Consider a simple model of photosynthesis in which the light absorbing molecule (e.g. chlorophyll) defines a “box” size for an active electron (box length = L). The electron initially sits in the ground state (n=1) before a photon “kicks” it into the first excited state (n=2).
1) Calculate the energy of the electron in the ground state
2) Calculate the energy of a photon needed for the n = 1 to n = 2 transition
3) How big of a box is needed to absorb a 475 nm photon of blue light?
uses En = 2 Π m e4 / n2 (4 Π ε0 )2 h2 When I plug in the constants, n=1, the value is off from 13.7 eV, after conversion from Joules, by a factor of 3.14, as if Pi doesn't belong in the denominator. I'm thinking that it is already included in the permitivity constant ε0. 2
E = (13.6 eV) [1/nf2 - 1/ni2]
Blue light: E=(6.626*10-34 Js)(3*108 m/s)/(450*10-9 m)=4.4*10-19 J=2.76 eV