21.1 Electromagnetic Waves

Classical Picture of Electromagnetic Waves

Electromagnetic (EM) waves are produced by accelerating electric charges. When a charge oscillates (e.g., electrons in a transmitting antenna), it creates time-varying electric and magnetic fields that propagate outward as an EM wave.

Structure of an EM Wave

In an EM wave:

• The electric field $\vec{E}$ and magnetic field $\vec{B}$ oscillate perpendicular to each other.
• Both fields are perpendicular to the direction of propagation — making EM waves transverse waves.
• The direction of propagation is given by $\vec{E}\times \vec{B}$.

Speed of EM Waves

All EM waves travel through vacuum at the speed of light:

$c=3\times 10^8\text{ m/s}$

This speed is independent of frequency — radio waves, visible light, X-rays, and gamma rays all travel at $c$ in vacuum.

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Particulate Nature of Electromagnetic Radiation

Classical wave theory successfully explains interference, diffraction, and polarisation of light. However, several phenomena — most notably the photoelectric effect and Compton scattering — cannot be explained by treating light purely as a wave.

These observations led to the conclusion that electromagnetic radiation has a particulate (quantum) nature: it is emitted, absorbed, and travels in discrete packets of energy called photons.

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The Photonic Model of Light (Planck–Einstein Relation)

Max Planck (1900) proposed that energy is quantised — emitted or absorbed only in discrete packets called quanta. Albert Einstein extended this to light itself, proposing that a photon carries energy:

$\boxed{E=hf}$

where:

• $E$ = energy of one photon (in joules, J)
• $h=6.626\times 10^{-34}$ J·s = Planck's constant
• $f$ = frequency of the radiation (Hz)

Since $c=f\lambda$, this can also be written as:

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

where $\lambda$ is the wavelength.

Key Points

• Higher frequency → higher photon energy.
• Energy is quantised: only whole-number multiples of $hf$ can be exchanged.
• A photon has zero rest mass but carries energy and momentum.

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The Electronvolt (eV)

Because photon energies are extremely small in joules, a more convenient unit is the electronvolt:

$1\text{ eV}=1.6\times 10^{-19}\text{ J}$

One electronvolt is the kinetic energy gained by an electron accelerated through a potential difference of 1 volt.

Useful shortcut for photon energy

Using $hc=1240\text{ eV⋅nm}$:

$E=\frac{1240\text{ eV⋅nm}}{\lambda \text{ (nm)}}$

Example: Find the energy of a photon of wavelength $500\text{ nm}$.

$E=\frac{1240}{500}=2.48\text{ eV}$

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Summary Table