Electrons of mass m and de Broglie wavelength λ strike an X-ray tube target. The cutoff wavelength λ₀ of emitted X-rays is:
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Question

Electrons of mass m and de Broglie wavelength λ strike an X-ray tube target. The cutoff wavelength λ₀ of emitted X-rays is:

G1 Physics · Accepted Answer

Electron momentum p = h/λ; kinetic energy K = p²/(2m) = h²/(2mλ²). At the short-wavelength limit, photon energy hc/λ₀ = K. So λ₀ = (2mc/h)λ². Answer: A.