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. $0.1eV$
• B. $0.5eV$
• C. $1.0eV$
• D. $2.0eV$

Answer 1

The correct option is A $0.1eV$

We know that:-

${\lambda }_{m}T=b$ , where ${\lambda }_m$ is the wavelength of maximum intensity

$T=temperature$ and $b=Stefa{n}^{\prime }sconstant$ $=2.88\times {10}^{-3}$

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

Hence, ${\lambda }_m=\frac{b}{T}=\frac{2.88\times {10}^{-3}}{310}m=9.3\times {10}^{-6}m$

Now, energy of photon,$E=\frac{hc}{{\lambda }_m}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{9.3\times {10}^{-6}}J$

$E=2.14\times {10}^{-20}J=\frac{2.14\times {10}^{-20}}{1.6\times {10}^{-19}}eV$

$⟹E\approx 0.1eV=Bandgapofsemi-conductor$

Hence, answer is option-(A).