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Chapter 12: Problem 89

True or false: (a) The band gap of a semiconductor decreases as the particle size decreases in the \(1-10-\mathrm{nm}\) range. (b) The light that is emitted from a semiconductor, upon external stimulation, becomes longer in wavelength as the particle size of the semiconductor decreases.

Short Answer

Expert verified
(a) False - Due to quantum confinement, the band gap of a semiconductor actually increases as the particle size decreases in the 1-10 nm range. (b) False - As the particle size of the semiconductor decreases, the band gap energy increases, resulting in shorter wavelengths of emitted light.

Step by step solution

01

Statement (a) Analysis and Conclusion

In the 1-10 nm range, semiconductors are considered to be in the "quantum confinement" regime. In this regime, the size of the particles significantly affects the electronic properties of the material. Due to quantum confinement, the energy levels of the semiconductor deviate from their bulk behavior and become discrete, like those of an atom or a molecule. As the particle size decreases, the energy levels in the conduction and valence bands become more discrete and spaced farther apart. This leads to an increase, not a decrease, in the band gap energy as the particle size is reduced. Thus, the statement (a) is False.
02

Statement (b) Analysis and Conclusion

The wavelength of the light emitted by a semiconductor is related to the size of the band gap. Larger band gap energies result in shorter wavelengths of emitted light, while smaller band gap energies result in longer wavelengths. From our analysis of statement (a), we know that as the particle size of the semiconductor decreases, the band gap energy increases due to quantum confinement. This means that emitted light would have a shorter wavelength as the particle size decreases. Thus, the statement (b) is also False.

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Most popular questions from this chapter

In their study of X-ray diffraction, William and Lawrence Bragg determined that the relationship among the wavelength of the radiation \((\lambda),\) the angle at which the radiation is diffracted \((\theta),\) and the distance between planes of atoms in the crystal that cause the diffraction \((d)\) is given by \(n \lambda=2 d \sin \theta .\) X-rays from a copper X-ray tube that have a wavelength of \(1.54 \AA\) are diffracted at an angle of 14.22 degrees by crystalline silicon. Using the Bragg equation, calculate the distance between the planes of atoms responsible for diffraction in this crystal, assuming \(n=1\) (first-order diffraction).

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