Test: Molecular Spectroscopy - Chemistry MCQ

Raman activity refers to a molecular vibration that can be observed using Raman spectroscopy, while infrared (IR) activity pertains to vibrations detectable by infrared spectroscopy. Some molecules may show characteristics in one type of spectroscopy but not the other.

To determine which molecule is IR-inactive but Raman-active, consider the following:

• N₂: A homonuclear diatomic molecule, which does not have a dipole moment. Therefore, it is IR-inactive and can be Raman-active due to its vibrational modes.
• HCl: This molecule is IR-active because it has a dipole moment when it vibrates, making it detectable in infrared spectroscopy.
• SO₂: This molecule is also IR-active as its vibration changes the dipole moment, allowing it to be detected in IR spectroscopy.
• Protein: Proteins typically exhibit both IR and Raman activity due to their complex structures and varying functional groups.

In conclusion, among the options provided, N₂ is the molecule that is IR-inactive but can be Raman-active.

The rotational (microwave) spectrum of a rigid diatomic rotor features lines that are evenly spaced. The spacing between these lines is determined by the rotational constant, denoted as B.

• The energy levels of a rigid diatomic rotor are quantised.
• Each transition between energy levels results in a spectral line.
• These lines are spaced equally, meaning the difference in energy corresponds to the constant B.
• The spacing is specifically 2B for the rotational transitions.

Thus, the spacing between the lines in the spectrum reflects the fundamental properties of the diatomic rotor's motion.

   J=1

The vibrational rotational spectrum is observed in the near infrared region.

The vibrational rotational spectrum is a key aspect of molecular spectroscopy, particularly in the near infrared part of the electromagnetic spectrum. This region is crucial for understanding molecular vibrations and rotations.

• The near infrared region typically spans wavelengths from approximately 0.75 to 2.5 micrometres.
• In this range, molecules absorb light, causing transitions in their vibrational and rotational energy levels.
• This absorption leads to unique spectral signatures that can help identify different molecules.
• Applications include chemical analysis, environmental monitoring, and studying biological processes.

By examining these spectra, scientists can gather important information about the structure and dynamics of various substances.

In a rotational spectrum, transitions are only observed between rotational levels of

• ΔJ = ±1
• ΔJ = ±2
• ΔJ = +1
• ΔJ = +3

This means that during transitions, molecules can change energy levels by either increasing or decreasing their rotational quantum number by 1 or 2. The most common transitions observed are those with a change of +1 or -1, as these are energetically favourable processes.

Vibrational transitions in molecules are always accompanied by rotational transitions. This is because:

• Molecular vibrations change the distribution of mass, affecting rotational energy levels.


• Vibrational energy levels are closely spaced, and transitions often overlap with rotational levels.


• Combined vibrational and rotational transitions are observed in the infrared region of the electromagnetic spectrum.


• This coupling is due to the molecular structure, enabling simultaneous changes in both vibrational and rotational states.


 

The increase in rotational energy is associated with the absorption spectrum in the microwave region. This occurs because the energy transitions involved in rotation are relatively low compared to other forms of energy transitions.

• Microwave radiation has longer wavelengths and lower frequencies.
• This type of radiation specifically interacts with the rotational states of molecules.
• As molecules absorb microwave energy, they undergo rotational transitions.
• These transitions lead to an increase in rotational energy.

In summary, the absorption spectrum linked to increased rotational energy is primarily found in the microwave region.

The increase in vibrational energy results in an absorption spectrum, which can be detected in specific regions of the electromagnetic spectrum.

• Infrared (IR) region: This region is directly associated with vibrational transitions. Molecules absorb IR radiation as their bonds stretch and bend.
• Visible region: Although not primarily linked to vibrational energy, some molecules can absorb light in this range, resulting in colour.
• Microwave region: Absorption in this region typically involves rotational transitions rather than vibrational energy changes.
• Ultraviolet (UV) region: This region is more relevant for electronic transitions than for vibrational energy absorption.

In summary, the most significant absorption due to increased vibrational energy occurs in the IR region.

UV radiation has a higher frequency than:

• Microwaves

• Infrared (IR) radiation

• Thus, it surpasses both categories.

In summary:

• Frequency comparison: UV radiation exceeds both microwaves and IR radiation.
• Implication: This indicates that UV radiation carries more energy.

Understanding these differences is crucial for various applications, such as:

• Safety measures in sun exposure.
• Technological advancements in communication.

Only certain molecules can exhibit a pure rotational microwave spectrum. This occurs when the molecule has a permanent dipole moment and is not symmetrical in all dimensions.

• N₂: This molecule is diatomic and homonuclear, meaning it has no dipole moment. Therefore, it cannot produce a rotational microwave spectrum.
• CO₂: Although this molecule is linear and has a dipole moment, its symmetrical structure leads to no pure rotational transitions in microwave spectroscopy.
• OCS: This molecule is polar and has a permanent dipole moment, making it capable of showing a pure rotational microwave spectrum.
• HCl: This molecule is also polar and exhibits a dipole moment, allowing it to show a pure rotational microwave spectrum.

In summary, among the given molecules, HCl can show a pure rotational microwave spectrum due to its polar nature, while N₂ and CO₂ cannot.

Diatomic molecules can exhibit different behaviours in spectroscopy. Some molecules will show rotational spectra, while others will not.

• N₂ (Nitrogen):

This molecule is homonuclear and symmetrical, which means it does not have a permanent dipole moment. As a result, it does not produce a rotational spectrum.

• CO (Carbon Monoxide):

CO is a heteronuclear molecule and has a significant dipole moment. This characteristic allows it to exhibit a rotational spectrum.

• NO (Nitric Oxide):

Similar to CO, NO is also heteronuclear and has a dipole moment, enabling it to produce a rotational spectrum.

• HF (Hydrogen Fluoride):

HF is another heteronuclear molecule with a permanent dipole moment, which allows it to display a rotational spectrum.

In summary, the only diatomic molecule among the options provided that does not give a rotational spectrum is N₂.

The selection rule for translation energy levels in the Raman spectrum is an important principle in understanding molecular vibrations and their interactions with light. This rule defines how energy levels change during the Raman scattering process.

• The primary rule states that a change in rotational quantum number, ΔJ, must be:
• ±1 - indicating that the rotational state can increase or decrease by one unit.
• Other possible changes include:
• ±2 - which does not typically apply to Raman transitions.
• +1 - representing an increase in rotational energy.
• +2 - which is also not relevant for Raman processes.

In summary, the relevant selection rule for Raman spectroscopy is a change in the rotational quantum number of ΔJ = ±1, allowing transitions that either increase or decrease the energy level by one. This is crucial for interpreting Raman spectra effectively.

The rotational spectrum of HI reveals a series of spectral lines with a separation of 12.8 cm^–1. This separation indicates the presence of quantised rotational energy levels in the molecule. To determine the moment of inertia for the HI molecule, we can use the formula relating the rotational constant to the moment of inertia:

• Rotational Constant (B): The value of the rotational constant is derived from the line separation.
• Moment of Inertia (I): The moment of inertia can be calculated using the formula: I = h/(8π²cB), where h is Planck's constant and c is the speed of light.
• Here, we can deduce that the moment of inertia for the HI molecule is approximately 4.36 x 10^-40 g cm².

Thus, based on the analysis of the rotational spectrum, the calculated moment of inertia confirms that the value is 4.36 x 10^-40 g cm².

First calculate the reduced mass μ of CN+:
μ = (12×14)/(12+14) ≈ 6.462 u, then μ = 6.462×1.6605×10−27 kg.
Rotational constant B in plain text:
B = h/(8*pi*pi*c*mu*r²).
Using h = 6.626×10−34 J·s, c = 2.998×108 m/s, r = 0.129×10−9 m and the μ above gives B ≈ 1.566 cm−1.
Microwave lines occur at ν(J→J+1) = 2B(J+1).
For the second line (J = 1 → 2): ν = 2B×2 = 4B = 4×1.566 = 6.264 cm⁻¹.
Therefore, the second line appears at 6.264 cm⁻¹.

Phosphorescence involves transitions between electronic states, primarily characterised as singlet (S), doublet (D), and triplet (T) states. In this process:

• The transition occurs from a triplet state (T) to a singlet state (S).
• This transition is significant because it explains the delayed emission of light often observed in phosphorescent materials.
• During this transition, the system undergoes a change in spin multiplicity, which is a key feature of phosphorescence.

Thus, the correct understanding of phosphorescence is critical for applications in lighting and displays, where materials can emit light over extended periods after being excited.

For pure vibrational spectra, the selection rule is:

• A: 0
• B: ±1
• C: 0, ±1
• D: ±1, 2

The correct answer is B.

The maximum rotational quantum number (J_max) for a rigid diatomic molecule at 300K can be determined using the given rotational constant.

For a rigid diatomic molecule:

• The rotational constant is 1.566 cm^–1.
• The relationship between the rotational constant and the maximum rotational quantum number is critical.
• At a temperature of 300K, the energy levels are populated according to the Boltzmann distribution.
• The maximum quantum number can typically be calculated using the formula:
• J_max is influenced by both the temperature and the rotational constant.

Based on these factors, we find that the maximum rotational quantum number for the molecule is 8.

The normal modes of vibration of N₂O refer to the distinct patterns in which the molecule can oscillate.

The analysis of these modes reveals:

• Each mode corresponds to a specific vibrational energy level.
• The total number of normal modes for a nonlinear molecule like N₂O is determined by the formula: 3N - 6, where N is the number of atoms.
• For N₂O, which consists of three atoms, the calculation is:
• 3 (for each atom) x 3 = 9
• 9 - 6 = 3 normal modes of vibration.

Thus, the normal modes of vibrations for N₂O total three.

The fundamental vibration frequency of the carbon monoxide molecule is 6.5 x 10¹³ s^-1. Its rotational constant is 1.743 x 10¹¹ s^-1. In quantum mechanics, the energy of rotational states is closely related to vibrational states.

When considering the energy of the molecule, it is important to note that the rotational energy in its first vibrational state can be calculated based on these constants. The energy levels of a molecule can be thought of as a combination of its vibrational and rotational energies.

• The first vibrational state corresponds to the lowest energy level of vibration.
• Rotational energy levels depend on the rotational constant, which influences the spacing of these energy levels.
• In this scenario, the rotational energy aligns with the vibrational states.

Hence, based on the given data, the rotational energy will match that of the first vibrational state. This relationship aids in determining the overall energy levels of the carbon monoxide molecule.

Correct Answer :- a

Explanation : g = 2.0025

u_N = 9.2741 * 10^-24J

B = 0.300 T

v = (u_N * (g) * B)/h

v = [(9.2741 * 10^-24) (2.0025) * (0.300)]/(6.626 * 10^-34)

= 8.408 * 10⁹ s^-1

The different types of energies associated with a molecule are electronic energy, vibrational energy, rotational energy and translational energy.

The pure rotational (microwave) spectrum of the gaseous molecule CN shows a series of evenly spaced lines. These lines are separated by 3.7978 cm^–1. To find the inter-nuclear distance of the CN molecule, we can use the provided molar masses:

• Carbon (C): 12.011 g mol^–1
• Nitrogen (N): 14.007 g mol^–1

The inter-nuclear distance can be assessed from the rotational spectrum and is commonly measured in picometres (pm). Here are the possible distances:

• 130 pm
• 117 pm
• 150 pm
• 93 pm

The correct inter-nuclear distance for the CN molecule is 117 pm.