Photons and band gaps in code

You will write four small functions that tie the colour of light to the band gap of a crystal.

The idea. A photon of wavelength $\lambda$ (in nm) has energy $E = \dfrac{1240}{\lambda}$ in eV. It can make an electron-hole pair if $E$ is at least the gap. Heat lifts a share $e^{-E_g/2kT}$ of the electrons.

Your tasks.

1. In photon_energy, return the energy in eV of a photon of the given wavelength in nm.
2. In cutoff_wavelength, return the longest wavelength in nm that can make a pair across the given gap in eV.
3. In can_make_pair, return True if a photon of the given wavelength has at least the energy of the gap.
4. In thermal_factor, return $e^{-E_g/2kT}$ for a gap in eV and a temperature in K. Use k = 8.617e-5 eV/K.