Question

The first LEDs were made from GaAs, which has a band gap of \(1.43 \mathrm{eV}\). What wavelength of light would be emitted from an LED made from GaAs? What region of the electromagnetic spectrum does this light correspond to: UV, visible, or IR?

Short answer

The wavelength of light emitted from a GaAs LED with a band gap of 1.43 eV is approximately \(864.9 \mathrm{nm}\), and it corresponds to the infrared region of the electromagnetic spectrum.

Step-by-step solution

Convert energy from eV to Joules

First, we need to convert the energy of the band gap from eV to Joules. We know that 1 eV is equal to 1.6 x 10^-19 J. E = 1.43 eV × (1.6 x 10^-19 J/eV) E = 2.288 x 10^-19 J

Calculate the wavelength of light emitted

Now we can use the energy-wavelength formula (E = hc / λ) to find the wavelength of light emitted. Here, E is the energy, 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 λ is the wavelength. We can rewrite the formula to solve for λ: λ = hc / E Substitute the values: λ = (6.626 x 10^-34 J·s) × (3.00 x 10^8 m/s) / 2.288 x 10^-19 J λ ≈ 8.649 x 10^-7 m To express the wavelength in nanometers, we can multiply by 10^9: λ ≈ 864.9 nm

Determine the region of the electromagnetic spectrum

Now that we have the wavelength, we can determine the region of the electromagnetic spectrum this light corresponds to. - UV (ultraviolet) region: 10 nm to 400 nm - Visible region: 400 nm to 700 nm - IR (infrared) region: 700 nm to 1 mm Since our calculated wavelength (864.9 nm) falls within the range of the infrared region, the light emitted from a GaAs LED is in the infrared region of the electromagnetic spectrum.

Summary

The wavelength of light emitted from a GaAs LED with a band gap of 1.43 eV is approximately 864.9 nm, and it corresponds to the infrared region of the electromagnetic spectrum.

Key concepts

LED

An LED, or Light Emitting Diode, is a semiconductor device that emits light when an electric current passes through it. LEDs are popular because they are efficient, long-lasting, and come in a variety of colors. Here's how they work:

• LEDs are made of semiconductor materials, typically including elements like gallium, arsenic, or phosphorus.
• When an electric current flows through the LED, electrons recombine with holes in the semiconductor.
• This recombination releases energy in the form of photons, which we see as light.

LEDs can emit different colors based on the materials used and the energy of the band gap between the semiconductor's conduction and valence bands. This makes them suitable for various applications, from small indicator lights to large displays and lighting fixtures.
LEDs are not only efficient in saving power but are also environmentally friendly as they do not contain harmful chemicals like mercury.

infrared radiation

Infrared radiation is a type of electromagnetic radiation with wavelengths longer than visible light but shorter than microwave radiation. It is commonly abbreviated as IR. Here's what you need to know about infrared radiation:

• It is part of the electromagnetic spectrum in the wavelength range of about 700 nm to 1 mm.
• Infrared radiation is emitted by all objects that have heat. Essentially, anything that is warm will emit IR radiation.
• It is mostly invisible to the naked eye, but we can feel it as warmth.
• Infrared is used in a variety of applications, such as remote controls, thermal imaging cameras, and heat lamps.

In the context of LEDs, when the emitted light's wavelength, such as 864.9 nm from a GaAs LED, falls into the IR range, it means the LED is emitting infrared radiation. These LEDs are often used in remote controls or sensors because the human eye cannot see infrared light, but electronic devices can detect it quite well.

band gap energy

The concept of band gap energy is crucial in understanding how semiconductors work, including LEDs. Band gap energy is the energy difference between the conduction band and the valence band in a semiconductor. Key points to know about band gap energy:

• Electrons need to gain energy equal to or more than the band gap to jump from the valence band to the conduction band, which is when conduction occurs.
• The energy of the emitted photon by recombination of electrons and holes is approximately equal to the energy of the band gap.
• Different materials have different band gaps, which determine the color or type of light that they emit.

In LEDs, the band gap energy directly influences the color of the light emitted. For example, Gallium Arsenide (GaAs) has a band gap of 1.43 eV. When it is used to make LEDs, this energy level corresponds to the infrared portion of the electromagnetic spectrum, producing light that we cannot see but can detect with special equipment. The band gap energy is a key player in the design of various semiconductor devices, dictating electrical conductivity and the nature of light emissions.