Given that the spacing of the lines in the microwave spectrum of ²⁴Al¹H is constant at 12.604 cm. Calculate the moment of inertia and bond length of the molecule.

To calculate the moment of inertia and bond length of the molecule AlH\text{AlH} (Aluminum Hydride), we can use the formula for rotational energy in the microwave spectrum of a diatomic molecule:

E=h28π2I⋅J(J+1)E = \frac{h^2}{8 \pi^2 I} \cdot J(J+1)

Where:

• EE is the energy of the rotational transition.
• hh is Planck's constant (6.626×10−34 J s6.626 \times 10^{-34} \, \text{J s}).
• II is the moment of inertia.
• JJ is the rotational ____ ___ _____ __________ ______ ___ ___.
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