(a) Correlation between Wavelength and System Size

• Step 1 (Governing Principle): [0.5 Mark] The wavelength ($\lambda$) of electromagnetic radiation is typically of the same order of magnitude as the physical dimensions of the source or the system interacting with the wave.
• Step 2 (Examples): [1.0 Mark]
  • Example 1: Gamma rays ($\lambda \approx 10^{-12} \text{ m}$) are produced by transitions of nuclei, which have dimensions of the order of $10^{-14} \text{ m}$ to $10^{-15} \text{ m}$.
  • Example 2: Radio waves ($\lambda \approx 10^2 \text{ m}$ to $10^4 \text{ m}$) are produced by the oscillation of electrons in large-scale antenna systems, which are designed with lengths comparable to these wavelengths to ensure efficient resonance.

(b) Reasoning for Wave Propagation and Detection

• Step 1 (Long-distance Radio Broadcasts): [0.75 Mark] Short-wave bands (typically in the range of $3 \text{ MHz}$ to $30 \text{ MHz}$) are used for long-distance communication because these waves undergo total internal reflection (refraction) by the ionosphere. This allows the waves to be reflected back to Earth, enabling communication beyond the line-of-sight (over the horizon).
• Step 2 (Telescope Placement): [0.75 Mark]
  • Optical and radio waves fall within the atmospheric windows, meaning they can pass through the Earth's atmosphere without being significantly absorbed.
  • X-rays have very high energy and short wavelengths; they are completely absorbed by the Earth's atmosphere (specifically by the ozone layer and other gases). Therefore, X-ray detectors must be placed in space (satellites) to receive these signals before they are attenuated.