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Question

Difficulty: MediumX-rays: Production, Properties, and Applications

In a standard Coolidge X-ray tube setup, the filament heating current is increased while maintaining a constant accelerating potential difference between the cathode and the target anode. Which of the following changes will be observed in the emitted X-ray beam?

  1. The intensity of the X-ray beam increases while its minimum cut-off wavelength remains unchangedAnswer
  2. B
    The penetrating power of the X-ray beam increases while its intensity remains constant
  3. C
    The minimum cut-off wavelength of the X-ray beam decreases while its intensity increases
  4. D
    Both the maximum frequency and the overall intensity of the X-ray beam increase

Answer

The intensity of the X-ray beam increases while its minimum cut-off wavelength remains unchanged
Increasing the filament current raises cathode temperature, causing thermionic emission of more electrons per second. This increases the total number of X-ray photons emitted per second, which means the intensity of the X-ray beam increases. Since the accelerating potential difference is held constant, the maximum kinetic energy imparted to each electron (eVe V) is unchanged. Consequently, the minimum cut-off wavelength given by λmin⁡=hceV\lambda_{\min} = \frac{h c}{e V} remains constant.

Step-by-Step Solution

1
Determine the physical effect of increasing the filament heating current
Higher filament current increases filament temperature, releasing a greater number of electrons per second via thermionic emission.
The rate of electron emission directly determines the number of X-ray photons generated per unit time, which defines the beam intensity.
2
Determine the physical effect of a constant accelerating potential difference
The maximum kinetic energy of striking electrons (Emax⁡=eVE_{\max} = e V) and minimum wavelength (λmin⁡=hceV\lambda_{\min} = \frac{h c}{e V}) remain constant.
The accelerating voltage controls individual electron energy, which governs X-ray hardness and minimum cut-off wavelength via the Duane-Hunt law.

Key Concept

Intensity vs Hardness Control in X-ray Tubes
Estimated Time:1m 0s
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Topics

X-rays: Production, Properties, and Applications

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