1. Use the relation between band gap and photon energy

For an LED, the emitted photon energy is approximately equal to the band gap energy:

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

So,

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

2. Convert energy gap from eV to joule

Given:

$E = 1.9\,\text{eV}$

Using

$1\,\text{eV} = 1.6 \times 10^{-19}\,\text{J}$

Therefore,

$E = 1.9 \times 1.6 \times 10^{-19} = 3.04 \times 10^{-19}\,\text{J}$

3. Substitute the given values

$h = 6.63 \times 10^{-34}\,\text{J s}$ $c = 3 \times 10^8\,\text{m s}^{-1}$

Thus,

$\lambda = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{3.04 \times 10^{-19}}$

$\lambda = \frac{19.89 \times 10^{-26}}{3.04 \times 10^{-19}}$

$\lambda \approx 6.54 \times 10^{-7}\,\text{m}$

4. Convert into nanometres

Since

$1\,\text{nm} = 10^{-9}\,\text{m}$

$\lambda = 6.54 \times 10^{-7}\,\text{m} = 654 \times 10^{-9}\,\text{m} = 654\,\text{nm}$

5. Determine the colour

A wavelength of about $654\,\text{nm}$ lies in the red region of the visible spectrum.

6. Evaluate options

• A: $654\,\text{nm}$ and orange colour — incorrect colour
• B: $654\,\text{nm}$ and red colour — correct
• C: $1046\,\text{nm}$ and red colour — incorrect wavelength
• D: $1046\,\text{nm}$ and blue colour — incorrect wavelength and colour

Therefore, the correct option is B.