The vibrational frequency (expressed in wavenumber) of ¹H³⁵Cl is 2990.6 cm⁻¹. Assuming that the force constant is same in both the cases, vibrational frequency (in cm⁻¹) of ²D³⁵Cl is ________.
vibrational frequency ²D³⁵Cl ¹H³⁵Cl 2990.6 cm⁻¹ – The vibrational frequency of 1H35Cl at 2990.6 cm-1 drops for 2D35Cl due to higher reduced mass from deuterium substitution, assuming identical force constant—a key concept in molecular spectroscopy for CSIR NET Life Sciences.
Vibrational Frequency Formula
ν̅ = 1/2πc √(k/μ)
Where c is the speed of light, k is the force constant, and μ is the reduced mass μ = m1m2/(m1+m2).
Reduced Mass Calculation
Masses used: 1H = 1.00784 u, 2D = 2.01410 u, 35Cl = 34.96885 u (converted to kg for precision).
| Molecule | Reduced Mass (kg) |
|---|---|
| 1H35Cl | 1.627 × 10-27 |
| 2D35Cl | 3.162 × 10-27 |
Ratio μHCl/μDCl = 0.7172, so ν̅DCl = 2990.6 × 0.7172 = 2145 cm-1 (rounded to nearest integer per typical exam precision).
Step-by-Step Solution
- Identify dependency: Frequency ν̅ ∝ 1/√μ, so heavier isotope lowers ν̅.
- Compute μ: μHCl ≈ mH (Cl dominates); μDCl ≈ 2mH, yielding 1/√2 ≈ 0.707 approximation, refined to 0.717.
- Final value: 2145 cm-1 matches literature estimates for DCl isotopologues.
CSIR NET Relevance
This tests harmonic oscillator model and isotope effects in vibrational spectroscopy, common in physical chemistry sections for exams like CSIR NET.
Why no options? Query specifies numerical fill-in; solution confirms 2145 over approximations like 2117 (√(1/2)×2990.6).
