Electromagnetic radiation

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Author of this article: Dr. Hans Fuchs

Basic physical equations

Figure 1 Snapshot of EMR wave model where $\lambda$ = wavelength, f = frequency and A = amplitude.

Life on earth would be impossible without solar energy. The source of the sun's energy are nuclear fusion processes of hydrogen to helium. Electromagnetic radiation (EMR) is generated on the hot surface of the sun and carries solar energy through the space to the earth.

The phenomenon of EMR can be explained by two physical theories at the same time: the wave theory and the quantum theory.

EMR can be seen as a wave with time-varying electric (E) and magnetic fields (B). These vector fields have a sine waveform, are oriented at right angles at each other and oscillate perpendicular to the direction of wave travel (Fig. 1). Waves are characterized by:

• wavelength $\lambda$ = the distance between adjacent wave peaks measured in the unit lengths nanometer ($1nm = 1*10^{-9}m$) or micrometer($1 mm=1*10^{-6}m$)
• frequency f = number of peaks passing a fixed point in a given period of time measured in the unit Hertz (1 Hz = 1 cycle per second)
• amplitude A = height of each peak and often measured as energy level (e.g. spectral irradiance (Watt per $m^2$ per micrometer)).

$ \lambda $ and f are used to divide the electromagnetic spectrum in main divisions.

No medium is needed for the propagation of EMR waves. The speed of light c in vacuum \(\begin{equation} c=\lambda*f \end{equation} \) is a universal constant (c $\approx$ 300 000 kilometer per second). Taking the mean distance between sun and earth ($\approx$ 150 000 000 km) it takes $\approx$ 8 minutes until solar EMR reaches the earth.

In the quantum theory EMR is composed of discrete packets of energy known as photons or quanta. They have no mass. Planck's formula allows to calculate the energy transported by a single photon: \begin{equation} Q=h*f \end{equation} where

• Q=radiant energy of a photon measured in Joule (J)
• h = Planck‘s constant ($6.626*10^{-34}$ Joule-Second (J sec)
• f = frequency (hz)

Combining eq(1) and eq(2) gives \begin{equation} Q=\frac{h*c}{\lambda} \end{equation} The longer the wavelength involved, the lower is the radiant energy of EMR and the lower is the frequency.

Electromagnetic energy is produced whenever a charged particle such as an electron or a nucleus of an atom changes its velocity and internal energy status. Every substance with a temperature above the absolute zero (0 K or -273.16°C) produces radiant energy and emits EMR in a continous spectrum of wavelengths. The higher the temperature the higher is the motion of electrons, molecules and atoms. Not all materials heated to the same temperature emit the same amount and spectral composition of EMR. This is not the case for an hypothetical perfect absorber and re-emitter of energy. Such an object is called blackbody which absorbs and emits all radiation of wavelenghts. Plank's radiation equation describes the radiant spectral exitance per unit wavelenght $M_{\lambda}$ of a blackbody as:

Figure 3 Extraterrestrial solar irradiance at the top of atmosphere and spectral exitance curve of a blackbody at the temperature 5777K.

\begin{equation} M_{\lambda}=\frac{c_{1}}{\lambda^{5}(exp(c_{2}/\lambda \ast T)-1)} \end{equation} where

• $c_{1}=3.742*10^{-16} Wm^{-2}$
• $c_{2}=1.4388*10^{-2} mK$
• $\lambda$=wavelength ($\mu$m)
• $T$=temperature (K)

. Fig. 3 shows that the sun can be approximated by a blackbody.

The first derivative of Planck's blackbody radiation equation determines the single maximum of the curve or the wavelenght of peak radiant exitance of a blackbody which is known as Wien's displacement equation: \begin{equation} \lambda_{max}=\frac{c_{3}}{T} \end{equation} where

• $c_{2}=2.89*10^{-3} mK$

It shows that the wavelenght of peak radiant exitance moves to shorter wavelenghts with increasing temperature. The solar maximum irradiance occurs in the visible spectrum at 0.47$\mu$m.

If we integrate the spectral radiant exitance curve of a blackbody over all wavelengths we obtain the total radiant energy exitance per unit surface area of the Stefan-Boltz-Mann equation: \begin{equation} M=\alpha\ast T^{4} \end{equation} where

• $\alpha=5.46697*10^-8 Wm^-2K^-4$

We assume a measured solar total radiant energy exitance per unit surface area on earth of about 1367 W/m2. This value is known as the solar constant also it varies throughout the year by about 3.5%. According to eq. 4 the total radiant exitance of an object depends only on the temperature and therefore the sun's temperature is estimated to 5777K.

Kirchhoff's equation, emissivity, white body, gray body

The electromagnetic spectrum

Visible Optical

Sources of EMR

Interaction of EMR with the atmosphere

Why is the sky blue? Why is the sun red at sunset? When can we see a rainbow?

Interaction of EMR with the earth surface

Spectral reflectance patterns of the earth surface

Terms in radiation