**Electromagnetic Spectrum: The Photon**

Most remote sensing texts begin by giving a survey of the main principles, to build a theoretical background, mainly in the physics of radiation. While it is important to have such a framework to pursue many aspects of remote sensing, we do not delve into this complex subject in much detail at this point. Instead, we offer here only an outline survey of the basics of relevant electromagnetic concepts.

The fundamental unit in electromagnetic (which may be abbreviated "EM") phenomena is the *photon* (one form of quanta, from quantum physics). This subatomic particle comprises radiation emitted by matter when it is excited thermally, or by nuclear processes (fusion, fission), or by bombardment with other radiation. Photons, which are massless, move at the speed of light: 300,000 km/sec (186,000 miles/sec). Surprisingly, these particles also move as waves and hence, have a "dual" nature. These waves follow a pattern that we described in terms of a sine (trigonometric) function, as shown in two dimensions in the figure below.

The distance between two adjacent peaks on a wave is its wavelength. The total number of peaks that pass by a reference in a second is that wave's frequency (in cycles per second and hertz). We say a photon energy which we determine using Planck's general equation:

where *h* is Planck's constant (6.6260... x 10^{-34} Joules-sec) *and *v* is the Greek letter, nu, representing frequency. Photons traveling at higher frequencies are therefore more energetic. If a material under excitation experiences a change in energy level from a higher level E_{2} to a lower level E_{1}, we restate the above formula as:

where *v* has some discrete value determined by (*v*_{2} - *v*_{1}). In other words, a particular energy change is characterized by producing emitted radiation (photons) at a specific frequency *v* and a corresponding wavelength **l**.

**I-4*** ***Is there something wrong with the equation just above? ****ANSWER**

Wavelength is the inverse of frequency (higher frequencies associate with shorter wavelengths; lower with longer), as given by the relationship:

where *c is* the constant that expresses the speed of light, so that we can also write the Planck equation as

**I-5 State a very simple mnemonic phrase (one that helps your memory) for associating the energy level (amount of energy) with wavelength. ANSWER **

**I-6: Calculate the wavelength of a quantum of radiation whose photon energy is 2.10 x 10 ^{-19} Joules; use 3 x 10^{8} m/sec as the speed of light c. ANSWER**

**I-7**:* ***A radio station broadcasts at 120 MHz (megahertz or a million cycles/sec); what is the corresponding frequency in meters (hint: convert MHz to units of Hertz).**** ANSWER **

_{The number 10-34 (incredibly small) or 1012 trillion (very large) is a shorthand notation that allows one to express very large and very small numbers without writing all of the digits. It allows one to "normalize" a number by expressing it in two parts: the first part expresses the value of the number as a real value between .9999... and 10 exclusive; the second part of the number tells the number of places to shift the decimal point to the right or the left. One multiplies the first part of the number by the power of ten in the second part of the number to get its value. Consider the second part of the number, values assigned to the number 10n where n can be any positive or negative integer. A +n indicates the number of zeros that follow the number 10, thus for n = 3, the value of 103 is 1 followed by three zeros, or 1000 (this is the same as the cube of 10); 106 is 1000000, i.e., a 1 followed by six zeros to its right (Note: 100 = 1). Thus, 1060 represents 1,000,000,000,000,000... out to 60 such zeros. Likewise, 10-3 (where n = -3) is equal to 0.001, equivalent to the fraction 1/1000, in which there are two zeros (three places) before the decimal point at 1. ; 10-6 is evaluated as 0.000001. Any number can be represented as the product of its decimal expression (between .99999... and 10) and the appropriate power of 10, (10n). Thus, we restate 8345 as 8.345 x 103; the number 0.00469 is given as 4.69 x 10-3. }

Primary Author: Nicholas M. Short, Sr. email: nmshort@epix.net

Collaborators: Code 935 NASA GSFC, GST, USAF Academy

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