Class 12 > Unit # 26: Atomic Physics > X Ray Spectra

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Inner Shell Transitions & Production of X-Rays

Inner Shell Transitions

“The passage of an electron from one energy level to another is called electron transition.”

Bohr's theory showed that the principal quantum number determines the energy and orbital radius of an electron. The inner shells, designated as K, L, M, etc., correspond to principal quantum numbers $n = 1, 2, 3$, respectively, with the K shell having the greatest binding energy and lying closest to the nucleus.

Other quantum numbers have a relatively small effect on energy, causing shells (other than the K shell) to split into subshells. When an electron transitions from an outer shell to an inner shell, electromagnetic radiation corresponding to a characteristic energy is generated.

Fig: Inner shell electron transitions resulting in characteristic X-ray emission.

X-Rays

X-rays are powerful electromagnetic waves of high energy capable of penetrating most objects, including human tissue. Their wavelengths typically range from $0.01\text{ nm}$ to $10\text{ nm}$ ($0.1\text{ \AA}$ to $100\text{ \AA}$), corresponding to frequencies from $3 \times 10^{19}\text{ Hz}$ down to $3 \times 10^{16}\text{ Hz}$. They are extensively used in medical imaging and structural analysis.

Production and Characteristics of X-Rays

X-rays are electromagnetic waves of very short wavelength (about $0.1\text{ nm}$ to $10\text{ nm}$). They are produced when fast-moving electrons (cathode rays) strike a metal target (anode) inside a high-vacuum discharge tube.

The Modern X-Ray Tube

In a modern X-ray tube (Coolidge tube), a high vacuum is maintained with a pressure of about $10^{-5}\text{ mm Hg}$.

• Cathode Filament (F): Electrons are supplied via thermionic emission from a white-hot tungsten filament heated by a low-tension (L.T.) AC supply of about $10\text{ V}$.
• Anode/Target (T): A high-tension (H.T.) supply of about $100\text{ kV}$ accelerates the electrons toward the target.

Fig: Schematic diagram of a modern X-ray tube setup.

Because there is extremely little gas in the tube, electrons do not lose noticeable energy to ionization on their way to the anode. The tube acts as its own self-rectifier: during half-cycles when the target is positive, electrons bombard it to produce X-rays; during alternate half-cycles when the target is negative, no current flows.

Note: The heat generated at the target by electronic bombardment is enormous, requiring artificial cooling systems.

Mechanism of Characteristic X-Ray Emission

When very energetic electrons bombard atoms in a metal target, an inner-shell electron is knocked out, leaving the atom in an excited state with a "hole" in its electron shell. When this vacancy is filled by an electron dropping from a higher outer shell, an X-ray photon is emitted.

The energy of the emitted X-ray photon equals the energy difference between the two electron levels ($\Delta E = E_{\text{outer}} - E_{\text{inner}}$), making the energy and frequency strictly characteristic of the target metal. Prominent characteristic lines include $K_\alpha$, $K_\beta$, and $L_\alpha$ corresponding to specific inner and outer shell transitions.

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