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At T = 300 K, the band gap and the intrinsic carrier concentration of GaAs are 1.42 eV and 10⁶ cm⁻³, respectively. In order to generate electron-hole pairs in GaAs, which one of the wavelengths (λc) ranges of incident radiation, is most suitable? (Given that: Planck's constant is 6.62 × 10⁻³⁴ J-s, velocity of light is 3 × 10⁸ cm/s and charge of electron is 1.6 × 10⁻¹⁹ C)

1. 1.42 μm < λc < 0.87 μm
2. 0.87 μm < λc < 1.42 μm
3. 1.42 μm < λc < 6.62 μm
4. 1.62 μm < λc < 6.62 μm

Correct answer: 1.42 μm < λc < 0.87 μm

Solution

The correct option indicates that the wavelength range must be shorter than the wavelength corresponding to the band gap energy of 1.42 eV, which is approximately 0.87 μm. This ensures that the incident photons have enough energy to generate electron-hole pairs in GaAs.

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