Electromagnetic Radiation PDF

____________________________________________________________________________________________________ Subject Physical Chemistry Paper No and Title 8/ Physical Spectroscopy Module No and Title 1 /Electromagnetic Radiation Module Ta...

____________________________________________________________________________________________________ Subject Physical Chemistry Paper No and Title 8/ Physical Spectroscopy Module No and Title 1 /Electromagnetic Radiation Module Tag CHE_P8_M1 CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 3. Waves and their properties 4. Classical Description of Electromagnetic Radiation 4.1 Introduction 4.2 Maxwell’s Equations 5. Regions of Electromagnetic Spectrum 6. Summary CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ 1. Learning Outcomes “We can easily forgive a child who is afraid of the dark; the real tragedy of life is when men are afraid of the light.” ― Plato To study matter using spectroscopy as a tool, understanding of radiation is necessary, as spectroscopy is all about the interaction of matter with radiation. After studying this module, you shall be able to learn about the nature and properties of electromagnetic waves. You will be introduced to the classical picture of light and electromagnetic waves. Later, its spectrum and, briefly, the kinds of spectroscopy observed in each region of the electromagnetic spectrum are discussed. http://science.pppst.com/space/electromagnetic-spectrum.html 2. Introduction Spectroscopy is the study of the interaction of radiation with matter. It is central to all the sciences, be it chemistry, physics, astrophysics, life sciences, geology, or any other science. Its study is therefore important because it allows us to have a peek at the internal structure of atoms and molecules. Though spectroscopy does not directly show us the molecule, it reveals a lot about its structure, i.e. it provides its image, as it were. In fact, the word “spectroscopy” is derived from the Latin word “spectron”—spectre (ghost or spirit)! CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ That is, in spectroscopy, you see the ghost or image of the molecule – not the molecule itself. Besides the determination of molecular structure, spectroscopy is used for the identification of unknown molecules, detection of known molecules, and measurement of concentrations for analytical purposes. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g. by a prism. Electromagnetic radiation is the source of radiated energy used in spectroscopic investigation. There are other kinds of radiation - for example the α and β particles emitted by radioactive nuclei, or the solar neutrinos bombarding the earth everyday, which are not electromagnetic in nature, but the γ-rays emitted by some nuclei most certainly are. These are high energy radiation, next only to the highest energy cosmic rays. The electromagnetic spectrum encompasses a wide range of energies, of which visible radiation is only a small part. CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ 3. Waves and their properties Light is also described as a wave. A wave is defined as a disturbance which travels and spreads out through some medium. We are all familiar with ripples in a pond and ocean waves. Now when you throw a cork on the water in a pond, you will observe waves going outwards, but the cork only bobs up and down. This means that the water does not move outwards. Indeed if it were to do so, all the water would end up at the banks of the ocean. It only moves up and down, normal to the direction of propagation of the wave. Such waves are called transverse waves, and light waves are also transverse. Waves in Naini Lake, Nainital The other kinds of waves are longitudinal, in which the motion is parallel to the direction of motion. Examples are sound waves, and such waves require a medium for their propagation, and are thus also known as mechanical waves. Transverse waves can travel in vacuum: In space no one can hear you scream - but they can see you. Characteristic properties of waves CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ Consider the transverse wave shown above moving to the right. The water molecules move only up and down. The high points in the wave are called crests and the low points are called troughs. The distance between two consecutive peaks or troughs in a wave is called the wavelength and is symbolized by λ. The height of the crest is termed the amplitude of the wave, and is usually given the symbol A. Therefore, the height of the water molecules (y) varies periodically between –A and +A through zero. Such a wave can be conveniently described as a sine function since at the starting point of the wave, the height is zero, and sin(0) is also zero. We thus write y(t ) = A sin θ (t ) (1) where θ is expressed in radians. We can trace y(t) by imagining an object moving counter- clockwise on the circumference of a circle of radius A. When the object has traversed 2π radians, it completes one cycle, as shown in Figure 1. If we express the angular frequency as ω radians per second, then θ(t) is given by ωt, so we can equivalently write y(t ) = A sin ωt (2) CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ Figure 1 Oscillation of a ball in circular motion The time taken for a complete cycle is called the time period of the wave and is denoted by T. A more important quantity than the time period is the frequency, defined as the number of waves (cycles) per second that pass a given point in space, and symbolized by ν. Evidently, the two quantities are related as ν = 1 / T. As we shall soon see, the energy of a radiation is directly proportional to its frequency. Also, since a cycle is complete when θ changes by 2π, the number of cycles per second (the frequency) is given by ν = ω / 2π. We therefore write y(t ) = A sin 2πνt (3) The speed of light The distance traversed in a cycle is λ; hence, the speed (v) of the wave is the distance travelled in a cycle divided by the time taken to complete a cycle, i.e. λ/T or λν. For light, the speed is given its own symbol c, since all electromagnetic radiation has the same speed, ~ 3×108 m s-1. It takes 1.33 second for light to travel from the earth to the moon and 8.33 minutes for it to travel from the sun to the earth. Einstein showed that, according to special relativity, nothing can exceed the speed of light. Even at this speed, the nearest star, α Centuri is a good 9 years round trip away. We may thus write, c = λν, a relation that allows us to interconvert between the wavelength (in which all spectroscopic measurements are made) and the frequency to which the energy is proportional. Thus, shorter wavelengths correspond to higher frequencies and larger energies and longer wavelengths to smaller energies. Light travels in a straight line. Though the speed of light is constant in vacuum, it depends on the refractive index of the medium of propagation. Equation (3) can be now rewritten as CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ y(t ) = A sin(2πct / λ ) (4) Light waves are travelling waves, and, for these waves, we may combine equations (2) and (4), and write y(t ) = A sin(ωt − 2πct / λ ) = A sin(ωt − kz) (5) where k = 2π/λ and we have substituted z = ct for the distance travelled by a wave travelling in the z direction. 4. Classical Description of Electromagnetic Radiation 4.1 Introduction Up till now, we have not defined the quantity y(t) for light waves. James Clerk Maxwell was the first to realize more than a century ago the connection between optics and electricity and magnetism through his famous four equations, which govern all !electromagnetic radiation. ! According to Maxwell’s equations, there are oscillating magnetic ( B ) and electric ( E ) fields perpendicular to the direction of propagation of the wave. Thus, the y(t) of equation (5) could refer to either the sinusoidally oscillating electric or magnetic field. ! ! Fields E and B are in phase, reaching their maximum and minimum values at the same time. The electric field oscillates in the xz plane and the magnetic field oscillates in the yz plane. This corresponds to a polarized wave. Conventionally, the plane in which the electric field oscillates is defined as the plane of polarization. In this case it is the xz plane. Figure 2 shows a harmonic ! ! plane wave propagating in the z-direction. Note that E , B and the direction of propagation k̂ form a right handed triad. CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ Figure 2 Sketch of the electric field and magnetic field vectors of a light wave 4.2 Maxwell’s Equation Maxwell postulated the theoretical model of light as electromagnetic waves during the time in history when the wave and particle pictures of light were still duelling. Now let us see how Maxwell’s equations can be manipulated to give classical wave equations for the space and time dependence of the electric and magnetic field. Maxwell’s equations for vacuum in SI units are: ! ! ∇.E = 0 (6a) ! ! ∇.B = 0 (6b) ! ! ! ∂B ∇× E = − (6c) ∂t ! ! ! ∂E ∇ × B = ε 0 µ0 (6d) ∂t where µ0 = 4π×10-7 N s2 C-2 is the permeability of free space and ε0 = 8.85×10-12 C2 N-1 m-2 is the permittivity of free space. The last two equations couple the electric and the magnetic fields. Equation (6c) implies that, if ! ! ! ! ! ∂B B is time dependent, ∇ × E is non-zero, i.e. E is a function of position. Further, if itself ! ! ! ! ∂t changes with time, so does ∇ × E. In such a case E also varies with time since the ∇ operator cannot cause time variation. Thus, in general, a time varying magnetic field gives rise to an CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ electric field which varies both in space and time. It will be seen that these coupled fields propagate in space. We will first examine whether the equations lead to transverse waves. For simplicity, let us assume that the electric field has only the x-component and the magnetic field only the y- component. Note that we are only making an assumption regarding their directions – the fields could still depend on all the space coordinates x, y, z, in addition to time t. Gauss’s law gives ! ! ∂E ∂E y ∂Ez ∇.E = x + + =0 ∂x ∂y ∂z Since only Ex ≠ 0, this implies that ∂E x =0 ∂x Thus Ex is independent of the x coordinate and can be written as Ex(y, z, t). A similar analysis shows that By is independent of the y coordinate and can be written explicitly as By(x, z, t). ! Consider now the time dependent equations (6c) and (6d). The curl equation for B gives, taking the z-component ∂By ∂Bx ∂Ez − = =0 ∂x ∂y ∂t Since Bx = 0, this gives ∂B y =0 ∂x showing that By is independent of x and hence depends only on z and t. In a similar manner we ! ! can show that Ex also depends only on z and t. Thus the fields E and B do not vary in the plane containing them. Their only variation takes place along the z-axis which is perpendicular to both ! ! E and B. The direction of propagation is thus the z-direction. CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ To see that the propagation is really a wave disturbance, take the y-component of equation (6c) and the x-component of equation (6d). ∂Ex ∂B =− y (7) ∂x ∂t ∂By ∂Ex − = µ0ε 0 (8) ∂z ∂t To get the wave equation for Ex, take the derivative of equation (7) with respect to z and substitute in equation (8) and interchange the space and time derivatives, ∂ 2 Ex − ∂ 2 By ∂ ⎛ ∂B y ⎞ ∂ 2 Ex = µ 0ε 0 =− ⎜ ⎟ = µ 0ε 0 ∂z 2 ∂z∂t ∂t ⎜⎝ ∂z ⎟ ⎠ ∂t 2 Similarly, we can show ∂ 2 By ∂ 2 By = µ0ε 0 ∂z 2 ∂t 2 Each of the above equations represents a wave disturbance propagating in the z-direction with a speed 1 c= µ 0ε 0 CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ On substituting numerical values, the speed of electromagnetic waves in vacuum turns out to be 2.99792× 108 m s-1. Consider plane harmonic waves of angular frequency ω and wavelength λ= 2π/k. We can express the waves as Ex = E0 sin( kz − ωt ) By = B0 sin( kz − ωt ) The amplitudes E0 and B0 are not independent as they must satisfy equations (7) and (8): ∂E x = E0 k cos( kz − ωt ) ∂z ∂B y = − B0ω cos( kz − ωt ) ∂z Using equation (7) we get E0 k = B0ω The ratio of the electric field amplitude to the magnetic field amplitude is given by E0 ω = =c B0 k Example : Determine the state of polarization and the direction of propagation of the wave if the electric field of a plane electromagnetic wave in vacuum is given as Ey = 0.5 cos[2π×108(t− x/c)] V/m, Ex = Ez = 0. Also determine the magnetic field. Solution : Comparing with the standard form for a harmonic wave ω = 2π×108 rad/s k = 2π×108/c CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ so that λ = c/108 = 3 m. The direction of propagation is the x- direction. Since the electric field oscillates in the xy plane, this ! is the plane of polarization. Since B must be perpendicular to both the electric field direction and ! the direction of propagation, B has only the z-component with an amplitude B0 = E0/c≃1.66 × 10−9 T. Thus Bz = 1.66×10−9cos[2π×108(t− x/c)]T Maxwell’s relations could explain most phenomena involving light: 1. Law of Reflection – Angle of Incidence = Angle of reflection 2. Law of Refraction – A light beam is bent towards the normal when passing into a medium of higher Index of Refraction, and it is bent away from the normal when passing into a medium of lower Index of Refraction. Speed of light in vacuum 3. Index of Refraction – Speed of light in a medium 4. Inverse square law – The light intensity diminishes with the square of distance from the source. Hence, Maxwell’s relations could provide explanations for all of light’s interesting properties such as diffraction (rainbows) and reflection (mirrors), and light was firmly established as a wave. The third property implies that the speed of light varies with the refractive index of the medium, and only its speed in vacuum can be considered a fundamental constant. The frequency remains constant in any medium, and is thus a more fundamental property. This means that the wavelength changes on changing the medium of propagation. Maxwell’s relations show that the electric and magnetic fields recreate each other as the wave propagates. Thus, the oscillating electric field creates magnetism, as in an electromagnet, and similarly, the oscillating magnetic field creates electricity as in electric generators, and this goes on until the electromagnetic wave meets an object. 5. Regions of Electromagnetic Spectrum Visible light ranges through seven major colours from short wavelengths (high frequency - violet) to long wavelengths (low frequency - red) – Violet, indigo, blue, green, yellow, orange, red (VIBGYOR) – the colours of the rainbow. Our eyes recognize ν (or λ) as colour! However, at the beginning of the nineteenth century, it became apparent that there is radiation beyond the visible and the electromagnetic spectrum is not restricted to the visible region. It encompasses a wide range of frequencies. This continuous range of frequencies is known as the electromagnetic spectrum. The entire range of the spectrum is often sub-divided into specific CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________ regions. The subdivision of the entire spectrum into smaller regions is done mostly on the basis of how each region of electromagnetic waves interacts with matter. In the various kinds of spectroscopy, depending upon the region of the electromagnetic spectrum that we are scanning, different kinds of energy changes occur. For example, in the microwave region, it is mainly the rotational energy that changes. In the next higher energy range, the infrared region, another degree of freedom, the vibrational motion is also affected. Similarly, electronic energy changes occur in a still higher energy range, i.e. the ultraviolet and visible regions. Other kinds of spectroscopy are classified according to the techniques adopted for their study. For example, the resonance techniques, the electron spin resonance and nuclear spin resonance techniques, involve smaller energy changes, and are studied in the microwave and radiofrequency regions, respectively. Photoelectron spectroscopy involves higher energy photons, while Raman spectroscopy is based on the scattering of light using high energy laser beams. The figure below shows the electromagnetic spectrum. We see that the wavelength has the dimension of length and is expressed in various units, depending upon the region of the electromagnetic spectrum. In the visible region, the units are nanometre (nm) and the range is 400 nm (violet) to 700 nm (red). White light is a mixture of the seven colours of the rainbow. No object has its own colour. When white light strikes the object, it may absorb a particular colour from the white light and reflect the remaining colour. Our eye detects the reflected colour, which is complementary to the absorbed colour. Variables and Units Wavelength units: length Nanometre (nm): 1 nm = 1×10-9 m; Micrometre (µm): 1 µm = 1×10-6 m; Frequency units: Cycles per second 1/s (or s-1) is called hertz (abbreviated Hz) after the physicist Heinrich Hertz, who discovered radiowaves in 1887, 22 years after Maxwell’s equations. CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION) ____________________________________________________________________________________________________. To keep the numbers manageable, the prefixes kilo (1 kHz = 103 Hz), mega (1 MHz = 106 Hz) and giga (1 GHz = 109 Hz) are often used. Wavenumber: In spectroscopy, the wavenumber is often used, particularly in infrared and UV/Vis spectroscopy. It is defined as a count of the number of wave crests (or troughs) in a given unit of length (symbolized byν~ ). It has the dimensions of inverse length and is given by ν/c = 1/λ. Though not an SI unit, cm-1 is the preferred unit. This means that in the expression ν~ = 1/λ, the wavelength must be expressed in cm. Alternatively, in the expression, ν~ = ν / c , c must be expressed in cm s-1 and ν in s-1. Quantity Symbol Unit Wavelength l m Frequency v s-1 or Hz Speed c m s-1 Wavenumber ν~ m-1 6. Summary The characteristics of a wave are direction, amplitude, wavelength, frequency, angular and linear velocity. In the classical picture, electromagnetic radiation is considered to be a transverse wave of mutually perpendicular electric and magnetic fields, oscillating in the direction of the wave. According to Maxwell’s relations, the electric and magnetic fields recreate each other as the wave propagates until the electromagnetic wave meets an object. Maxwell’s relations explained all interesting properties of light such as diffraction (rainbows) and reflection (mirrors), and established light as a wave The regions of electromagnetic radiation range from the low energy radiofrequency up to the highest energy γ rays where nuclear transitions take place. CHEMISTRY PAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 1 (ELECTROMAGNETIC RADIATION)