Problem 78 - Chemistry The Central Science

Question

The first LEDs were made from GaAs, which has a band gap of 1.43 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: ultraviolet, visible, or infrared?

Step-by-Step Solution

Answer

= 2.29 × 10⁻¹⁹ J #tag_title

Step 1: Identify given information

List all given data and unknowns.

Step 2: Determine relevant principles

Identify applicable chemical laws.

Step 3: Set up and solve

Apply equations and solve.

Step 4: State the answer

The answer is: = 2.29 × 10⁻¹⁹ J #tag_title

Key Concepts

Band Gap Energy

The concept of band gap energy is fundamental to understanding how light-emitting diodes (LEDs) function. In the simplest terms, the band gap is the energy difference between the top of the valence band (where the electron normally resides) and the bottom of the conduction band (where the electron can move freely, allowing for conduction). This band gap energy determines the energy of the photons that the material can emit when an electron transitions back down from the conduction band to the valence band.

For instance, Gallium Arsenide (GaAs) is a common material used in the production of LEDs and has a band gap of 1.43 electron volts (eV). This value is crucial since it directly relates to the color of the light emitted by an LED. The lower the band gap energy, the longer the wavelength of the emitted light, and consequently, the closer the light is to the red end of the visible spectrum. Conversely, a higher band gap energy corresponds to shorter wavelengths and light closer to the violet end.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which range from very short wavelengths (like gamma rays) to very long wavelengths (like radio waves). Visible light is just a small part of this spectrum, which also includes ultraviolet (UV) light, infrared (IR) light, and others. Each type of electromagnetic radiation is characterized by its wavelength or frequency.

When discussing LEDs, it's important to identify where the emitted light falls on the electromagnetic spectrum. For example, if the wavelength of light emitted from a GaAs LED is calculated, it is crucial to determine whether this wavelength is within the visible range (approximately 380 nm to 750 nm), the ultraviolet range (less than 380 nm), or the infrared range (greater than 750 nm). Understanding the placement of this light within the electromagnetic spectrum allows us to predict its visibility to the human eye and potential applications.

Energy to Wavelength Conversion

Energy to wavelength conversion is a piece of essential scientific knowledge used to describe the relationship between a photon's energy and its wavelength within the electromagnetic spectrum. According to Planck's equation, the energy of a photon (\( E \) in Joules) is directly proportional to its frequency (\( u \) in Hertz) and inversely proportional to its wavelength (\( u \) in meters), with the proportionality constant being Planck's constant (\( h \) approx. equal to 6.626 x 10⁻³⁴ J·s).

The equation is written as: \[ E = h u \]Since the speed of light (\( c \) = 3.00 x 10⁸ m/s) is equal to the wavelength times the frequency (\( c = \lambda u \)), we can rearrange the equation to solve for wavelength (\( \lambda \) in meters): \[ \lambda = \frac{hc}{E} \]
For an LED with a specified band gap energy, such as the GaAs LED with 1.43 eV mentioned earlier, we first convert the energy from eV to Joules (since Planck's constant is in Joule·seconds) and then apply the equation above to determine the wavelength of the emitted light. This enables us to understand the color of the light and its position in the electromagnetic spectrum.