Question

The intensity of X-rays from a Coolidge tube is plotted against wavelength $\lambda$ as shown in the figure. The minimum wavelength found is ${\lambda }_C$ and the wavelength of the $K_{\alpha }$ line ${\lambda }_K$. As the accelerating voltage is increased :

• A. ${\lambda }_K-{\lambda }_C$ increases
• B. ${\lambda }_K-{\lambda }_C$ decreases
• C. ${\lambda }_K$ increases
• D. ${\lambda }_K$ decreases

Answer 1

The correct option is A ${\lambda }_K-{\lambda }_C$ increases

In case of coolidge tube.

${\lambda }_{min}=\frac{hc}{eV}={\lambda }_c$ (as given here)

Thus, the cut -off wavelength is inversely proportional to acclerating voltage. As V increases ${\lambda }_c$ decreases.

λk is the wavelength of $K_{\infty }$ luine which is a characteristic of an atom and does not depend on accelerating voltage of bombarding electron since λk always refers to a photon wavelength of transition of e from the target element from 2→1

the above two facts lead to the conclusion that λk−λc increases as accelerating voltage is increased.