Rotational quantum number for the rotational spectrum of diatomic molecule for maximum populated level is given by:a)b)c)d)OneCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

C

Answer

Rotational quantum number for the rotational spectrum of a diatomic molecule at the maximum populated level can be determined using specific equations and principles of quantum mechanics.

The rotational spectrum is influenced by several factors:

Quantum Number (J): This number indicates the rotational energy levels of the molecule.
Population Distribution: At thermal equilibrium, the distribution of these levels follows the Boltzmann distribution, where higher energy levels are less populated.
Temperature Effect: As temperature increases, higher rotational levels become more populated.

The rotational energy levels are given by:

The energy of a level is proportional to J(J+1), where J is the rotational quantum number.
For diatomic molecules, the maximum populated level can be identified by the condition that the population in that level is greatest.

In practical terms, to find the maximum populated level, one would typically look for the rotational quantum number J that corresponds to the highest population at a given temperature. This often leads to determining the value of J using statistical mechanics principles.

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