Q175 / 180 · KCET 2015 · Physics
An LED is constructed from a pn junction based on a certain semi-conducting material whose
energy gap is \( 1.9 \mathrm{eV} \). Then the wavelength of the emitted light is
energy gap is \( 1.9 \mathrm{eV} \). Then the wavelength of the emitted light is
- A\( 2.9 \times 10^{-9} m \)
- B\( 1.6 \times 10^{-8} \mathrm{~m} \)
- Correct answerC\( 6.5 \times 10^{-7} \mathrm{~m} \)
- D\( 9.1 \times 10^{-5} \mathrm{~m} \)
Solution
Energy gap, \( E_{g}=\frac{h c}{\lambda} \)
Given \( E_{g}=1.9 \mathrm{eV}=1.9 \times 1.6 \times 10^{-19} \)
Therefore,
\( \lambda=\frac{h c}{E_{g}}=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{1.9 \times 1.6 \times 10^{-19}}=6.513 \times 10^{-7} \mathrm{~m} \sim 6.5 \times 10^{-7} \mathrm{~m} \)
Thus, wave length of emitted light is \( 6.5 \times 10^{-7} \mathrm{~m} \)
Given \( E_{g}=1.9 \mathrm{eV}=1.9 \times 1.6 \times 10^{-19} \)
Therefore,
\( \lambda=\frac{h c}{E_{g}}=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{1.9 \times 1.6 \times 10^{-19}}=6.513 \times 10^{-7} \mathrm{~m} \sim 6.5 \times 10^{-7} \mathrm{~m} \)
Thus, wave length of emitted light is \( 6.5 \times 10^{-7} \mathrm{~m} \)
Hence, the correct answer is option: 'C'.