How Much Energy Do CO Molecules Need for a Rotational Transition?

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SUMMARY

The energy required for carbon monoxide (CO) molecules to transition from the lowest to the next highest rotational energy level is calculated using the formula E = hv, where h is Planck's constant (6.626 x 10^-34 J s) and v is the frequency of light (1.16 x 10^11 Hz). This results in an energy value of approximately 0.0463 kJ/mol. The calculation confirms that the correct answer is option d: 0.0463 kJ/mol. This energy transition is critical for understanding molecular behavior in quantum chemistry.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with Planck's constant and its application
  • Knowledge of molecular rotational energy levels
  • Basic skills in unit conversion (J to kJ/mol)
NEXT STEPS
  • Research the implications of rotational transitions in spectroscopy
  • Learn about the role of Planck's constant in quantum mechanics
  • Explore the concept of energy quantization in molecular systems
  • Study the calculation of energy levels in diatomic molecules
USEFUL FOR

Chemists, physicists, and students studying quantum mechanics or molecular spectroscopy will benefit from this discussion, particularly those interested in energy transitions of molecules.

Soaring Crane
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The absorption of light of frequency 1.16 x 10^11 Hz is required for CO molecules to go from the lowest rotational energy level to the next highest rotational energy level. Determine the energy for this transition in kJ/mol. h = 6.626 x 10-34 J s
a. 7.69 x 10-23 kJ/mol
b. 949 kJ/mol
c. 46.3 kJ/mol
d. 0.0463 kJ/mol
E = hv
= (1.16*10^11 Hz)(6.626*10^-34 J*s)
= 7.686 *10^-23 J = 7.69*10^-26 kJ* (6.02*10^23 molecules/ 1 mol) = 0.04629 kJ/mol
Thanks.
 
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