When we talk about an x-ray tube and the effects of increasing the potential difference (p.d.), it's essential to understand how this change influences both the intensity and the minimum wavelength of the emitted radiation. Let's break this down step by step to clarify why the correct answer is indeed (a) and not (c).
Understanding X-ray Production
X-rays are produced when high-energy electrons collide with a target material, typically made of tungsten. The energy of these electrons is determined by the potential difference applied across the x-ray tube. When you increase the p.d., you effectively increase the kinetic energy of the electrons.
Effects of Increased Potential Difference
- Intensity of Radiation: The intensity of the emitted x-ray radiation is directly related to the number of high-energy electrons striking the target. When the p.d. is increased, more electrons gain sufficient energy to produce x-rays, leading to an increase in the overall intensity of the emitted radiation.
- Minimum Wavelength: The minimum wavelength of the emitted x-rays is inversely related to the energy of the electrons. According to the equation \(E = \frac{hc}{\lambda}\), where \(E\) is energy, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength, as the energy increases (due to higher p.d.), the minimum wavelength decreases.
Analyzing the Options
Now, let’s analyze the options provided:
- (a) Intensity will increase: This is true because more electrons with higher energy contribute to a greater number of x-ray photons being emitted.
- (b) Minimum wavelength increases: This is incorrect. As explained, increasing the p.d. decreases the minimum wavelength.
- (c) Intensity remains the same while minimum wavelength decreases: This is also incorrect. The intensity does not remain constant; it increases with higher p.d.
- (d) Intensity decreases while minimum wavelength increases: This is false for the same reasons as above.
Conclusion
Based on the principles of x-ray production, the correct answer is indeed (a) — the intensity of the emitted radiation increases when the potential difference is raised, while the minimum wavelength decreases. The confusion may arise from misinterpreting the relationship between intensity and wavelength, but understanding the physics behind x-ray generation clarifies this point. Always remember that higher energy leads to both increased intensity and shorter wavelengths in the context of x-ray tubes.
