Question

LED is constructed from Ga-As-P semiconducting material. The energy gap of this LED is$1.9eV$. Calculate the wavelength of light emitted and its color.$[\mathrm{h}=6.63\times {10}^{-34}\mathrm{Js}\mathrm{and}\mathrm{c}=3\times {10}^8{\mathrm{ms}}^{-1}]$

• A. $654nm$and red color
• B. $1046nm$ and blue color
• C. $1046nm$ and red color
• D. $654nm$ and orange color

Answer 1

Answer: (A), (D)

$654nm$ and orange color

Step 1. Given data:

1. The energy gap of this LED $\mathrm{E}=1.9\mathrm{eV}$
2. Planck's constant $\mathrm{h}=6.63\times {10}^{-34}\mathrm{Js}$
3. Speed of light $c=3\times {10}^{8}8{\mathrm{ms}}^{-1}$

Step 2. Formula used:

The energy gap is related to the wavelength as,

$∆\mathrm{E}=\frac{\mathrm{hc}}{\mathrm{\lambda }}$ (where $\mathrm{\lambda }=$The wavelength of light)

Step 3. Calculating the wavelength of light:

The wavelength of emitted light can be calculated as,

$\begin{array}{rcl}\mathrm{\lambda }& =& \frac{\mathrm{hc}}{∆\mathrm{E}}\\ & =& \frac{6.63\times {10}^{-34}\times 3\times {10}^8}{1.9\times 1.6\times {10}^{-19}}\mathrm{m}\left(\mathrm{where}1\mathrm{eV}=1.6\times {10}^{-19}\mathrm{J}\right)\\ & =& 654\times {10}^{-9}\mathrm{m}\\ & =& 654\mathrm{nm}\end{array}$

And the wavelength of red-colored light is from $620\mathrm{nm}$to$750\mathrm{nm}$.

Thus, the wavelength of the emitted light$654\mathrm{nm}$ and the color is red.

Hence, option A is the correct answer.