What is the wavelength of light (in nm) emitted when an electron moves from the conduction band to the valence band in a sample of diamond, which has a band gap of 5.5 eV?

Verified step by step guidance

1. Convert the band gap energy from electron volts (eV) to joules (J) using the conversion factor: 1 eV = 1.602 x 10^{-19} J.
2. 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.
3. Rearrange the equation to solve for wavelength: \lambda = \frac{hc}{E}.
4. Substitute the values for h, c, and the converted energy E into the equation to calculate the wavelength in meters.
5. Convert the wavelength from meters to nanometers by multiplying by 10^9, since 1 meter = 10^9 nanometers.