Question

The semiconductor band gap energy determines the color of an LED. Knowing what you learned in Chapter 6 about the energies of photons of different colors of light, which semiconductor would have the larger band gap: the one in a green exit sign's LEDs, or the one in a red traffic signal?

Short answer

The semiconductor in green LEDs has a larger band gap than red LEDs.

Step-by-step solution

Understand the Relationship Between Wavelength and Energy

The energy of a photon is inversely proportional to its wavelength. This means photons with shorter wavelengths have higher energy. In terms of visible light, blue and green light have shorter wavelengths than red light, so they have higher energy.

Identify the Wavelength Range of Green and Red Light

Green light has a wavelength range of approximately 495-570 nm, whereas red light has a range of about 620-750 nm. This indicates that green light has a shorter wavelength than red light.

Apply Energy-Wavelength Relationship to Band Gap

Since the energy of green light is higher than that of red light, and knowing that the color emitted by an LED is determined by the semiconductor's band gap, the semiconductor used in green LEDs has a larger band gap energy compared to the one used in red LEDs.

Key concepts

Photon Energy

Photon energy is a crucial concept in understanding the behavior of light. Every photon, which is essentially a packet of light, possesses a specific amount of energy. This energy is dictated by its frequency and inversely by its wavelength. The relationship between photon energy (\( E \)) and its frequency (\( u \)) is given by the equation \( E = h u \). Here, \( h \) is Planck's constant, a fundamental constant in physics.For visible light, the energy varies across different colors. Blue light photons, for example, have higher energy compared to red light photons. This is due to their higher frequency and shorter wavelength. When discussing LEDs and their colors, photon energy plays a crucial role because it determines the color of the light emitted by the LED.

Wavelength

Wavelength refers to the distance between consecutive peaks of a wave. For light waves, it is measured in nanometers (nm) and determines the color of the light. In the context of the visible spectrum, wavelengths range broadly from about 380 nm to 750 nm. Different colors of light correspond to different wavelengths:

• Violet light has the shortest wavelength, around 380-450 nm.
• Blue light follows with 450-495 nm.
• Green light lies between 495-570 nm.
• Yellow and orange cover 570-620 nm.
• Red light has the longest wavelength, ranging from 620-750 nm.

The inverse relationship between wavelength and energy means that longer wavelengths correspond to lower energy photons. Thus, red light photons are less energetic than green or blue ones. This is vital for understanding semiconductor behavior in LEDs, as the wavelength also determines the necessary band gap for emitting specific colors.

LED Color

The color of light an LED emits is directly linked to the band gap energy of the semiconductor material. A semiconductor's band gap is the energy difference between its valence and conduction bands. When this gap matches the energy of a photon, light is emitted. For instance:

• A lower band gap emits lower-energy red photons.
• A medium band gap emits green photons.
• A high band gap emits even higher-energy blue photons.

This relationship is critical to LED technology, where diverse semiconductor materials are engineered to produce desired light colors. Knowing the band gap helps in selecting the right material for efficient LED design, catering to applications where specific colors are needed, such as traffic signals or decorative lights.

Visible Light Spectrum

The visible light spectrum is the portion of the electromagnetic spectrum discernible by the human eye. It ranges from approximately 380 nm to 750 nm, unfolding as various colors. This segment of the spectrum is what we perceive as light. Here are a few key points:

• Short wavelengths appear as violet and blue.
• Middle-range wavelengths show as green.
• Long wavelengths are seen as red.

Each color corresponds to specific photon energy levels. Understanding the visible spectrum is essential when designing optical devices like LEDs, allowing them to emit light within this perceptible range. The visible spectrum not only defines color in lighting systems but also has applications in art, photography, and even in scientific tools like spectrometers.