Problem 74 - Chemistry: The Central Science

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: ultraviolet, visible, or infrared?

Step-by-Step Solution

Answer

The wavelength of light emitted from the GaAs LED is calculated as \(\lambda = 8.640 \times 10^{-7}\: m\) or 864 nm, which falls within the infrared region of the electromagnetic spectrum.

Step 1: Convert the bandgap energy to Joules

We are given the bandgap energy (E) in electron volts (eV). Let's convert it to Joules (J) using the following conversion factor: 1 eV = \(1.602 \times 10^{-19}\) J So, E (in J) = 1.43 eV x \(1.602 \times 10^{-19}\) J/eV E = \(2.295 \times 10^{-19}\) J

Step 2: Calculate the wavelength of emitted light

Using the energy-wavelength relationship: \(E = h \times \frac{c}{\lambda}\) we can find the wavelength (λ) by rearranging the formula as follows: \(\lambda = \frac{h \times c}{E}\) To calculate the value of λ, we need Planck's constant (h) and the speed of light (c): \(h = 6.626 \times 10^{-34}\) Js (Planck's constant) \(c = 2.998 \times 10^8\) m/s (speed of light) Now, we can plug in all the values: \(\lambda = \frac{(6.626 \times 10^{-34}\: Js) \times (2.998 \times 10^8\: m/s)}{2.295 \times 10^{-19}\: J}\) \(\lambda = 8.640 \times 10^{-7}\: m\)

Step 3: Identify the region of the electromagnetic spectrum

Now, we need to determine whether the calculated wavelength corresponds to ultraviolet, visible, or infrared light. The general ranges for these regions of the spectrum are: - Ultraviolet (UV): 10 nm to 400 nm - Visible: 400 nm to 700 nm - Infrared (IR): 700 nm to 1 mm To compare, we can convert our calculated wavelength in meters to nanometers. 8.640 \(\times 10^{-7}\) m \(\times\) \(10^9 nm/m\) = 864 nm Since the wavelength of light emitted from the GaAs LED is 864 nm, it falls within the infrared region of the electromagnetic spectrum.