The blue color of the sky results from the scattering of...

The blue color of the sky results from the scattering of sunlight by one of the components of air. The blue light has a frequency of about $7.5 \times 10^{14} \mathrm{~Hz}$. (a) Calculate the wavelength (in nanometers) associated with this radiation, and (b) calculate the energy (in joules) of a single photon associated with this frequency.

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Key Concepts

Wavelength-Frequency Relationship

This concept establishes that the speed of light (c) is the product of its wavelength (?) and frequency (f), expressed by the equation c = ?f. It is fundamental in understanding how light propagates and allows for the conversion between frequency and wavelength, which is essential when discussing various properties of electromagnetic radiation.

Photon Energy

Photon energy is determined using the relationship E = hf, where E is the energy of the photon, h is Planck's constant, and f is the frequency of the photon. This concept highlights the quantized nature of electromagnetic radiation and is key in fields such as quantum mechanics and spectroscopy, where energy exchanges occur in discrete amounts.

Fundamental Constants in Electromagnetism

The speed of light (c) and Planck's constant (h) are crucial constants in electromagnetic theory. The speed of light is a universal constant that defines how fast electromagnetic waves propagate in a vacuum, while Planck's constant is central to the quantization of energy and the study of photon behavior. Both constants serve as bridges between classical and quantum descriptions of light.

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