Indicate whether each statement is true or false: (a) The band ga...

Question

Indicate whether each statement is true or false: (a) The band gap of a semiconductor decreases as the particle size decreases in the 1–10-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.

Accepted Answer

Step 1: Understand the relationship between particle size and band gap in semiconductors. In the 1–10 nm range, as the particle size decreases, the band gap typically increases due to quantum confinement effects.. Step 2: Analyze statement (a). Given the relationship from Step 1, if the band gap increases as the particle size decreases, then the statement 'The band gap of a semiconductor decreases as the particle size decreases in the 1–10-nm range' is false.. Step 3: Understand the relationship between band gap and emitted light wavelength. The energy of emitted light is inversely related to its wavelength (E = hc/λ). A larger band gap corresponds to higher energy and thus shorter wavelength.. Step 4: Analyze statement (b). If the band gap increases with decreasing particle size, the emitted light should have higher energy and shorter wavelength. Therefore, the statement 'The light that is emitted from a semiconductor, upon external stimulation, becomes longer in wavelength as the particle size of the semiconductor decreases' is false.. Step 5: Conclude that both statements (a) and (b) are false based on the analysis of the relationship between particle size, band gap, and emitted light wavelength in semiconductors.

주요 개념

Band Gap Energy

Quantum Confinement

Photoluminescence