Glass is transparent to visibile light under normal conditions; however, at extremely high intensities, glass will absorb most of the light incident upon it. This works through a process known as multiphoton absorption. In this process, several photons are absorbed at the same time. If very intense light whose photons carry 2eV of energy is shined onto a material with a band gap of 4eV, that light can be absorbed through two-photon absorption, because two photons have the right amount of energy to bridge the band gap. What is the minimum number of photons of 800-nm light that are needed to equal or exceed the band gap of fused silica glass?

Where [tex]h[/tex] corresponds to Plank constant (6.626070x10^-34Js), [tex]c[/tex] is the speed of light in the vacuum (299792458m/s) and [tex]\lambda[/tex] is the wavelength of the photon(in this case 800nm).

[tex]E=\frac{hc}{\lambda}=\frac{(6.626070\times10^{-34})(299792458)}{800\times10^{-9}}=\frac{1.986445812\times10^-25}{800}=2.483057265\times10^{-19}J[/tex]

Tranform the units

[tex]1eV=1.602176634\times10^{-19}J\\2.483057265\times10^{-19}J(\frac{1eV}{1.602176634\times10^{-19}J})=1.549802445eV[/tex]

The band Gap is 4eV, divide the band gap between the energy of the photon:

[tex]\frac{4ev}{1.549802445eV}=2.508974118[/tex]

Rounding to the next integrer: 3.

Three photons are the minimum to equal or exceed the band gap.