Question

In X-ray tube, when the accelerating voltage $V$ is halved, the difference between the wavelength of $K_{\alpha }$ line and minimum wavelength of continuous X-ray spectrum

• A. Remains constant
• B. Becomes more than two times
• C. Becomes half
• D. Becomes less than two times

Answer 1

The correct option is D Becomes less than two times

Let initial difference be ${\lambda }_{K\alpha }-{\lambda }_{min}$. As, ${\lambda }_{min}=hc/eV$ so as $V$ is halved, the ${\lambda }_{min}$ is doubled.

But there would not be any effect on the characteristic wavelength ${\lambda }_{K\alpha }$, as it depends upon the metal properties. Thus new difference is ${\lambda }_{K\alpha }-2{\lambda }_{min}<2({\lambda }_{K\alpha }-{\lambda }_{min})=2\times initialdifference$. So it is less than the two times the initial difference.