Topic 2: Electromagnetic Radiation

Electromagnetic Radiation

Introduction

• Electromagnetic radiation is a crucial topic (Topic 2 of 7) in SOEE1541 Physics for Environmental Science.

• Lectures 3 and 4, presented on Monday, February 3rd, and Tuesday, February 4th, by Dr. Graham Mann.

Learning Outcomes

• Define electromagnetic radiation.

• Describe the nature of electromagnetic radiation.

• Identify different wavelengths within the electromagnetic spectrum.

• Explain the energy carried by radiation.

• Differentiate between emitters and absorbers of radiation.

• Apply Wien's Displacement Law to determine wavelengths emitted.

• Apply the Stefan-Boltzmann Law to quantify energy radiated.

• Explain absorption in the atmosphere and the greenhouse effect.

What is Electromagnetic Radiation?

• Electromagnetic radiation can transport energy through a vacuum, such as solar radiation.

• It is a travelling wave characterized by oscillating electric and magnetic fields perpendicular to each other.

• The speed of electromagnetic radiation in a vacuum is the speed of light, approximately $3 x 10^8 ms^{-1}$.

• James Clark Maxwell developed the theory of electromagnetism.

Types of Electromagnetic Radiation

• The electromagnetic spectrum includes:

  • Radio waves

  • Microwaves

  • Infrared (IR)

  • Visible light

  • Ultraviolet (UV)

  • X-rays

  • Gamma rays

• Frequency ($\nu$) increases from radio waves to gamma rays.

• Wavelength ($\lambda$ )increases from gamma rays to radio waves.

• Visible light ranges from approximately 400 nm to 740 nm.

Gamma Rays

• Emitted by radioactive substances during nuclear reactions.

• Wavelength: <0.01 nm (< 10^{-11} m).

• Highly penetrating and biologically hazardous due to their high energy, capable of damaging bone marrow and internal organs.

X-Rays

• Emitted when fast-moving electrons strike a metal target (anode).

• Example: Medical X-rays use a vacuum tube where electrons strike a tungsten anode.

• Penetrating.

• Wavelength: 0.01-10 nm ($10^{-11} - 10^{-8}$ m).

Ultraviolet (UV) Radiation

• Wavelength range: 10 nm < $\lambda$ < 400 nm.

• Higher energy than visible light.

• Emitted by the sun and partially absorbed by the ozone layer.

• Harmful to human health in excessive amounts.

• Causes chemical reactions in the atmosphere.

• Induces fluorescence in certain substances.

Visible Light

• Wavelength: 400 nm < $\lambda$ < 740 nm.

• The sun emits strongly at visible wavelengths.

• Detected by human eyes.

• Flame tests: elements emit characteristic colors of light when heated due to electron excitation and subsequent return to the ground state.

• Spectroscopy: wavelengths emitted or absorbed by atoms/molecules can identify the species present.

• Emission spectrum: vertical colored lines indicate emitted wavelengths.

• Absorption spectrum: vertical black lines indicate absorbed wavelengths.

Infra-Red (IR) Radiation

• Wavelength: 740 nm < $\lambda$ < $10^{}50$ nm.

• Major component of thermal radiation.

• Invisible to the human eye but detectable with IR cameras.

• Wavelengths emitted depend on the temperature of the emitting body.

• Detected as heat.

• Slightly less energetic than visible light.

• Strongly absorbed by greenhouse gases like CO2.

Radio Waves

• Lowest energy and longest wavelength.

• Used for radio, terrestrial TV, and police communications.

• Heinrich Hertz demonstrated radio waves in 1886-89.

• Invention of radar in 1935 by Robert Watson-Watt.

Microwave Radiation

• Wavelength: 1 mm < $\lambda$ < 30 cm.

• Higher energy than radio waves.

• Artificially generated by high-frequency electrical oscillators.

• Used in radar, air traffic control, communication satellites, and cooking.

• Mobile phone masts transmit shorter-wavelength radio waves.

• Satellite TV broadcasts at high frequencies (~10 GHz).

Interaction Between Radiation and Physical Bodies

1. Emission: Radiation emitted from the surface, extracting internal energy (e.g., the Sun).

2. Absorption: Radiation absorbed into a body and re-emitted as heat (e.g., the Sun's radiation on Earth).

3. Reflection: Radiation reflected without heating the body (e.g., visible light on a mirror).

4. Transmission: Radiation passes through the body (e.g., gamma rays through skin, light through glass).

5. Scattering: Radiation reflected in different directions (e.g., solar radiation by molecules/particles in the atmosphere).

• These interactions often occur simultaneously, and different wavelengths are affected to varying degrees.

Overview of Electromagnetic Radiation Absorption

• Spectroscopy involves focusing a white beam of light on a sample.

• Photons matching the energy gap of the molecules are absorbed, exciting the molecule.

• Other photons transmit unaffected.

Blue Skies and Hazy Sunsets

• Three types of light scattering in the atmosphere:

  • Rayleigh scattering (by gases)

  • Mie scattering (by haze particles)

  • Geometric-regime scattering (by cloud particles)

• Mie scattering occurs when the wavelength of light matches the size of particles.

• Rayleigh scattering is strongly wavelength-dependent (~$\lambda^{-4}$), greater for blue light.

• Blue sky results from Rayleigh scattering.

• Sunlight appears yellow because blue light is scattered away.

• Sunset colors are due to both Mie and Rayleigh scattering.

• Enhanced sunsets occur with aerosol haze from pollution or volcanic eruptions.

• After volcanic eruptions, aerosols in the stratosphere cause longer sunsets with unusual colors.

Radiative Flux

• Radiation as a flow of energy, expressed as radiative flux (flux = flow).

• Radiative flux: rate at which energy is transmitted per unit area (Wm-2).

• The Sun's rate of energy radiation ($L$) = $3.84 x 10^{26}$ W (Joules/s), known as solar luminosity.

Kelvin Scale & Black Body Radiation

• Absolute temperature is measured in Kelvin (K).

• 0 K = -273.15 degrees Celsius.

• All bodies above absolute zero (T=0K) emit electromagnetic radiation, causing cooling.

• A black body is a perfect absorber and emitter of radiation.

• In thermal equilibrium, emits black body radiation at a wavelength distribution determined by temperature.

What Wavelengths Are Emitted?

• Wien’s Displacement Law: The wavelength at which maximum radiation is emitted depends on temperature.

• $\lambda_{max} T = constant = 2.9 x 10^{-3} mK$

  • $\lambda_{max}$ is the wavelength in meters.

  • $T$ is the temperature in Kelvin.

• At higher temperatures, peak emission shifts to shorter wavelengths.

Wien’s Law Examples

1. Solar Radiation: For the sun at 5800K:
   $\lambda_{max} = \frac{2.9 x 10^{-3} mK}{5800K} = 5 x 10^{-7} m = 500 nm$

2. Light Bulb: For a conventional incandescent light bulb:

   • T = 2000K, $\lambda_{max} = 1.45 x 10^{-6} m$

   • T = 3000K, $\lambda_{max} = 0.97 x 10^{-6} m$

   • T = 4000K, $\lambda_{max} = 0.73 x 10^{-6} m$

   • The glass bulb is cooler (373 to 433K).

   • Bulb design balances glow temperature, cooler glass bulb and visible range (400-740nm).

Stefan-Boltzmann Law

• Total energy $E$ (radiative flux in $Wm^{-2}$) radiated by a black body at temperature $T$ (in K): $E = \sigma T^4$

• $\sigma$ is the Stefan-Boltzmann constant: $\sigma = 5.67 x 10^{-8} Wm^{-2}K^{-4}$

Stefan-Boltzmann Law Examples

1. Sun: Calculate the total energy radiated by the sun at 5800K:
   $E = 5.67 x 10^{-8} Wm^{-2}K^{-4} x (5800 K)^4 = 6.4 x 10^7 Wm^{-2}$

2. Earth: Calculate the total energy radiated for a region of Earth at 290 K with emissivity 0.95:
   $E = 0.95 x (5.67 x 10^{-8} Wm^{-2}K^{-4}) x (290 K)^4 = 380 Wm^{-2}$

3. Object: An object with emissivity 0.9 emits 270 $Wm^{-2}$ of radiation. To find its temperature:
   $270 Wm^{-2} = 0.9 x (5.67 x 10^{-8} Wm^{-2}K^{-4}) x T^4$
   $T = (\frac{270}{0.9 x 5.67 x 10^{-8}})^{1/4} = 269.7 K$

Non-Perfect Emitters and Absorbers

• For non-black bodies, the Stefan-Boltzmann Law is generalized to: $E = \varepsilon \sigma T^4$

• $\varepsilon$ is emissivity (0 to 1).

• A black body has $\varepsilon = 1$.

• Good emitters are good absorbers; reflecting bodies are poor emitters.

Greenhouse Effect

• Gases in the atmosphere absorb radiation at different wavelengths.

• Absorption in the infrared (IR) part of the spectrum causes the greenhouse effect.

• Traps outgoing IR, warming the surface climate.

• Good IR absorbers:

  • Molecules with more than two atoms (e.g., CO2, H2O).

  • Molecules with a strong dipole moment.

• Poor IR absorbers:

  • Molecules with two identical atoms (e.g., O2, N2, Cl2) due to no dipole moment.

Why do these gases absorb in the IR?

• The natural frequency of vibration of molecules is about $10^{14}$ Hz (IR frequencies).

• Radiation is absorbed if its frequency matches the molecule's natural frequency (resonance).

Radiation as Particles

• Radiation exhibits wave-particle duality.

• Particles of radiation are called photons.

• The photoelectric effect demonstrates particle behavior.

• Einstein: We must use both wave and particle theories to fully explain light.

Photons

• Photons are important in: photolytic reactions, photosynthesis and skin damage by UV radiation.

• The energy $E$ of a photon is: $E = hf$

  • $h$ is Planck’s constant ($h = 6.6 x 10^{-34} Js$).

  • $E$ is energy in Joules (J)

Summary

• Electromagnetic radiation has many forms (visible light, UV, IR, microwaves, radio waves, gamma & X-rays).

• Radiation can be emitted, transmitted, scattered, reflected, and absorbed.

• Two fundamental laws for radiating black bodies: Wien’s Displacement Law and the Stefan-Boltzmann Law.

• Atmospheric absorption of Earth's emitted IR radiation leads to the greenhouse effect.

• The photoelectric effect demonstrates the particle nature of light (photons).