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Electrons of mass m with de Broglie wavelength λ fall on the target in an X-ray tube. The cut-off wavelength λ₀ of the emitted X-ray is:

Asked in NEET 2016 Phase-II · X-ray cut-off wavelength

• (1) λ₀=(2mcλ²)/h
• (2) λ₀=(2h)/(mc)
• (3) λ₀=(2m²c²λ³)/(h²)
• (4) λ₀=λ

Step-by-step solution

Why the other options are wrong

• (2) comes from has the shape of the Compton wavelength h/mc, which is a fixed property of the electron and carries no dependence on the incident wavelength at all
• (3) comes from no single slip reproduces it. The check: the answer must go as λ², because the electron's kinetic energy goes as 1/λ² and the X-ray wavelength is inversely proportional to that energy
• (4) comes from assumes the X-ray photon simply inherits the electron's de Broglie wavelength; the photon's wavelength is fixed by the electron's kinetic energy, which is far smaller than hc/λ

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