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Chapter 37: Problem 30

A molecule absorbs a photon and jumps to the next higher rotational state. If the photon energy is three times what would be needed for a transition from the rotational ground state to the first rotational excited state, between what two levels is the transition?

Short Answer

Expert verified
The transition is happening between the ground state (level 0) and level 3.

Step by step solution

01

Understanding rotational energy levels

The energy difference between rotational levels is constant. If we denote the energy difference between levels \(n=0\) and \(n=1\) as \( \Delta E \), then the energy difference between levels \(n=a\) and \(n=b\) would be \( \Delta E \times |b-a| \). This understanding is based on the quantization of rotational energy levels.
02

Determine the photon energy

The problem states that the absorbed photon energy is three times the energy needed for a transition from the ground state to the first excited state. This implies the energy of the photon is \( 3 \Delta E \).
03

Identify the energy levels

We need to find two levels, \( a \) and \( b \), such that \( \Delta E \times |b-a| = 3 \Delta E \). Since the energy difference between any two consecutive levels is \( \Delta E \), the difference in the level numbers must be 3. That is, \( |b-a| = 3 \). Taking \( a = 0 \) (i.e., the ground state), we find \( b = a + 3 = 3 \). So, the transition is between the ground state (level 0) and level 3.

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