Question

In an $X$-ray tube, electrons emitted from a filament (cathode) carrying current $I$ hit a target (anode) at a distance $d$ from the cathode. The target is kept at a potential $V$ higher than the cathode resulting in emission of continuous and characteristic $X$-rays. If the filament current $I$ is decreased to $\frac{I}{2}$, the potential difference $V$ is increased to $2 V$, and the separation distance $d$ is reduced to $\frac{ d }{2}$, then

• A. the cut-off wavelength will reduce to half, and the wavelengths of the characteristic X-rays will remain the same
• 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 decrease
• D. the cut-off wavelength will become two times larger, and the intensity of all the X-rays will decrease

Answer 1

Answer: (A), (C)

$\lambda_{c} \propto \frac{1}{V}$, current $\propto$ Intensity