What is the relationship between energy and wavelength

General
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what is the relationship between energy and wavelength

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What is the relationship between energy and wavelength?

Answer: The relationship between energy (E) and wavelength (\lambda) is critical in understanding the behavior of electromagnetic waves, particularly in the context of light and other forms of electromagnetic radiation. This relationship is governed by two key equations in physics:

  1. Planck’s Equation:

    • This equation relates the energy of a photon to its frequency (\nu):
    E = h\nu

    where E is the energy of the photon, h is Planck’s constant (6.626 \times 10^{-34} \, \text{Js}), and \nu is the frequency of the photon.

  2. Wave Equation:

    • This equation connects the frequency of a wave to its wavelength:
    c = \lambda \nu

    where c is the speed of light in vacuum (3 \times 10^8 \, \text{m/s}), \lambda is the wavelength, and \nu is the frequency of the wave.

By combining these two equations, we can express the energy of a photon directly in terms of its wavelength:

Derivation:

  1. Start with Planck’s equation:

    E = h\nu

  2. Substitute the wave equation (c = \lambda \nu) into Planck’s equation to eliminate \nu:

    E = h \left(\frac{c}{\lambda}\right)

  3. Simplify to find the relationship between energy and wavelength:

    E = \frac{hc}{\lambda}

Thus, the energy of a photon is inversely proportional to its wavelength. This means that as the wavelength decreases, the energy increases, and vice versa.

Key Points to Remember:

  • Higher Energy = Shorter Wavelength: Photons with higher energies have shorter wavelengths (e.g., X-rays, gamma rays).
  • Lower Energy = Longer Wavelength: Photons with lower energies have longer wavelengths (e.g., radio waves, microwaves).

Applications:

  • In physics, particularly in quantum mechanics and spectroscopy, this relationship is fundamental for understanding phenomena such as the absorption and emission of light by atoms and molecules.
  • In various technologies like laser engineering and even medical imaging, knowing how energy relates to wavelength is crucial for design and application.

Understanding the relationship between energy and wavelength helps in comprehending the broader spectrum of electromagnetic waves and their interaction with matter.