Electromagnetic Radiation Basics

Electromagnetic (EM) Radiation

• EM radiation includes visible light, radio waves, and X-rays
• It has no mass and isn't affected by electric or magnetic fields
• Travels at a constant speed in a given medium
• Travels in straight lines, but its trajectory can be altered by interacting with matter
• Absorption reduces radiation
• Scattering changes radiation's trajectory

EM Wave Characteristics

• EM waves are characterized by amplitude, wavelength (λ), frequency (f), and period (T)
• Speed (v or c), wavelength, and frequency are related by λ=vT or v = λf
• Wavelengths are typically measured in nanometers (10⁻⁹ m)
• Frequencies are expressed in hertz (Hz) (1 Hz = 1 cycle/second =1 sec⁻¹)
• For EM waves, v is the speed of light

Sinusoidal EM Wave

• EM waves oscillate in electric and magnetic fields that are perpendicular to each other and to the direction of wave travel.
• Wavelength (λ) is the distance between corresponding points on two consecutive waves.
• Amplitude is the maximum displacement from the zero position along the direction of oscillation.
• The electric and magnetic fields are 90° out of phase.

Sinusoidal Wave Function

• The sinusoidal wave function can be written as y(x, t) = A sin(kx − ωt + φ), where:
  • A is the amplitude
  • k is the wave number (2π/λ)
  • ω is the angular frequency (2πf)
  • φ is the phase constant
• It can also be expressed as a cosine function.
• In 3D, x is replaced by the position vector (x, y, z).

The Spectrum of the EM Waves

• Includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays
• Types of waves often overlap
• Distinguished by frequency or wavelength.
• Specific wavelengths correlate to specific color/radiation types
• There is a relationship between wavelength, frequency, and energy.
• Different frequencies/wavelengths are used for different applications

Notes on the EM Spectrum

• Radio waves have wavelengths greater than 10⁴ m to ~0.1 m. Used in radio & TV
• Microwaves have wavelengths from ~0.3 m to 10⁻⁴ m. Useful for radar and ovens
• Infrared wavelengths are ~10⁻³ m to 7 x 10⁻⁷ m. Produced by heat, readily absorbed by materials
• Visible light is detected by the human eye. Most sensitive to ~ 5.5 x 10⁻⁷ m (yellow-green)
• Ultraviolet light covers ~ 4 × 10⁻⁷ m to 6 × 10⁻¹⁰ m. Important radiation source from the sun and absorbed in the stratosphere by ozone
• X-rays have wavelengths ~10⁻⁸ m to 10⁻¹² m. Produced by high-energy electrons, used in medicine (diagnostic / therapeutic).
• Gamma rays have wavelengths ~10⁻¹⁰ m to 10⁻¹⁴ m. Emitted by radioactive nuclei, highly penetrating, and damaging. Used in medicine.

Particulate Radiation

• Protons: Found in nuclei of all atoms, have a single positive charge
• Electrons: Exist in atomic orbits, emitted from some radioactive atoms (beta particles ⁻)
• Positrons: Positively charged electrons (β⁺), emitted by some nuclei during radioactive decay
• Neutrons: Uncharged nuclear particles, released by nuclear fission and used for radionuclide production

Mass Energy Equivalence

• Einstein's theory of relativity: Mass and energy are interchangeable
• E = mc² (E representing energy, m representing mass, and c representing the speed of light)

Fundamental Properties of Particulate Radiation

• Table including particles (proton, electron, positron, neutron), their symbols, relative charge in multiples of the electron charge, and approximate energy in MeV.

Structure of the Atom

• Smallest division of an element with maintained chemical identity
• Composed of a dense, positively charged nucleus containing protons and neutrons, with a cloud of negatively charged electrons outside the nucleus.
• Electrically neutral in its nonionized state

Bohr Model of the Atom

• Electrons orbit a dense, positively charged nucleus at fixed distances
• Each electron occupies a discrete energy state in a given electron shell
• Shells are assigned letters (K, L, M, N...) and quantum numbers (1, 2, 3, 4...)
• Each shell can hold a maximum of (2n²) electrons, with n being the quantum number

Electron Shells

• Diagram showing electron energy levels (K, L, M, N...) around the nucleus
• Quantum number, maximum number of electron capacity

Binding Energy of Electron

• Energy required to remove an electron completely from an atom
• Conventionally negative and increases with closeness to the nucleus
• Binding energy increases with the number of protons in the nucleus (atomic number)

Atomic Nucleus

• Composed of protons and neutrons (collectively, nucleons)
• The number of protons is the atomic number (Z)
• The total number of protons and neutrons is the mass number (A)
• Notation for an atom is ᴬₓ (with chemical symbol X)

Nuclear Energy Levels

• Nuclei have energy levels analogous to electron shells
• Lowest energy state is called the ground state
• Nuclei with higher energy are in the excited state
• Excited states that last longer than 10−¹² seconds are metastable, also called isomeric states, denoted by the letter m after the mass number (e.g., Tc-99m).

Nuclear Families

• Table with categories (isotopes, isobars, isotones, and isomers) showing nuclides with similar properties
• Examples for each family

Nuclear Stability

• Only specific neutron-proton combinations are stable
• Heavy elements require a higher neutron-to-proton ratio to offset electrostatic forces between protons
• Nuclei with odd numbers of both neutrons and protons tend to be unstable

Nuclear Stability (Diagram)

• Graph showing the relationship between neutron and proton numbers in stable nuclei against unstable nuclei

Nuclear Structure

• The nucleus of an atom consists of nucleons (protons and neutrons)
• Atomic number (Z) represents the number of protons
• Nucleon number (A) represents the total number of protons and neutrons
• Notation for an atom is often expressed by the chemical symbol and nucleon number (A)
• Atoms of the same element can have different numbers of neutrons. These are called isotopes.

Nuclear Structure (Radius)

• Nuclei are clustered together to form a spherical region
• The radius of the nucleus depends on the atomic mass A by a formula (r ≈ (1.2×10⁻¹⁵ m) A^(1/3))
• Isotopes: Nuclei with the same number of protons (Z) but different mass numbers (A)

Ionizing vs. Nonionizing Radiation

• EM radiation with higher frequency than near-UV removes electrons, producing ionized atoms/molecules
• This is called ionizing radiation
• Lower-frequency radiation is non-ionizing (e.g., visible light)

Additional Slides (Self Study)

Radioactivity

• Unstable nuclei undergo radioactive decay to achieve stability by emitting different particles or transforming nucleons.
• Unstable nuclei change their number of protons and neutrons
• The process is accompanied by the emission of energy.
• The emission can be particulate or electromagnetic.

Alpha Decay

• An alpha particle is a helium nucleus (²⁴He)
• It has a charge of +2e and a nucleon number of 4
• Alpha decay involves the emission of an alpha particle and the release of energy (kinetic energy) shared between the alpha particle and recoiling daughter nucleus

Alpha Decay (calculations)

• Mass conservation is imperative in alpha decay; the total initial mass before decay equals the total mass after decay. There is slight mass difference that represents released binding energy

Beta Decay

• A beta particle is an electron (⁻₁e) with a negative charge (-e)
• Beta decay transforms a neutron into a proton (or vice-versa) which means there is a change in the number of protons in the nucleus
• Beta decay is accompanied by the emission of an antineutrino

Neutrino and Antineutrino

• Neutrinos are neutral subatomic particles with small mass and half-integral spin
• Rarely interact with normal matter
• Created in radioactive or nuclear reactions, as well as when cosmic rays hit atoms.
• Antineutrinos are the antiparticles of neutrinos
• Emitted during beta decay.

Beta+ Decay

• Beta particle is a positron (+₁e) with a positive charge (+e)
• Beta plus decay converts a proton in a nucleus to a neutron
• Accompanied by emission of a neutrino

Beta+ Decay (Medical Applications)

• Positron emitters are used in PET scans for functional imaging
• A positron emitter radionuclide is injected into an area and accumulates in a tissue
• Positrons undergo annihilation with electrons, resulting in two gamma photons emitted at opposite directions which are detected for diagnostic purposes.

Electron Capture

• An orbital electron (from inner shells, K or L) is captured by a proton in the nucleus
• This process forms a neutron
• Accompanied by emission of a neutrino

Gamma Decay

• EM radiation emitted as the nucleus goes from one excited state to a lower energy state/ground state
• Also produced if the nucleus is in a metastable excited state (isomeric state), the decay is called an Isomeric Transition
• Gamma decay involves no change in the number of protons or neutrons in the nucleus

Internal Conversion Electrons

• Alternative to gamma emission, internal conversion electrons are emitted when orbital electrons absorb the energy from the nucleus transitioning to a lower energy state, causing the ejection of an electron from the atom