Microwave (Rotational) Spectroscopy

📘 Microwave (Rotational) Spectroscopy – Notes, Formula, Applications & Examples

🔍 What is Microwave (Rotational) Spectroscopy?

Microwave spectroscopy is a powerful analytical technique used to study the rotational motion of molecules. It involves the absorption of microwave radiation by molecules, leading to transitions between rotational energy levels.

👉 Microwave (Rotational) spectroscopy is mainly used for:

• Determining molecular structure
• Measuring bond length
• Identifying dipole moments

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📡 Microwave Region in Electromagnetic Spectrum

• Frequency range: 3 to 300 GHz
• Wavelength range: 0.1 to 30 cm

👉 These frequencies correspond to rotational transitions in molecules.

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⚙️ Basic Principle of Microwave Spectroscopy

When a molecule rotates, it possesses rotational energy. This energy is quantized, meaning molecules can only rotate at specific energy levels.

📌 Rotational Energy Equation

E_J = (h² / 8π²I) × J(J + 1)

Where:

• J = rotational quantum number (0, 1, 2, …)
• I = moment of inertia
• h = Planck’s constant

👉 Key point:

• Energy increases with increasing J

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⚖️ Moment of Inertia

For a diatomic molecule:

I = μr²

Where:

• μ = reduced mass = (m₁m₂) / (m₁ + m₂)
• r = bond length

👉 This helps determine molecular structure.

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Rotational Constant (B)

B = h / (8π²Ic)

👉 Energy in practical units:

E_J = B × J(J + 1)

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Selection Rule

For microwave absorption:

ΔJ = ±1

👉 Only transitions between adjacent rotational levels are allowed.

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Rotational Spectral Lines

Frequency of absorption:

ν = 2B(J + 1)

👉 Important features:

• Lines are equally spaced
• Separation = 2B

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Condition for Microwave Activity

✔ A molecule must have a permanent dipole moment

Examples:

• ✔ Active: HCl, CO, NO, H₂O
• ❌ Inactive: H₂, N₂, O₂

👉 Therefore:

• Polar molecules → Active
• Non-polar molecules → Inactive

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Types of Molecules (Rotors)

1. Linear Molecules

• Iₐ = 0, I_b = I_c
• Example: CO, HCl

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2. Symmetric Top Molecules

Two moments equal

Types:

• Prolate (NH₃)
• Oblate (BF₃)

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3. Spherical Top Molecules

• Iₐ = I_b = I_c
• No dipole → No spectrum

Examples: CH₄, CCl₄

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4. Asymmetric Top Molecules

• All moments different
• Complex spectra

Examples: H₂O, SO₂

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Non-Rigid Rotor Effect

Real molecules are not perfectly rigid.

Corrected energy equation:

E_J = B × J(J + 1) − D × J²(J + 1)²

Where:

• D = centrifugal distortion constant

👉 Effect:

• Spectral lines become slightly uneven

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Effect of Isotopic Substitution

• Mass increases → moment of inertia increases

Therefore:

👉 Rotational constant (B) decreases
👉 Line spacing decreases

✔ Used to determine:

• Bond lengths
• Atomic masses

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Intensity of Spectral Lines

Intensity depends on:

• Population of molecules in each level
• Transition probability

📌 Boltzmann Distribution

N_J ∝ (2J + 1) × e^(−E_J / kT)

👉 Maximum intensity occurs at an intermediate J value.

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Stark Effect

• Splitting of spectral lines in an electric field

Types:

• First order → directly proportional to field
• Second order → proportional to square of field

👉 Used to measure dipole moment accurately.

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Nuclear Spin Interaction

• Interaction between nuclear spin and rotation

👉 Results in:

• Hyperfine splitting of spectral lines

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Inversion Spectrum of Ammonia (NH₃)

• Nitrogen atom moves through hydrogen plane

👉 Leads to:

• Splitting of energy levels

✔ Cause:

• Quantum tunnelling

👉 This produces inversion doubling in microwave spectra.

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⚙️ Instrumentation of Microwave Spectroscopy

Main components:

1. Source (Klystron) – generates microwave radiation
2. Waveguide – carries radiation
3. Sample Cell – contains gaseous sample
4. Detector – detects absorption
5. Recorder – records spectrum

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🌍 Applications of Microwave Spectroscopy

✔ Determination of:

• Bond length
• Bond angle
• Molecular geometry

✔ Study of:

• Isotopes
• Dipole moments
• Molecular symmetry

✔ Used in:

• Atmospheric chemistry
• Astrochemistry
• Molecular identification

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⚠️ Limitations of Microwave Spectroscopy

Following are the limitations of the microwave (rotational) spectroscopy:

• Only molecules with dipole moment
• Only gaseous samples
• Not suitable for large molecules

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📌 Key Points for Quick Revision

• Microwave spectroscopy → rotational transitions
• Condition → permanent dipole moment
• Selection rule → ΔJ = ±1
• Line spacing → 2B
• Energy ∝ J(J + 1)

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🔎 Learning

Microwave spectroscopy is a highly precise technique for studying molecular rotation and structure. It provides accurate information about bond length, molecular geometry, and dipole moment, making it an essential tool in physical chemistry.