Question

{"given":"Energy of incident electrons: $E = 80$ keV $= 80 \\times 10^3$ eV; K-shell binding energy of tungsten: $E_K = 72.2$ keV","key_observation":"When electrons strike a target, they always produce Bremsstrahlung (continuous) X-rays. Characteristic X-rays are additionally produced only if the incident electron energy exceeds the binding energy of an inner-shell electron.","option_analysis":[{"label":"(A)","text":"Only a continuous X-ray spectrum (Bremsstrahlung) with a minimum wavelength of $0.155$ Å","verdict":"incorrect","explanation":"While the minimum wavelength is correctly $0.155$ Å, this option is incomplete because it ignores the characteristic X-rays that are also produced since $80$ keV $> 72.2$ keV."},{"label":"(B)","text":"Only a continuous X-ray spectrum (Bremsstrahlung) with all wavelengths","verdict":"incorrect","explanation":"Bremsstrahlung has a minimum wavelength cutoff ($\\lambda_{\\min} = 0.155$ Å), not all wavelengths; also, characteristic X-rays are missing from this description."},{"label":"(C)","text":"Only the characteristic X-ray spectrum of tungsten","verdict":"incorrect","explanation":"Characteristic X-rays alone cannot be produced without the accompanying continuous Bremsstrahlung spectrum; both are always present simultaneously."},{"label":"(D)","text":"A continuous X-ray spectrum (Bremsstrahlung) with a minimum wavelength of $0.155$ Å and the characteristic X-ray spectrum of tungsten","verdict":"correct","explanation":"The minimum wavelength is $\\lambda_{\\min} = \\frac{12375}{80000} \\approx 0.155$ Å, and since $80$ keV $> 72.2$ keV, K-shell electrons can be knocked out, producing characteristic X-rays as well."}],"answer":"(D)","formula_steps":[]}