The energy band gap of semiconducting material to produce violet (wavelength $$= 4000$$ $$\mathring{A}$$) LED is ______ eV. (Round off to the nearest integer).

The energy of a photon corresponding to the wavelength of the LED is equal to the band gap energy of the semiconductor.

Given: Wavelength $$\lambda = 4000 \text{ Å} = 4000 \times 10^{-10} \text{ m} = 4 \times 10^{-7} \text{ m}$$

The energy band gap is:

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

where $$h = 6.626 \times 10^{-34} \text{ J s}$$ and $$c = 3 \times 10^8 \text{ m s}^{-1}$$.

$$E = \dfrac{6.626 \times 10^{-34} \times 3 \times 10^8}{4 \times 10^{-7}}$$

$$E = \dfrac{19.878 \times 10^{-26}}{4 \times 10^{-7}} = 4.9695 \times 10^{-19} \text{ J}$$

Converting to electron volts ($$1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$$):

$$E = \dfrac{4.9695 \times 10^{-19}}{1.6 \times 10^{-19}} = 3.106 \text{ eV}$$

Rounding off to the nearest integer:

$$E \approx 3 \text{ eV}$$

Therefore, the energy band gap is $$\boxed{3}$$ eV.