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Question

The intensity of radiation from a human body is maximum around a certain wavelength. A photon of this wavelength can just excite an electron from the valence to the conduction band of a semiconductor used in a night vision device. Assume that the black body radiation law holds for the human body. The band gap of such a semiconductor is close to


A
0.1eV
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B
0.5eV
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C
1.0eV
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D
2.0eV
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Solution

The correct option is A $$0.1 eV$$
We know that:-
              $$\lambda_mT=b$$ , where $$\lambda_m$$ is the wavelength of maximum intensity
              $$T= temperature$$   and $$b=Stefan's \hspace{1mm}constant$$ $$=2.88\times 10^{-3}$$

Here,$$T=$$ body temperature $$37^{o}C=310K$$

Hence, $$\lambda_m=\dfrac{b}{T}=\dfrac{2.88\times 10^{-3}}{310}m=9.3\times 10^{-6}m$$

Now, energy of photon,$$E=\dfrac{hc}{\lambda_m}=\dfrac{6.63\times10^{-34}\times 3\times 10^8}{9.3\times 10^{-6}}J$$

$$E=2.14\times10^{-20}J=\dfrac{2.14\times10^{-20}}{1.6\times10^{-19}}eV$$

$$\implies E \approx0.1eV=Band \ gap \ of \ semi-conductor$$

Hence, answer is option-(A).

Physics
NCERT
Standard XII

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