A continuous spectrum is produced by Bremsstrahlung, the electromagnetic radiation produced when free electrons are accelerated during collisions with ions. A line spectrum results when an electron having sufficient energy collides with a heavy atom, and an electron in an inner energy level is ejected from the atom. An electron from an outer energy level then fills the vacant inner energy level, resulting in emission of an X-ray photon. For example if an electron in the n = 1 energy level is ejected from an atom, an electron in the n = 2 level of the atom can fill the vacancy created in the n = 1 level, and a photon with an energy equal to the energy difference between the two levels will be emitted. A scientist produced both types of spectra using the X-ray tube shown in the Fig.1. The tube contains a heated filament cathode (C), which emits electrons. A power supply (LV) regulates the filament temperature, the electrical current in the tube, and the number of X-rays produced at the anode (A). Another power supply (HV) regulates electron acceleration. The scientist used an X-ray tube to determine the relationship between X-ray wavelength, $\mathrm{\lambda }$ and X-ray intensity I, which is proportional to the number of X-ray photons emitted at $\mathrm{\lambda }$. The scientist then graphed the results of the experiment, as shown in Fig. 2.

Detailed Solution: X-ray Spectrum Experiment

1. Types of X-ray Spectra

(a) Continuous Spectrum (Bremsstrahlung):

• Produced when fast electrons from the cathode strike the anode and are decelerated.
• This yields photons of various energies, creating a broad, continuous spectrum.
• Called "Bremsstrahlung" (braking radiation) due to electron deceleration.

(b) Line Spectrum (Characteristic X-rays):

• Occurs when an electron has enough energy to eject an inner-shell electron (usually K or L shell) from the anode atom.
• An outer electron falls into the vacancy, emitting an X-ray photon of fixed energy (difference between levels).
• Produces sharp peaks (lines) superimposed on the continuous spectrum.

2. X-ray Tube Apparatus (Fig. 1)

• Cathode (C): Heated filament emits electrons via thermionic emission.
• LV Supply: Controls filament current (degree of electron emission).
• HV Supply: Accelerates electrons toward the heavy metal anode (A).
• Anode (A): Target where electrons strike and produce X-rays.
• This setup enables production of both continuous and characteristic X-ray spectra.

3. Experiment and Graph (Fig. 2)

• X-rays produced in the tube are analyzed by their wavelength (λ) and intensity (I).
• Continuous spectrum: Broad curve representing a range of energies.
• Sharp lines: High-intensity peaks at specific λ corresponding to characteristic X-rays.
• Intensity (I) at a given λ shows the number of X-ray photons emitted at that wavelength.

4. Energy Relationships

• Minimum wavelength (λ_min): Determined by the maximum kinetic energy of the electrons:eV = hν_max = \(\frac{hc}{\lambda_{min}}\)where e = charge of electron, V = tube voltage, h = Planck's constant, c = speed of light.
• Characteristic lines: Energy of emitted X-ray photon = difference between atomic level energies.

5. Analysis & Reasoning

• Both continuous and line spectra are observed in the same experiment, as shown in the figures.
• Continuous spectrum arises from electron deceleration; characteristic lines are due to atomic transitions.
• The graph in Fig. 2: broad baseline (continuous) with sharp spikes (characteristic X-rays).
• Increasing tube voltage (HV) increases maximum kinetic energy, shifting λ_min left (shorter wavelength) and increasing X-ray intensity.

Conclusion:

Both types of X-ray spectra are explained by the apparatus and graphs. Continuous (Bremsstrahlung) and characteristic (electronic transition) X-rays are fundamental to understanding the emission process and are widely used in X-ray imaging and analysis.