JEE Advanced 2020 Physics question

In an X-ray tube, electrons emitted from a filament (cathode) carrying current hit a target (anode) at a distance from the cathode. The target is kept at a potential higher than the cathode resulting in emission of continuous and characteristic X-rays. If the filament current is decreased to , the potential difference is increased to , and the separation distance is reduced to , then

(A)the cut-off wavelength will reduce to half, and the wavelengths of the characteristic X-rays will remain the sameCorrect
(B)the cut-off wavelength as well as the wavelengths of the characteristic X-rays will remain the same
(C)the cut-off wavelength will reduce to half, and the intensities of all the X-rays will decreaseCorrect
(D)the cut-off wavelength will become two times larger, and the intensity of all the X-rays will decrease

Answer: (A),(C)

Solution

The cut-off (minimum) wavelength of the continuous spectrum corresponds to the full kinetic energy of an electron going into one photon: . It depends only on the accelerating potential, not on the filament current or on the separation ; when , becomes

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Question ID VK-033795