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Electromagnetic Waves
Electromagnetic Waves and their Properties
Physics Textbooks Boundless Physics Electromagnetic Waves Electromagnetic Waves and their Properties
Physics Textbooks Boundless Physics Electromagnetic Waves
Physics Textbooks Boundless Physics
Physics Textbooks
Physics
Concept Version 5
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Energy and Momentum

Electromagnetic waves have energy and momentum that are both associated with their wavelength and frequency.

Learning Objective

  • Relate energy of an electromagnetic wave with the frequency and wavelength


Key Points

    • Max Planck proved that energy of a photon (a stream of which is an electromagnetic wave) is quantized and can exist in multiples of "Planck's constant" (denoted as h, approximately equal to 6.626×10-34 J·s).
    • $E=hf=\frac {hc}{\lambda}$ describes the energy (E) of a photon as a function of frequency (f), or wavelength (λ).
    • $p=\frac {E}{c}=\frac {hf}{c}=\frac {h}{\lambda}$describes the momentum (p) of a photon as a function of its energy, frequency, or wavelength.

Terms

  • wavelength

    The length of a single cycle of a wave, as measured by the distance between one peak or trough of a wave and the next; it is often designated in physics as λ, and corresponds to the velocity of the wave divided by its frequency.

  • photon

    The quantum of light and other electromagnetic energy, regarded as a discrete particle having zero rest mass, no electric charge, and an indefinitely long lifetime.

  • frequency

    The quotient of the number of times n a periodic phenomenon occurs over the time t in which it occurs: f = n / t.


Full Text

Electromagnetic radiation can essentially be described as photon streams. These photons are strictly defined as massless, but have both energy and surprisingly, given their lack of mass, momentum, which can be calculated from their wave properties.

Waves were poorly understood until the 1900s, when Max Planck and Albert Einstein developed modern corrections to classical theory.

Planck theorized that "black bodies" (thermal radiators) and other forms of electromagnetic radiation existed not as spectra, but in discrete, "quantized" form. In other words, there were only certain energies an electromagnetic wave could have. In his work he developed what is now known as "Planck's constant," which is approximately equal to 6.626×10-34 J·s.

Energy

The energy (E) of a photon can be related to its frequency (f) by Planck's constant (h):

$E=hf=\frac {hc}{\lambda}$

The ratio of speed of light (c) to wavelength (λ) can be substituted in place of f to give the same equation to energy in different terms . Note that energy cannot take any value: it can only exist in increments of frequency times Planck's constant (or Planck's constant times c divided by wavelength). Energy of a wave is therefore "quantized. "

Wavelength

Wavelength of the sinusoidal function is represented by λ.

Momentum

Momentum is classically defined as the product of mass and velocity and thus would intuitively seem irrelevant to a discussion of electromagnetic radiation, which is both massless and composed of waves.

However, Einstein proved that light can act as particles in some circumstances, and that a wave-particle duality exists. And, given that he related energy and mass (E=mc2), it becomes more conceivable that a wave (which has an energy value) not only has an equation to mass but a momentum as well.

And indeed, Einstein proved that the momentum (p) of a photon is the ratio of its energy to the speed of light.

$p=\frac {E}{c}=\frac {hf}{c}=\frac {h}{\lambda}$

Substituting E with hc/λ cancels the c terms, making momentum also equal to the simple ratio of Planck's constant to wavelength.

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