How to Calculate the Confinement Length of π Electrons in Hexatriene?

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In summary, we are considering a polyene with N double bonds and a length of the box in which the π electrons are confined equal to Na. We are asked to determine the length for hexatriene, which has 3 double bonds and 2 single bonds. One attempt at a solution is to average the length of a single C-C bond and a C=C bond, and then multiply it by the total number of double bonds and 2. This leads to a length of 18.48, assuming a bond length of 0.77.
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Homework Statement



Consider a polyene consisting of N double bonds and assume the length of the box in which the π electrons are confined is Na, where a is a suitable lenght.

What would the length for hexatriene be? You will need to choose a value for a, and should justify your choice.

Hexatriene has 3 double bonds and 2 single bonds.

The Attempt at a Solution



The only thing I can think of us: doing avarage of length of c-c and c=c bonds, multiplying it by the number of double bonds and then by 2?

Lenght= N*2*BL BL= bond length
though you don't really have 2 time the number of double bonds.. that's what is messing me up.

hence a=2BL ?
 
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so N*2*BL*2=6*2*BL*2 Lenght= 24BL BL= length of single c-c bond/2 BL= 1.54/2 BL= 0.77 Length= 24*0.77 Length= 18.48
 

Related to How to Calculate the Confinement Length of π Electrons in Hexatriene?

What is a polyene and particle in a box?

A polyene is a type of molecule that contains multiple alternating single and double bonds, resulting in a long conjugated system. A particle in a box is a theoretical model used in quantum mechanics to describe the behavior of a particle confined to a one-dimensional space.

How does the size of the box affect the energy levels of the particle?

The size of the box directly affects the energy levels of the particle. A larger box will have more energy levels, while a smaller box will have fewer energy levels. This is because the size of the box determines the allowed wavelengths of the particle, which in turn determines its energy levels.

What is the significance of the polyene in this model?

The polyene serves as a potential energy barrier for the particle in the box. It affects the shape and height of the potential energy well, which in turn affects the energy levels of the particle. The polyene also allows for the study of the particle's behavior in a more realistic and complex environment.

Can this model be applied to real-world systems?

Yes, this model can be applied to real-world systems. The particle in a box model is commonly used to study the behavior of electrons in a solid material, and the inclusion of a polyene in the model allows for a more accurate representation of the molecule's electronic structure.

What are the limitations of this model?

One of the main limitations of this model is that it assumes the particle is confined to a one-dimensional space, which is not always the case in real-world systems. Additionally, the model does not account for the effects of temperature, pressure, and other external factors that may affect the behavior of the particle and the polyene.

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