Question

In the Vibrational Raman Spectra, the value of transition energy for the first overtone \( \Delta E_{\text{overtone}} \) is:

• A. \( \omega_e(1 - 2\chi_e) \, \text{cm}^{-1} \)
• B. \( 2\omega_e(1 - 3\chi_e) \, \text{cm}^{-1} \)
• C. \( 3\omega_e(1 - 4\chi_e) \, \text{cm}^{-1} \)
• D. \( 4\omega_e(1 - 5\chi_e) \, \text{cm}^{-1} \)

Hint:

In Vibrational Raman Spectra, the transition energy for the first overtone involves the anharmonicity constant \( \chi_e \), and it differs from the fundamental transition energy.

Answer 1

The Correct Option is A

The transition energy for the first overtone in the Vibrational Raman spectra is given by the formula: \[ \Delta E_{\text{overtone}} = \omega_e(1 - 2\chi_e) \] Where: - \( \omega_e \) is the fundamental vibrational frequency, - \( \chi_e \) is the anharmonicity constant. This formula represents the energy change during the overtone transition in a Raman spectrum. Final Answer: \[ \boxed{\text{(1) } \omega_e(1 - 2\chi_e) \, \text{cm}^{-1}} \]