Physics

Physics

Problem

Determine the energy, in kJ mol−1\text{kJ\,mol}^{-1}, of photons with wavelength 4.50 μm4.50\,\mu\text{m}. State which type of molecular transition (rotational, vibrational, or electronic) these photons would most likely promote.
Intuitive explanation

Photon energy depends on wavelength through the relationship E=hc/λE = hc/\lambda—shorter wavelengths pack more energy per photon. Once you find the energy of one photon, multiply by Avogadro's number to get the molar energy. The key insight is then comparing your result to the typical energy scales of molecular transitions: electronic transitions live in the visible/UV (hundreds of kJ/mol), vibrational in the infrared (tens of kJ/mol), and rotational in the far-infrared/microwave (fractions of kJ/mol). Your wavelength falls in a specific region of the spectrum that matches one of these.

Intuitive explanation

Photon energy depends on wavelength through the relationship E=hc/λE = hc/\lambda—shorter wavelengths pack more energy per photon. Once you find the energy of one photon, multiply by Avogadro's number to get the molar energy. The key insight is then comparing your result to the typical energy scales of molecular transitions: electronic transitions live in the visible/UV (hundreds of kJ/mol), vibrational in the infrared (tens of kJ/mol), and rotational in the far-infrared/microwave (fractions of kJ/mol). Your wavelength falls in a specific region of the spectrum that matches one of these.

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