Which of the following is closest to the wavelength of light emitted by an LED made from GaAs (gallium arsenide), given that its band gap energy is approximately 1.43 eV?

• A. 870 nm
• B. 1200 nm
• C. 550 nm
• D. 400 nm

Answer: (A)

Verified step by step guidance

1. Identify the relationship between the energy of the emitted photon and its wavelength. The energy of a photon is related to its wavelength by the equation \(E = \frac{hc}{\lambda}\), where \(E\) is the energy, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.
2. Convert the band gap energy from electron volts (eV) to joules (J) if necessary, using the conversion factor \$1\ \text{eV} = 1.602 \times 10^{-19}\ \text{J}$. This step is optional if you use constants in eV and nm units.
3. Rearrange the equation to solve for the wavelength \(\lambda\): \(\lambda = \frac{hc}{E}\). Here, \(h\) and \(c\) should be in consistent units to match the energy units.
4. Substitute the known values: Planck's constant \(h = 6.626 \times 10^{-34}\ \text{J}\cdot\text{s}\), speed of light \(c = 3.00 \times 10^{8}\ \text{m/s}\), and the band gap energy \(E = 1.43\ \text{eV}\) (converted to joules if needed).
5. Calculate the wavelength \(\lambda\) in meters, then convert it to nanometers by multiplying by \$10^{9}$. Compare the result to the given options to determine which wavelength is closest to the calculated value.