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/n_{f}^{2} - 1/n_{i}^{2}]

E=13.6(1/4-1)=-10.2 ev

3

Blue light: E=(6.626*10^{-34 }Js)(3*10^{8 }m/s)/(450*10^{-9 }m)=4.4*10^{-19 }J=2.76 eV