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At $T=300 \:K$, the band gap and the intrinsic carrier concentration of GaAs are $1.42$ eV and $10^6 \: cm^{-3}$, respectively. In order to generate electron hole pairs in GaAs, which one of the wavelength $(\lambda_C)$ ranges of incident radiation, is most suitable? (Given that: Plank’s constant is $6.62 \times 10^{-34} \: J-s$, velocity of light is $3 \times 10^{10} \: cm/s$ and charge of electron is $1.6 \times 10^{-19} \:C$)

  1. $0.42 \: \mu m < \lambda _C < 0.87 \: \mu m$
  2. $0.87 \: \mu m< \lambda _C < 1.42 \: \mu m $
  3. $1.42 \: \mu m < \lambda _C < 1.62 \: \mu m$
  4. $1.62 \: \mu m < \lambda _C < 6.62 \: \mu m$
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