An X-ray tube operates at an accelerating potential $V$, producing both continuous and characteristi

Question

An X-ray tube operates at an accelerating potential $V$, producing both continuous and characteristic X-ray spectra from a target material of atomic number $Z$. Let $\lambda_c$ be the cutoff wavelength of the continuous spectrum and $\lambda_{K\alpha}$ be the wavelength of the $K_{\alpha}$ characteristic line. Which of the following is/are correct?

Professor PC Thomas Classes · Answer

•	(A) Duane-Hunt Law: $\lambda_c = \frac{hc}{eV}$, so $\lambda_c \propto 1/V$.
•	(B) False. Characteristic wavelengths depend solely on the energy levels of the target material ($Z$), not on the applied potential $V$ (as long as $V$ is sufficient to excite the series).
•	(C) The $K_{\alpha}$ transition ($n=2 ightarrow n=1$) involves less energy difference than the $K_{\beta}$ transition ($n=3 ightarrow n=1$). Since $E = hc/\lambda$, a smaller energy means a longer wavelength. So $\lambda_{K\alpha} > \lambda_{K\beta}$.
•	(D) Energy levels: $E_{K\beta} - E_{K\alpha} = (E_M - E_K) - (E_L - E_K) = E_M - E_L = E_{L\alpha}$. Dividing by $h$ gives $
u_{K\beta} - 
u_{K\alpha} = 
u_{L\alpha}$.