Given information:
- Rotational constant of a rigid diatomic molecule = 1.566 cm^-1 at 300K

To find:
- Jmax value for the given molecule

Explanation:
- For a rigid diatomic molecule, the rotational energy levels are given by the expression: EJ = J(J+1)h^2/8π^2I
- Where EJ is the energy of the Jth rotational level, J is the rotational quantum number, h is Planck's constant, and I is the moment of inertia of the molecule.
- The moment of inertia of a rigid diatomic molecule is given by the expression: I = μr^2, where μ is the reduced mass of the molecule and r is the bond length.
- At a given temperature, the population of different rotational levels is given by the Boltzmann distribution: N(J) = N0 exp(-EJ/kT)
- Where N(J) is the number of molecules in the Jth rotational level, N0 is the total number of molecules, k is the Boltzmann constant, and T is the temperature in Kelvin.
- The maximum value of J, i.e., Jmax, is the value of J for which the population in the (J+1)th level is negligible compared to that in the Jth level.
- Mathematically, this can be expressed as: N(J+1)/N(J) ≈ exp(-EJ+1/kT) < />
- Taking the natural logarithm of both sides and simplifying, we get: Jmax ≈ 2.303kT/hB
- Where B is the rotational constant of the molecule.

Calculation:
- Substituting the given values, we get: Jmax ≈ 2.303(1.38×10^-23)(300)/(6.626×10^-34)(1.566×10^3)
- Solving this expression, we get: Jmax ≈ 8

Therefore, the Jmax value for the given rigid diatomic molecule is 8 (option C).