To a crude first approximation, an electron in a linear polyene may be considered to be...
To a crude first approximation, an electron in a linear polyene may be considered to be a particle in a one-dimensional box. The polyene - carotene contains 22 conjugated C atoms, and the average inter-nuclear distance is 140 pm. Each state up to n =11 is occupied by two electrons. Calculate the separation in energy between the ground state and the first excited state in which one electron occupies the state with n=12.
Homework Answers
Particle (electron ) in a one diamentional box ,Energy equation is,
En = n2 h2 /8mL2
Where n is the quantum number, 1,2,3 ...
m isthe mass of the particle (electron)
L is the length of the barrior
Here En is n=11 to n=12
so the change in energy ΔE=E12-E11
ΔE=(122-112)*h2/8mL2
(144-122)h2/8mL2
=23h2/8mL2
Here the average internuclear distance L=140 pm=1.4*10-10m
In polyene - carotene contains 22 conjugated C atoms
so we want tocalculat 22 conjugateted c atoms L =22*140pm =3080pm=3.08*10-9m
ΔE12-->ΔE11= 23h2/8mL2
=(23*(6.626*10-34)2)/(8*(9.1*10-31Kg)*(3.08*10-9)2)
= 1009.789*10-68/690.60*10-49
=1.463*10-19J
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