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 2 eV of energy is shined onto a material with a band gap of 4 eV, 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?
E = hf
c = Yf ... (I mean the Y here to be delta)
The Attempt at a Solution
The energy of a photon with a wavelength of 800 nm is:
f = c/Y = c/(800E-9) = 3.7375E14 Hz
f = 3.7375E14 Hz
E = hf = h(3.37375E14) = 2.476E-19 Joules
E = 2.476E-19 J
The energy of a 800-nm photon is 2.476E-19 Joules per photon.
... The band gap is 4 eV, which = 6.408E-19 J
So I do the band gap energy divided by the energy of one photon to give me the number of photons, right? ...
(6.408E-19 Joules)/ [2.476E-19 Joules/photon] = 2.588 photons.
But MasteringPhysics says no. Where did I go wrong?