Matching Atomic Laws and Processes with Physical Phenomena

To determine the correct matches between Column I and Column II, we analyze each entry individually:

1. (A) Transition between two atomic energy levels:

   • Characteristic X-rays (p): When high-energy incident electrons create a vacancy in an inner shell (such as the $K$ or $L$ shell) of an atom, an outer-shell electron transitions to this lower vacant energy level, releasing the difference in energy as a characteristic X-ray photon.
   • Hydrogen spectrum (r): The emission or absorption line spectrum of hydrogen arises from the transitions of an electron between quantized atomic energy levels according to Bohr's model ($\Delta E = E_n - E_m = h\nu$).
   • Therefore, (A) matches with (p) and (r).

2. (B) Electron emission from a material:

   • Photoelectric effect (q): When electromagnetic radiation of suitable frequency strikes the surface of a material, electrons (photoelectrons) are ejected from the material.
   • $\beta$-decay (s): In nuclear $\beta^-$-decay, a neutron decays into a proton, an antineutrino, and an electron ($\text{n} \to \text{p} + \text{e}^- + \bar{\nu}_e$), leading to the emission of high-speed electrons from the radioactive material.
   • Therefore, (B) matches with (q) and (s).

3. (C) Moseley's law:

   • Moseley's law relates the frequency $\nu$ of the characteristic X-ray lines emitted by an element to its atomic number $Z$:
     $\sqrt{\nu} = a(Z - b)$
     where $a$ and $b$ are constants for a given spectral series.
   • Thus, Moseley's law governs the emission of Characteristic X-rays (p).
   • Therefore, (C) matches with (p).

4. (D) Change of photon energy into kinetic energy of electrons:

   • Photoelectric effect (q): According to Einstein's photoelectric equation:
     $h\nu = \Phi + K_{\max}$
     The energy of an incident photon ($h\nu$) is absorbed by an electron, overcoming the work function ($\Phi$) and imparting kinetic energy ($K$) to the emitted electron.
   • Therefore, (D) matches with (q).

---

Final Matching:

• (A) $\to$ (p), (r)
• (B) $\to$ (q), (s)
• (C) $\to$ (p)
• (D) $\to$ (q)