91Ó°ÊÓ

In X-ray spectroscopy, the characteristic lines (Kα and Kβ) represent the specific wavelengths of X-rays emitted when electrons from an atom transition between different energy levels, while the continuous spectrum represents the wavelength of X-rays emitted as electrons are decelerated near the anode.

The energy difference between the energy levels in an atom determines the wavelength of the characteristic lines. These are fixed values and do not change upon increasing the potential difference in the Coolidge tube. Therefore, both \(\lambda_{k \alpha}\) and \(\lambda_{k \beta}\) will remain constant as the potential difference is increased.

The border wavelength \(\lambda_{0}\) of the continuous X-ray spectrum is given by the formula: \[\lambda_0 = \frac{h c}{e V} \] Where \(h\) is the Planck's constant, \(c\) is the speed of light, \(e\) is the electronic charge, and \(V\) is the potential difference in the Coolidge tube. From this equation, we can see that increasing the potential difference will lead to a decrease in the border wavelength \(\lambda_{0}\).

Now that we have analyzed the effects of increasing the potential difference on \(\lambda_{k \alpha}\), \(\lambda_{k \beta}\), and \(\lambda_{0}\), we can compare their changes: - The interval between \(\lambda_{k \alpha}\) and \(\lambda_{k \beta}\) does not change since both wavelengths remain constant. Hence, option (A) is incorrect. - The interval between \(\lambda_{k \alpha}\) and \(\lambda_{0}\) increases because \(\lambda_{0}\) decreases while \(\lambda_{k \alpha}\) remains constant. Hence, option (B) is correct. - The interval between \(\lambda_{k \beta}\) and \(\lambda_{0}\) increases because \(\lambda_{0}\) decreases while \(\lambda_{k \beta}\) remains constant. Hence, option (C) is correct. - \(\lambda_{0}\) does change as shown in our analysis, therefore option (D) is incorrect. To summarize, the correct options are (B) and (C).