5. Calculate wavenumber for C=C and C=C by Hook's law. stronger bond higher frequency --- f = force constant m = mass k = constant Hooke's law V = k/ smaller mass --→ higher frequency The force constant (f) of C=C 10 x 105 dyne/cm and C=C, 15 x 105 dyne/cm The mass (m) is the mass of atoms (or weights). The smaller the value of m, the higher the V of vibration. CH30. HO capsaicin (spicy component of hot peppers)

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## Understanding Wavenumber Calculation Using Hooke's Law

### Problem Statement
5. Calculate the wavenumber for C=C and C≡C using Hooke's law.

### Hooke's Law
Hooke's Law for vibration frequency is given by the formula:

\[
\tilde{\nu} = k \sqrt{\frac{f}{m}}
\]

- \( \tilde{\nu} \): wavenumber
- \( f \): force constant
- \( m \): mass
- \( k \): constant

**Principles:**
- **Stronger Bond ➔ Higher Frequency**
- **Smaller Mass ➔ Higher Frequency**

### Force Constants
- **C=C (Double Bond):** \( f = 10 \times 10^5 \, \text{dyne/cm} \)
- **C≡C (Triple Bond):** \( f = 15 \times 10^5 \, \text{dyne/cm} \)

The mass (\( m \)) is the mass of atoms (or weights). The smaller the value of \( m \), the higher the wavenumber (\( \tilde{\nu} \)) of vibration.

### Structure of Capsaicin
Below the explanation, the chemical structure of capsaicin, a spicy component found in hot peppers, is provided.

![Capsaicin](structure)

- **Key Structural Details:**
  - CH₃O (methoxy group)
  - HO (hydroxy group)
  - N-H (amide group)
  - Various hydrocarbon chains and rings

Understanding the vibration principles and structural details of molecules helps in studying their chemical behavior and interactions efficiently.
Transcribed Image Text:## Understanding Wavenumber Calculation Using Hooke's Law ### Problem Statement 5. Calculate the wavenumber for C=C and C≡C using Hooke's law. ### Hooke's Law Hooke's Law for vibration frequency is given by the formula: \[ \tilde{\nu} = k \sqrt{\frac{f}{m}} \] - \( \tilde{\nu} \): wavenumber - \( f \): force constant - \( m \): mass - \( k \): constant **Principles:** - **Stronger Bond ➔ Higher Frequency** - **Smaller Mass ➔ Higher Frequency** ### Force Constants - **C=C (Double Bond):** \( f = 10 \times 10^5 \, \text{dyne/cm} \) - **C≡C (Triple Bond):** \( f = 15 \times 10^5 \, \text{dyne/cm} \) The mass (\( m \)) is the mass of atoms (or weights). The smaller the value of \( m \), the higher the wavenumber (\( \tilde{\nu} \)) of vibration. ### Structure of Capsaicin Below the explanation, the chemical structure of capsaicin, a spicy component found in hot peppers, is provided. ![Capsaicin](structure) - **Key Structural Details:** - CH₃O (methoxy group) - HO (hydroxy group) - N-H (amide group) - Various hydrocarbon chains and rings Understanding the vibration principles and structural details of molecules helps in studying their chemical behavior and interactions efficiently.
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