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## Explanation & Answer

Hello there, here you have your answers! :)

Answer 1:

(a) We can write the probability of population as a function of temperature as:

(

(

)

)

The rotational quantum number (J) for the associated to the most highly populated

rotational energy level will correspond to the derivate of the equation above with respect to

J, equal to zero. Because is when probability reaches its maximum value:

(

(

)

(

)

) (

[(

(

(

)

(

)

(

)

)

(

√

(

))

(

)

(

)

)

)

]

√

√

(b) Jmax for CH4 at 25 oC =298 K is equal to:

√

(

√

)(

(

) (

)

) (

)

Answer 2:

Naphthalene is an aromatic molecule as shown in the figure below, it has 5 pair of pi

electrons that can move through the molecule by resonance.

This conjugation gives additional stabilization energy (E D) to the total energy (E). To

calculate this delocalization energy the localization energy (EL) must be subtracted from

the total energy (E). It’s well-known that applying the secular determinant on the easier

organic system (ethylene) with 2 electrons, the E= 2 + 2as ethylene hasn’t

delocalization, this magnitude of energy can be considered as the localization energy per

pair of electrons. So in the case of naphthalene, it has 5 pair...