For LED's to emit light in visible region of electromagnetic light, it should have energy band gap in the range of:

To determine the energy band gap required for LEDs to emit light in the visible region, we need to recall that the visible spectrum ranges from approximately 400 nm (violet) to 700 nm (red). The energy $$E$$ of a photon is related to its wavelength $$\lambda$$ by the formula:

$$E = \frac{hc}{\lambda}$$

where $$h$$ is Planck's constant ($$4.135667662 \times 10^{-15}$$ eV·s), $$c$$ is the speed of light ($$3 \times 10^8$$ m/s), and $$\lambda$$ is the wavelength in meters. However, it is convenient to use nanometers for wavelength and the approximation $$hc \approx 1240$$ eV·nm, so the formula simplifies to:

$$E \text{ (in eV)} = \frac{1240}{\lambda \text{ (in nm)}}$$

Now, calculate the energy for the shortest visible wavelength (400 nm, violet light, highest energy):

$$E_{\text{violet}} = \frac{1240}{400} = 3.1 \text{ eV}$$

Next, calculate the energy for the longest visible wavelength (700 nm, red light, lowest energy):

$$E_{\text{red}} = \frac{1240}{700} \approx 1.771 \text{ eV}$$

Thus, the energy range for visible light photons is approximately 1.771 eV to 3.1 eV. For an LED to emit visible light, its energy band gap must match the energy of the photons in this range because the emitted photon energy equals the band gap energy.

Comparing this range with the given options:

• Option A: 0.1 eV to 0.4 eV → Too low (corresponds to infrared, not visible)
• Option B: 0.5 eV to 0.8 eV → Too low (corresponds to infrared)
• Option C: 0.9 eV to 1.6 eV → Too low (1.6 eV is about 775 nm, which is in the infrared; 1.6 eV is less than the 1.771 eV required for red light)
• Option D: 1.7 eV to 3.0 eV → This covers energies from 1.7 eV (about 729 nm, near red) to 3.0 eV (about 413 nm, violet). While 3.0 eV is slightly less than 3.1 eV (400 nm), it still covers most of the visible spectrum, including blue and violet regions (since 413 nm is violet). The lower limit of 1.7 eV is very close to the 1.771 eV for red light.

Therefore, the band gap range for visible LEDs is 1.7 eV to 3.0 eV, which corresponds to Option D.

Hence, the correct answer is Option D.