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?

Verified step by step guidance

Understand that the band gap energy of CdS is 2.4 eV, which is the energy of the emitted light when illuminated with UV light.

Convert the energy from electron volts (eV) to joules (J) using the conversion factor: 1 eV = 1.602 x 10^{-19} J.

Use the energy-wavelength relationship given by the equation: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy in joules, \( h \) is Planck's constant (6.626 x 10^{-34} J·s), \( c \) is the speed of light (3.00 x 10^8 m/s), and \( \lambda \) is the wavelength in meters.

Rearrange the equation to solve for wavelength: \( \lambda = \frac{hc}{E} \). Substitute the values for \( h \), \( c \), and the energy in joules to find the wavelength.

Determine the color of the emitted light by comparing the calculated wavelength to the visible light spectrum, where different wavelengths correspond to different colors.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Band Gap Energy

The band gap energy is the energy difference between the valence band and the conduction band in a semiconductor or insulator. It determines the wavelengths of light that a material can absorb or emit. In the case of CdS, a band gap of 2.4 eV indicates that it can absorb photons with energy equal to or greater than this value, leading to the emission of light when excited.

Photon Energy and Color

The energy of a photon is directly related to its wavelength and frequency, as described by the equation E = hf, where E is energy, h is Planck's constant, and f is frequency. The color of light emitted by a material corresponds to its photon energy; for CdS, a band gap of 2.4 eV corresponds to a wavelength of approximately 517 nm, which falls within the green region of the visible spectrum.

Ultraviolet Light and Excitation

Ultraviolet (UV) light has higher energy than visible light and can excite electrons in a semiconductor like CdS. When large crystals of CdS are illuminated with UV light, electrons are promoted from the valence band to the conduction band, creating electron-hole pairs. When these electrons return to their ground state, they release energy in the form of light, which corresponds to the band gap energy.