Animated Solution for Physics - Atoms and Nuclei: Some laws/processes are given in Column-I. Match these with the physical phenomena given in Column-II.

Let's begin our journey by exploring the fascinating world of atomic transitions. According to the Bohr model, electrons orbit the nucleus in discrete energy levels. When an electron jumps from a higher energy state ($n_2$) to a lower energy state ($n_1$), it must shed the excess energy. It does this by emitting a photon of electromagnetic radiation, where the energy of the photon is exactly equal to the energy difference between the two levels:

If this transition happens in a simple hydrogen atom, the emitted photons fall into specific series (like Lyman, Balmer, or Paschen), creating the beautiful Hydrogen spectrum.

However, if we look at heavy elements (like Tungsten or Molybdenum), the energy gaps between the innermost shells (K, L, M) are massive. If a high-speed electron knocks out an inner-shell electron, an outer-shell electron plummets down to fill the void. The photon emitted in this high-energy transition is what we call a Characteristic X-ray. Therefore, the physical process of atomic transitions is responsible for both the hydrogen spectrum and characteristic X-rays.

Light as Particles

Next, we encounter one of the most revolutionary concepts in modern physics: the Photoelectric effect. Imagine shining a beam of light onto a pristine metal surface. Classical wave theory predicted that any light, if shone long enough, would eventually transfer enough energy to eject an electron.

Einstein proved this wrong. He showed that light behaves as a stream of particles called photons. If a single photon has a frequency ($ u$) greater than the material's threshold frequency, it can instantly transfer its energy to an electron, overcoming the material's work function ($extW$) and ejecting the electron with kinetic energy:

Thus, the physical phenomenon of electron emission from a material under the influence of light is exclusively matched with the photoelectric effect.

Ordering the Elements

Finally, we arrive at Moseley's law. In 1913, Henry Moseley conducted a brilliant experiment measuring the frequencies of characteristic X-rays emitted by various elements. He discovered a striking empirical relationship:

Here, $ u$ is the frequency of the X-ray, $Z$ is the atomic number of the target element, and $a$ and $b$ are constants for a specific spectral line (like $K_{\alpha }$).

This law was a monumental breakthrough. It proved that the atomic number ($Z$)—the number of protons in the nucleus—is the true fundamental property that defines an element, rather than its atomic mass. Because Moseley's law specifically governs the frequencies of characteristic X-rays, it is a perfect match for them.

By weaving together these fundamental principles of modern physics, we can confidently construct our final matrix match:

A. Transition between two atomic energy levels $\to$ (p) Characteristic X-rays, (r) Hydrogen spectrum B. Electron emission from a material $\to$ (q) Photoelectric effect C. Moseley's law $\to$ (p) Characteristic X-rays