For a diatomic molecule AB , the energy of the rotational transition from J = 0 to J = 1 state is 3.9 cm^-1 . The energy for the rotational transition from J = 3 to J = 4 state would be

For a diatomic molecule, the rotational energy levels are given by the formula:

\[
E_J = B \cdot J \cdot (J + 1)
\]

where:
- \( E_J \) is the energy of the rotational level with quantum number \( J \).
- \( B \) is the rotational constant in units of cm\(^{-1}\).
- \( J \) is the rotational quantum number (0, 1, 2, ...).

Given that the energy of the rotational transition from \( J = 0 \) to \( J = 1 \) is 3.9 cm\(^{-1}\), we can calculate the rotational constant \( B \).

For the transition from \( J = 0 \) to \( J = 1 \):

\[
\Delta E = E_1 - E_0 = B \cdot 1 \cdot (1 + 1) - B \cdot 0 \cdot (0 + 1) = 2B
\]

Given that \( \Delta E = 3.9 \) cm\(^{-1}\):

\[
2B = 3.9 \, \text{cm}^{-1}
\]

\[
B = \frac{3.9}{2} = 1.95 \, \text{cm}^{-1}
\]

Now, let's find the energy for the transition from \( J = 3 \) to \( J = 4 \):

\[
\Delta E = E_4 - E_3 = B \cdot 4 \cdot (4 + 1) - B \cdot 3 \cdot (3 + 1) 
\]

Simplifying this:

\[
\Delta E = B \cdot (4 \cdot 5 - 3 \cdot 4) = B \cdot (

For a diatomic molecule AB, the energy of the rotational transition from J = 0 to J = 1 state is 3.9 cm^-1. The energy for the rotational transition from J = 3 to J = 4 state would be

Discover how to calculate the energy of rotational transitions for diatomic molecules. This problem involves quantum mechanics concepts and the rotational energy level formula, ideal for undergraduate physics students. Example: From J = 0 to J = 1, the transition energy is 3.9 cm^-1.

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