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An LED is constructed from a p-n junction diode using GaAsP. The energy gap is $1.9 \mathrm{eV}$. The wavelength of the light emitted will be equal to
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Verified Answer
The correct answer is:
$654 \mathrm{~nm}$
The energy of light of wavelength $\lambda$ is given by
$$
\mathrm{E}=\mathrm{hv}=\frac{\mathrm{hc}}{\lambda} \Rightarrow \lambda=\frac{\mathrm{hc}}{\mathrm{E}}
$$
Here, $\mathrm{h}=$ Planck's constant $=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}$
$\mathrm{c}=$ speed of light $=3 \times 10^8 \mathrm{~m} / \mathrm{s}$
$\mathrm{E}=$ energy gap $=1.9 \mathrm{eV}=1.9 \times 1.6 \times 10^{-19} \mathrm{~J}$
Substituting the given values in Eq. (i), we get
$$
\begin{aligned}
\Rightarrow \quad \lambda & =\frac{6.63 \times 10^{-34} \times 3 \times 10^8}{1.9 \times 1.6 \times 10^{-19}} \\
& =6.54 \times 10^{-7} \mathrm{~m} \approx 654 \mathrm{~nm}
\end{aligned}
$$
Thus, the wavelength of light emitted from LED will be $654 \mathrm{~nm}$.
$$
\mathrm{E}=\mathrm{hv}=\frac{\mathrm{hc}}{\lambda} \Rightarrow \lambda=\frac{\mathrm{hc}}{\mathrm{E}}
$$
Here, $\mathrm{h}=$ Planck's constant $=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}$
$\mathrm{c}=$ speed of light $=3 \times 10^8 \mathrm{~m} / \mathrm{s}$
$\mathrm{E}=$ energy gap $=1.9 \mathrm{eV}=1.9 \times 1.6 \times 10^{-19} \mathrm{~J}$
Substituting the given values in Eq. (i), we get
$$
\begin{aligned}
\Rightarrow \quad \lambda & =\frac{6.63 \times 10^{-34} \times 3 \times 10^8}{1.9 \times 1.6 \times 10^{-19}} \\
& =6.54 \times 10^{-7} \mathrm{~m} \approx 654 \mathrm{~nm}
\end{aligned}
$$
Thus, the wavelength of light emitted from LED will be $654 \mathrm{~nm}$.
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