The bright yellow light emitted by a sodium vapor lamp...

The bright yellow light emitted by a sodium vapor lamp consists of two emission lines at $589.0$ and $589.6 \mathrm{~nm}$. What are the frequency and the energy of a photon of light at each of these wavelengths? What are the energies in $\mathrm{kJ} / \mathrm{mol}$ ?

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Key Concepts

Molar Energy Conversion

To connect microscopic energy measurements to macroscopic quantities, the energy of a single photon is converted to energy per mole by multiplying by Avogadro's number. This conversion enables the expression of energy in units like kJ/mol, facilitating comparisons and calculations in chemistry and materials science, particularly in studies dealing with reaction energetics and spectroscopic analysis.

Photon Energy Calculation

Photon energy is calculated using the relationship E = h?, where E is the energy of the photon, h is Planck's constant, and ? is the frequency. This concept is fundamental in quantum mechanics and explains how discrete energy packets, or quanta, of light carry energy, which is integral in phenomena such as emission spectra and electronic transitions.

Wavelength-Frequency Relationship

This concept involves the inverse proportionality between the wavelength and the frequency of electromagnetic waves, encapsulated in the equation c = ??, where c is the speed of light. Understanding this relationship is crucial because it allows for the determination of the frequency of light from its wavelength, forming the basis for further calculations in photon energy and spectroscopy.

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