X-ray Production
The minimum wavelength of X-rays produced when electrons are accelerated through a potential difference of 12.4 kV is: (h = 6.63 × 10⁻³⁴ J·s, e = 1.6 × 10⁻¹⁹ C, c = 3 × 10⁸ m/s)
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About This Question
- Subject
- physics
- Chapter
- atoms and nuclei
- Topic
- x-ray production
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
0.1 nm
- Duane-Hunt Law: The minimum wavelength λmin corresponds to the case where the whole kinetic energy of an electron is converted into a single photon.
- E=eV=λminhc.
- Formula: λmin=eVhc.
- Substitute Constants:
- λmin=1.6×10−19×12.4×1036.63×10−34×3×108.
- Simplified Ratio: Using the common approximation hc≈12400 eV⋅A˚:
- λmin=1240012400=1 A˚=0.1 nm.
This hard difficulty physics question is from the chapter atoms and nuclei, covering the topic of x-ray production. It appeared in the 2025 exam.
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