the inner shells of the target's atoms are ejected, and other electrons fall to fill the vacancies. This process releases X-rays of distinct energies that are characteristic of the target material.

Understanding the X-ray spectrum is crucial for applications in medicine, material science, and security screening.

The spectrum informs us about the energies of the emitted X-rays, which reflect the properties of the target material and the conditions under which X-rays are produced.

K-series

The K-series consists of characteristic X-rays generated by electron transitions to the K-shell (or innermost electron shell) of an atom. When an electron is ejected from the K-shell, higher energy electrons from outer shells fall into the vacant spot, releasing energy in the form of X-rays.

The primary lines in the K-series include:

• K_α: Transition from the L-shell to the K-shell.
• K_β: Transition from the M-shell to the K-shell.

The energies of these transitions are unique to each element, making the K-series useful in identifying elements through X-ray spectroscopy techniques.

In the context of the original problem, if a K_α line is observed, it does not necessarily mean that L-series lines will also appear. K-series lines only indicate that there are electron transitions specifically to the K-shell.

L-series

The L-series refers to characteristic X-rays produced by electron transitions to the L-shell (the second innermost electron shell) of an atom. When an electron is knocked out from the L-shell, electrons from higher energy levels drop into the vacancy, releasing X-rays with energies characteristic of the element.

The primary components of the L-series include:

• L_α: Transition from the M-shell to the L-shell.
• L_β: Transition from the N-shell to the L-shell.

Each element emits L-series X-rays at specific energies, making them valuable for elemental analysis.

In the original problem, the presence of L-series lines indicates that L-shell transitions are happening. However, it usually implies that K-shell transitions (the K-series) are also occurring since X-ray production often involves multiple shells.

Filament current

Filament current refers to the electric current passing through the filament (or cathode) in an X-ray tube. The filament heats up, releasing electrons through a process called thermionic emission. These electrons are then accelerated towards the anode to produce X-rays.

Some key points about filament current are:

• Increasing the filament current increases the number of emitted electrons.
• A greater number of electrons results in higher X-ray intensity, as more electrons collide with the target material.
• The filament current does not affect the cutoff wavelength of X-rays; that is determined by the accelerating voltage of the electrons.

Thus, in the context of the exercise, increasing the filament current directly increases the intensity of the X-rays generated.