Atomic Physics

To determine the relationship between the minimum wavelength of X-rays and the potential difference through which electrons are accelerated, we use the concept of X-ray production in a Coolidge tube. When electrons are accelerated through a potential difference , their kinetic energy becomes , where is the charge of the electron. Upon collision with a target, this energy can be converted into a photon of X-ray, obeying the energy conservation principle. The energy of a photon is given by , where is Planck's constant, is the speed of light, and is the wavelength. Thus, equating the energy, we have:

Rearranging to find the minimum wavelength , we obtain:

This expression shows that the minimum wavelength is inversely proportional to the potential difference . Therefore, the correct proportionality for the minimum wavelength is:

In order to solve this problem, we need to analyze both statements individually and assess their accuracy based on fundamental concepts in physics:

Statement I: Atoms are electrically neutral as they contain an equal number of positive and negative charges.
This statement is correct. An atom comprises protons, which are positively charged, and electrons, which are negatively charged. In a neutral atom, the number of protons equals the number of electrons, resulting in no net charge.

Statement II: Atoms of each element are stable and emit their characteristic spectrum.
This statement is incorrect. While atoms do emit a characteristic spectrum, they are not inherently stable. Stability varies among atoms; some are stable while others may be radioactive. The emission of characteristic spectra is often due to electrons moving between energy levels, not because atoms themselves are stable.

After evaluating both statements, we conclude: Statement I is correct but Statement II is incorrect.