Question

Intensity of X - rays from a Coolidge tube is plotted against wavelength $\lambda$ as shown in the figure.

Minimum wavelength is ${\lambda }_0$ and the wavelength of the $K_{\alpha }$ - line is ${\lambda }_K$. As, the accelerating voltage is increased.

• A. ${\lambda }_k-{\lambda }_c$ increases
• B. ${\lambda }_k-{\lambda }_c$ decreases
• C. ${\lambda }_{k}a$ increases
• D. ${\lambda }_k\beta$ increases

Answer 1

The correct option is A ${\lambda }_k-{\lambda }_c$ increases

Characteristics X - rays are prorduced when bombarding electron knocks out an electron knocks out an electron from outer shell. $k_{\alpha }$ wavelength is produced due to electronic transition of an electron
(n = 2 to n = 1) of target metal atom.
So, ${\lambda }_{k\alpha }=X_k=\frac{hc}{\Delta E_{2\to 1}}=\frac{hc}{10.2(Z-1{)}^2}$

Note $E_{K\alpha }$ = Energy of $K_{\alpha }$ photon $=10.2(Z-1{)}^2$ and
Also minimum wavelength is produced when the bombarding electron lost complete KE in only one collision.
Then, ${\lambda }_{min}=\frac{hc}{E_{electron}}=\frac{hc}{e{V}_0}$
Where, $V_0$ = accelerating voltage for bombarding electron. So, when $V_0$ = accelerating voltage for bombarding electron.
So, when $V_{(}0)$ is increased, ${\lambda }_{min}$ is reduced but ${\lambda }_K$ is constart So ${\lambda }_K-{\lambda }_C$ increases.