" Radiation with the minimum wavelength as well as the K x-ray lines are detected for a certain target. The energy of the incident electrons is then doubled, with the result that"
A. the minimum wavelength increases and the wavelengths of the K lines remain the same
B. the minimum wavelength decreases and the wavelengths of the K lines remain the same
C. the minimum wavelength and the wavelengths of the K lines all increase
D. the minimum wavelength and the wavelengths of the K lines all decrease
E. the minimum wavelength increases and the wavelengths of the K lines all decrease"
E = hc/wavlength or
wavelength = hc/E.So if E is doubled then wavelength must be smaller. The K radiation from an element is a constant.
Thanks for helping DrBob222.
In order to answer this question, we need to understand the relationship between the energy of incident electrons and the wavelength of radiation emitted by a certain target.
The energy of incident electrons is directly related to the energy of the emitted radiation. According to the wave-particle duality of nature, the energy of a photon (radiation) is proportional to its frequency. And since frequency is inversely proportional to wavelength (higher frequency means shorter wavelength), we can conclude that higher energy corresponds to shorter wavelength.
Now, let's analyze the options given:
A. the minimum wavelength increases and the wavelengths of the K lines remain the same
B. the minimum wavelength decreases and the wavelengths of the K lines remain the same
C. the minimum wavelength and the wavelengths of the K lines all increase
D. the minimum wavelength and the wavelengths of the K lines all decrease
E. the minimum wavelength increases and the wavelengths of the K lines all decrease
If we double the energy of the incident electrons, it means that their energy has increased. According to what we discussed earlier, an increase in energy leads to a decrease in wavelength. Therefore, we can eliminate options C and D.
Now let's specifically consider the K x-ray lines. K x-ray lines are characteristic X-rays emitted when an inner-shell electron is knocked out and an outer-shell electron fills the vacancy. They have specific energies and wavelengths corresponding to the energy levels of the target material. These energy levels are determined by the atomic structure of the target.
Since the energy levels and transitions within the target are not affected by the energy of the incident electrons, we can conclude that the wavelengths of the K x-ray lines will remain the same. That eliminates options A and B.
Therefore, the correct answer is option E: the minimum wavelength increases and the wavelengths of the K lines all decrease.