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Chapter 12: Problem 88

CdS has a band gap of 2.4 eV. If large crystals of CdS are illuminated with ultraviolet light, they emit light equal to the band gap energy. (a) What color is the emitted light? (b) Would appropriately sized CdS quantum dots be able to emit blue light? (c) What about red light?

Short Answer

Expert verified
The emitted light from CdS is green with a wavelength of 518 nm. Appropriately sized CdS quantum dots could potentially emit blue light due to the tunability of the band gap with size. However, CdS quantum dots would not emit red light, as their band gaps are larger than that of the bulk material.

Step by step solution

01

Calculate the Wavelength of Emitted Light

First, we need to convert the band gap energy from electron-volts (eV) to Joules (J) using: 1 eV = 1.60 x 10⁻¹⁹ J So, \(E = 2.4 eV * (1.60 * 10^{-19} J/eV) = 3.84 * 10^{-19} J\) Now, we can find the wavelength of the emitted light using the equation: \(\lambda = \dfrac{h \cdot c}{E}\) Where \(h = 6.626 \times 10^{-34} Js, c = 3 \times 10^8 m/s\), and \(E = 3.84 * 10^{-19} J\) Plugging the values into the equation, we get: \(\lambda = \dfrac{6.626 \times 10^{-34} Js \cdot 3 \times 10^8 m/s}{3.84 * 10^{-19} J}\) \(\lambda = 5.18 \times 10^{-7} m\), or 518 nm
02

Determine the Color of Emitted Light

Based on the calculated wavelength of 518 nm, the emitted light is in the green portion of the visible spectrum. Hence, the color of the emitted light is green.
03

Blue Light Emission from CdS Quantum Dots

Blue light has a wavelength range of approximately 450-495 nm, which corresponds to a higher energy than the 2.4 eV band gap of bulk CdS. In quantum dots, due to quantum confinement effects, the band gap can be tuned depending on their size. Smaller quantum dots have larger band gaps, resulting in higher-energy (shorter-wavelength) light emission. To emit blue light, CdS quantum dots must have a band gap energy greater than that required for the blue wavelength range. Thus, appropriately sized CdS quantum dots could potentially emit blue light.
04

Red Light Emission from CdS Quantum Dots

Red light has a wavelength range of approximately 620-750 nm, which corresponds to a lower energy than the 2.4 eV band gap of bulk CdS. Since quantum dots can have larger band gaps than the bulk material, the red light (lower-energy light) emission would not be possible from CdS quantum dots. In summary, (a) the emitted light from CdS is green, (b) appropriately sized CdS quantum dots would be able to emit blue light, and (c) CdS quantum dots would not emit red light.

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