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?

Verified step by step guidance

1. Step 1: Understand that the energy of the emitted light from an LED is equal to the band gap energy of the semiconductor material, which in this case is 1.43 eV for GaAs.
2. Step 2: Convert the energy from electron volts (eV) to joules (J) using the conversion factor: 1 eV = 1.602 x 10^-19 J.
3. Step 3: Use the energy-wavelength relationship given by the equation \( E = \frac{hc}{\lambda} \), where \( E \) is the energy in joules, \( h \) 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 \( \lambda \) is the wavelength in meters.
4. Step 4: Rearrange the equation to solve for wavelength: \( \lambda = \frac{hc}{E} \). Substitute the values for \( h \), \( c \), and the converted energy \( E \) to find \( \lambda \).
5. Step 5: Convert the wavelength from meters to nanometers (1 m = 10^9 nm) and determine the region of the electromagnetic spectrum it falls into by comparing the wavelength to known ranges: ultraviolet (10-400 nm), visible (400-700 nm), or infrared (700 nm and above).