Step 1: Concept
Light Emitting Diodes (LEDs) work on the principle of injection luminescence, where photons are emitted when electrons recombine with holes across the bandgap ($E_{g}$). To emit visible light, the emitted photon energy must fall within the visible spectrum range ($1.8\text{ eV}$ to $3.0\text{ eV}$).
Step 2: Meaning
The boundary of longest visible wavelength (red light) corresponds to a photon energy of approximately $1.8\text{ eV}$. Therefore, a semiconductor must have a minimum bandgap of $1.8\text{ eV}$ to produce visible light.
Step 3: Analysis
Elemental semiconductors like Silicon ($1.1\text{ eV}$) or Germanium ($0.7\text{ eV}$) have smaller energy gaps and emit light in the infrared region. Compound semiconductors like Gallium Arsenide Phosphide (GaAsP) are specifically manufactured with a bandgap of at least $1.8\text{ eV}$ to emit visible light.
Step 4: Conclusion
Thus, the minimum energy gap required for a visible light emitting diode is 1.8 eV.
Final Answer: (D)