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In a rotational spectrum, transitions are only observed between rotational levels of ΔJ =
- a)±1
- b)±2
- c)+1
- d)+3
Correct answer is option 'A'. Can you explain this answer?
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In a rotational spectrum, transitions are only observed between rotati...
Molecular rotations require little energy to excite them. Pure rotation spectra occur in the microwave region of the spectrum (~1 - 200 cm-1). It is important to note that a molecule cannot rotate about some arbitrary axis - the principle of conservation of angular momentum dictates that only a few rotations are possible. In general, rotation must be about the centre of mass of a molecule, and the axis must allow for conservation of angular momentum. In simple cases, this can often be recognised intuitively through symmetry - such as with the water molecule.
A pure rotation spectrum can only arise when the molecule possesses a permanent electric dipole moment. Like with vibrational spectroscopy, the physical effect that couples to photons is a changing dipole moment. Since molecular bond lengths remain constant in pure rotation, the magnitude of a molecule's dipole cannot change. However, since electric dipole is a vector quantity (it has both size and direction) rotation can cause a permanent dipole to change direction, and hence we observe its spectra. Since homonuclear molecules such as dinitrogen (N2) have no dipole moment they have no rotation spectrum. Highly symmetric polyatomic molecules, such as carbon dioxide, also have no net dipole moment - the dipoles along the C-O bonds are always equal and opposite and cancel each other out. It is important to recognise also that if a molecule has a permanent dipole, but this dipole lies along the main rotation axis, then the molecule will not have a rotational spectrum - such as for a water molecule.
In pure rotational spectroscopy for a simple diatomic molecule, the energy levels - as displayed below - are given by EJ = BJ(J+1), where J is the rotational quantum number, B is the rotational constant for the particular molecule given by B = h2 / 8π2I with the unit of Joules, where I is the moment of inertia, given by I = μr2 - where r is the bond length of this particular diatomic molecule and μ is the reduced mass, given by μ = m1m2 / m1 + m2.
Most energy level transitions in spectroscopy come with selection rules. These rules restrict certain transitions from occuring - though often they can be broken. In pure rotational spectroscopy, the selection rule is ΔJ = +_1.
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In a rotational spectrum, transitions are only observed between rotati...
Rotational Spectrum and Transitions
Rotational spectrum is a type of molecular spectrum that arises due to the rotational motion of a molecule. It is observed when a molecule absorbs or emits electromagnetic radiation in the microwave or far-infrared region of the electromagnetic spectrum.
Transitions in Rotational Spectrum
The rotational spectrum is characterized by the transitions between different rotational energy levels of the molecule. These transitions are observed only between specific rotational levels of the molecule, and the selection rules for these transitions depend on the quantum mechanical properties of the molecule.
Selection Rules for Rotational Spectrum
The selection rules for rotational spectrum are based on the following principles:
- The change in the rotational quantum number (J) between the initial and final states of the molecule must be ΔJ = ±1.
- The molecule must have a permanent electric dipole moment, which allows it to interact with the electromagnetic radiation.
- The molecule must not undergo any changes in its electronic or vibrational states during the rotational transition.
Answer
Based on the selection rules for rotational spectrum, transitions are only observed between rotational levels of J = 1. This is because the rotational quantum number can only change by ±1, and the lowest energy level of a molecule is J = 0, which cannot undergo a transition.
Therefore, the correct option is A, which states that transitions are only observed between rotational levels of J = 1.
Rotational spectrum is a type of molecular spectrum that arises due to the rotational motion of a molecule. It is observed when a molecule absorbs or emits electromagnetic radiation in the microwave or far-infrared region of the electromagnetic spectrum.
Transitions in Rotational Spectrum
The rotational spectrum is characterized by the transitions between different rotational energy levels of the molecule. These transitions are observed only between specific rotational levels of the molecule, and the selection rules for these transitions depend on the quantum mechanical properties of the molecule.
Selection Rules for Rotational Spectrum
The selection rules for rotational spectrum are based on the following principles:
- The change in the rotational quantum number (J) between the initial and final states of the molecule must be ΔJ = ±1.
- The molecule must have a permanent electric dipole moment, which allows it to interact with the electromagnetic radiation.
- The molecule must not undergo any changes in its electronic or vibrational states during the rotational transition.
Answer
Based on the selection rules for rotational spectrum, transitions are only observed between rotational levels of J = 1. This is because the rotational quantum number can only change by ±1, and the lowest energy level of a molecule is J = 0, which cannot undergo a transition.
Therefore, the correct option is A, which states that transitions are only observed between rotational levels of J = 1.
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In a rotational spectrum, transitions are only observed between rotational levels of ΔJ =a)±1b)±2c)+1d)+3Correct answer is option 'A'. Can you explain this answer?
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