Sodium is easily identified in a solution by its strong emission at λ=589 nm. According to Einst

step 1 Hi, this is problem number 144. In problem number 144, we are given the wavelength for a sodium

Sodium is easily identified in a solution by its strong...

Sodium is easily identified in a solution by its strong emission at $\lambda=589 \mathrm{nm}$. According to Einstein's equation, $E=m c^{2}$ (where $m$ is mass), this amount of energy can be converted into mass. What is the mass equivalent of one photon emitted by an excited sodium atom? $\left(1 J=1 \mathrm{~kg} \cdot \mathrm{m}^{2} / \mathrm{s}^{2}\right)$

Key Concepts

Einstein's Mass-Energy Equivalence

This principle, expressed by the equation E = mc², states that energy and mass are interconvertible. It forms one of the cornerstones of modern physics and demonstrates that a given amount of energy has an equivalent mass. This concept is crucial for understanding how energy carried by photons can be related to a corresponding, albeit very small, mass.

Photon Energy Calculation Using Planck's Equation

Planck's equation, E = h? (or equivalently E = hc/?), is used to determine the energy of a photon based on its frequency or wavelength. This quantization of energy is a fundamental concept in quantum mechanics and helps explain phenomena such as atomic emission spectra by linking the discrete energy levels of atoms to the energy of emitted or absorbed photons.

Relationship Between Wavelength, Frequency, and the Speed of Light

The connection between wavelength and frequency is established by the equation c = ??, where c is the speed of light. This relationship allows the conversion between a photon's wavelength and its frequency, which is essential when applying Planck's equation to calculate photon energy from its observed spectral wavelength.

Energy-Mass Conversion

After determining the energy of a photon, the mass equivalent can be calculated using the rearranged form of Einstein's equation, m = E/c². This conversion demonstrates the profound link between energy and mass, showing that even light, which is massless in the traditional sense, embodies an equivalent mass corresponding to its energy content.

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