General Properties of Electromagnetic Radiation

1. General Properties of ElectromagneticRadiation Lecture 1

2. Electromagnetic radiation is looked at as sinusoidal waves which are composed of a combination of two fields. An electric field (which we will use, in this course, to explain absorption and emission of radiation by analytes) and a magnetic field at right angle to the electric field (which will be used to explain phenomena like nuclear magnetic resonance in the course of special topics in analytical chemistry offered to Chemistry students only).

3. The classical wave model The classical wave model describes electromagnetic radiation as waves that have a wavelength, frequency, velocity, and amplitude. These properties of electromagnetic radiation can explain classical characteristics of electromagnetic radiation like reflection, refraction, diffraction, interference, etc. However, the wave model can not explain the phenomena of absorption and emission of radiation.

4. We will only deal with the electric field of the electromagnetic radiation and will thus refer to an electromagnetic wave as an electric field having the shape of a sinusoidal wave. The arrows in the figure below represent few electric vectors while the yellow solid sinusoidal wave is the magnetic field associated with the electric field of the wave.

5. Wave Properties of Electromagnetic Radiation

6. Wave Parameters 1. Wavelength () The wavelength of a wave is the distance between two consecutive maxima or two consecutive minima on the wave. It can also be defined as the distance between two equivalent points on two successive maxima or minima. This can be seen on the figure below:

8. 2. Amplitude (A) The amplitude of the wave is represented by the length of the electrical vector at a maximum or minimum in the wave. In the figure above, the amplitude is the length of any of the vertical arrows perpendicular to the direction of propagation of the wave.

9. 3. Frequency The frequency of the wave is directly proportional to the energy of the wave and is defined as the number of wavelengths passing a fixed point in space in one second. 4. Period (p) The period of the wave is the time in seconds required for one wavelength to pass a fixed point in space.

10. 5. Velocity (v) The velocity of a wave is defined as the multiplication of the frequency times the wavelength. This means: V =  The velocity of light in vacuum is greater than its velocity in any other medium

11. Since the frequency of the wave is a constant and is a property of the source, the decrease in velocity of electromagnetic radiation in media other than vacuum should thus be attributed to a decrease in the wavelength of radiation upon passage through that medium.

12. Electromagnetic Radiation, Cont…. Lecture 2

14. 6. Wavenumber () The reciprocal of wavelength in centimeters is called the wavenumber. This is an important property especially in the study of infrared spectroscopy.  = k 

15. Electromagnetic Spectrum The electromagnetic radiation covers a vast spectrum of frequencies and wavelengths. This includes the very energetic gamma-rays radiation with a wavelength range from 0.005 – 1.4 Ao to radiowaves in the wavelength range up to meters (exceedingly low energy). However, the region of interest to us in this course is rather a very limited range from 180-780 nm. This limited range covers both ultraviolet and visible radiation.

18. Mathematical Description of a Wave A sine wave can be mathematically represented by the equation: Y = A sin (t + ) Where y is the electric vector at time t, A is the amplitude of the wave,  is the angular frequency, and  is the phase angle of the wave. The angular frequency is related to the frequency of radiation by the relation: = 2 This makes the wave equation become: Y = A sin (2t+ )

19. Superposition of Waves When two or more waves traverse the same space, a resultant wave, which is the sum of all waves, results. Where the resultant wave can be written as: Y = A1 sin (2t+ ) + A2 sin (2t+ ) + ........ + An sin (2nt+ n)

20. Constructive Interference The resultant wave would have a greater amplitude than any of the individual waves which, in this case, is referred to as constructive interference. The opposite could also take place where lower amplitude is obtained.

22. The decrease in the intensity is a result of what is called a destructive interference. When the multiple waves have the same wavelength, maximum constructive interference takes place when 1 - 2 is equal to zero, 360 deg or multiple of 360 deg. Also maximum destructive interference is observed when 1 – 2 is equal to 180 deg, or 180 deg + multiples of 360 deg.

24. The blue and yellow shaded waves interfere to give the brown shaded wave of less amplitude, a consequence of destructive interference of the two waves.

27. The Period of a Beat When two waves of the same amplitude but different frequencies interfere, the resulting wave exhibit a periodicity and is referred to as beat (see figure below). The period of the beat can be defined as the reciprocal of the frequency difference between the two waves: Pb = 1/()

30. Fourier Transform The resultant wave of multiple waves of different amplitudes and frequencies can be resolved back to its component waves by a mathematical process called Fourier transformation. This mathematical technique is the basis of several instrumental techniques like Fourier transform infrared, Fourier transform nuclear magnetic resonance, etc.

32. Diffraction of Radiation Diffraction is a characteristic of electromagnetic radiation. Diffraction is a process by which a parallel beam of radiation is bent when passing through a narrow opening or a pinhole. Therefore, diffraction of radiation demonstrate its wave nature. Diffraction is not clear when the opening is large.

35. Coherence of Radiation Two beams of radiation are said to be coherent if they satisfy the following conditions: 1. Both have the same frequency and wavelength or set of frequencies and wavelength. 2. Both have the same phase relationships with time. 3. Both are continuous.

36. Electromagnetic Radiation Cont…. Lecture 3

37. Transmission of Radiation As mentioned before, the velocity of radiation in any medium is less than that in vacuum. The velocity of radiation is therefore a function of the refractive index of the medium in which it propagates. The velocity of radiation in any medium can be related to the speed of radiation in vacuum ( c ) by the relation: ni = c/vi Where, vi is the velocity of radiation in the medium i, and ni is the refractive index of medium i.

38. The decrease in radiation velocity upon propagation in transparent media is attributed to periodic polarization of atomic and molecular species making up the medium. By polarization we simply mean temporary induced deformation of the electronic clouds of atoms and molecules as a result of interaction with electric field of the waves.

39. Dispersion of Radiation If we look carefully at the equation ni = c/vi and remember that the speed of radiation in vacuum is constant and independent on wavelength, and since the velocity of radiation in medium i is dependent on wavelength, therefore the refractive index of a substance should be dependent on wavelength. The variation of the refractive index with wavelength is called dispersion.

41. Refraction of Radiation When a beam of radiation hits the interface between two transparent media that have different refractive indices, the beam suffers an abrupt change in direction or refraction. The degree of refraction is quantitatively shown by Snell's law where: n1 sin 1 = n2 sin 2

45. Reflection of Radiation An incident beam hitting transparent surfaces (at right angles) with a different refractive index will suffer successive reflections. This means that the intensity of emerging beam will always be less than the incident beam.

47. Scattering of Radiation When a beam of radiation hits a particle, molecule, or aggregates of particles or molecules, scattering occurs. The intensity of scattered radiation is directly proportional to particle size, concentration, the square of the polarizability of the molecule, as well as the fourth power of the frequency of incident beam. Scattered radiation can be divided into three categories:

48. Rayleigh Scattering Rayleigh Scattering is scattering of electromagnetic radiation by particles much smaller than the wavelength of the radiation. Rayleigh Scattering usually occurs in gasses. The scattering of solar radiation by earth’s atmosphere is one of the main reasons why the sky is blue. Rayleigh Scattering has a strong dependence on wavelength having a l-4 relationship.

49. 2. Mie scattering Mie scattering is caused by dust, smoke, water droplets, and other particles in the lower portion of the atmosphere. It occurs when the particles causing the scattering are close in dimension to the wavelengths of radiation in contact with them. Mie scattering is responsible for the white appearance of the clouds.

50. 3. Tyndall Effect (nonspecific scattering) It occurs in the lower portion of the atmosphere when the particles are much larger than the incident radiation. This type of scattering is not wavelength dependent and is the primary cause of haze.