A light-emitting diode (LED) has the property that electrons...

A light-emitting diode (LED) has the property that electrons can be excited into the conduction band by the electrical energy from a battery; a photon is emitted when the electron drops back to the valence band. (a) If the band gap for this diode is $2.36 \mathrm{eV}$, what is the wavelength of the light emitted by the LED? (b) What color is the light emitted? (c) What is the minimum battery voltage required in the electrical circuit containing the diode?

Key Concepts

Photon Energy-Wavelength Relationship

The energy of a photon is inversely proportional to its wavelength, as described by the formula E = hc/?, where h is Planck’s constant and c is the speed of light. This relationship allows one to determine the wavelength of the emitted light from the energy provided by the band gap.

Minimum Voltage Requirement for LED Operation

The minimum battery voltage required to power an LED must meet or exceed the energy needed to excite an electron across the band gap. In terms of electrical units, the energy band gap expressed in electron-volts also indicates the approximate minimum voltage needed in the circuit to overcome the barrier for electron excitation.

Visible Spectrum and Color Identification

The wavelength of light falls into the visible spectrum, which is perceived as different colors based on the wavelength. By comparing the computed wavelength of emitted light with the known range of wavelengths for colors (for example, green light typically falls between roughly 495–570 nm), one can identify the color of the light from an LED.

Semiconductor Band Gap

The band gap in a semiconductor is the energy difference between the conduction band and valence band. In LEDs, electrons excited from the valence band to the conduction band lose energy when they recombine and drop back, releasing energy in the form of photons. The magnitude of the band gap directly determines the energy of the emitted photon, and consequently, its wavelength.

Electron-Volt to Joule Conversion

Electron-volts (eV) are a unit of energy commonly used in atomic and semiconductor physics. The conversion factor, where 1 eV equals about 1.602 x 10^-19 Joules, is crucial when applying formulas that involve fundamental physical constants expressed in SI units.

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