An X-ray tube is operated with an accelerating potential of 50 kV. Electrons emitted from the heated cathode are accelerated through the full potential difference before striking the target. Neglect their initial kinetic energy. Take hc = 1240 eV·nm. If the short-wavelength cutoff of the continuous X-ray spectrum is (N ÷ 1000) nm, find N.
Physics · Atomic Structure and X-rays · x-rays and its types
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Question

An X-ray tube is operated with an accelerating potential of 50 kV. Electrons emitted from the heated cathode are accelerated through the full potential difference before striking the target. Neglect their initial kinetic energy. Take hc = 1240 eV·nm. If the short-wavelength cutoff of the continuous X-ray spectrum is (N ÷ 1000) nm, find N.

Physics · Atomic Structure and X-rays · x-rays and its types

G1 Physics · Accepted Answer

The maximum kinetic energy acquired by one electron is K(max) = eV = 50 keV = 5.0×10⁴ eV. The shortest possible X-ray wavelength occurs when one electron gives essentially all of this kinetic energy to one photon: E(max photon) = hc ÷ λ(min). Therefore, λ(min) = 1240 ÷ (5.0×10⁴) nm = 0.0248 nm. This is 24.8 ÷ 1000 nm, which rounds to 25 ÷ 1000 nm. Hence N = 25.