Physics

Nuclear Physics Important Vocabulary

Photon

Chargeless bundles of energy that travel at the speed of light

(3 x 10^8 m/s)

How does radiation behave? High vs Low Frequencies?

High frequencies: behave like particles

Low frequencies: behave like waves.

How does energy and frequency differ with wavlength? Long vs Short

Longer wavelength: lower frequency and less energy (radio and heat)

Shorter wavelength: higher frequency and higher energy (gamma rays and x-rays)

What is matter?

Anything that occupies space and has a mass

What is an atom?

The smallest quantity of an element that retains all its chemical properties.

Proton (Symbol: p or p+)

Positively Charged, Massive, centrally located on atom

What is the numerical charge of a proton?

Charge: +1.6 x 10^-19 Coulombs

What is the mass of a proton ?

1.672^-24 grams

What is atomic number? what letter is it represented by?

The total number of protons found in the nucleaus of an atom. Represented as letter Z

Neutrons (Symbol: n)

Electrically neutral, massive centrally located atom

What is the charge of a neutron and mass ?

No Charge. Mass number 1.675 x 10^-24 grams

Electrons (Symbol: e or e-)

Negatively charged, extranuclear region of atom

What is the numerical charge of an electron?

-1.6 x 10^-19 Coulombs

What is the mass of an electron?

9.1 x 10^-28 grams

What holds and electron in orbit?

Binding energy + motion, and centrifual force keeps them from being attracted into positively charged nucleus

Nucleons

Protons + Neutrons

Which shell has the greatest binding energy?

The innermost shell, the K shell which has a binding energy of n=1

How to find the maximum number of electrons in each shell?

2n² example: K shell n=1 2(1²) = 2

What happens the further an electron is from the nucleus?

Nuclear atraction and binding energy decrease and electron become easier to move

How to find n values for shell?

Shells got K, L, M, N, O, P, Q. K shell is n=1 L shell is n=2 etc. add one to each shell

Molecules

A group of atoms that are chemically bonded together. Can be same or different element. Ex O2 molecule H20 molecule + compound

Compound

Different types of atoms/elements bonded together H20 molecule + compound

What is nuclear stability?

The nucleus ability to remain together without spontaneously changing. As atoms get bigger due to more protons, you have more positive charges repelling each other (proton-proton repulsion). So the nucleus needs extra neutrons to provide strong nuclear force to hold everything together.

Small Nucleus: N=P 1:1 (first 20 elements)

Large Nucleus: N>P 1.6:1 (elements after 20)

Stable Nucleus

Has appropriate balnace and configuration of protons and neutrons and sufficient nuclear binding

Unstable Nucleus

Unfavorable proton to neutron balance or configurationa and may undergo redioactive decay to become more stable

What are the 3 things nuclear stability depend on?

1. Number of protons
How many protons are in the nucleus?

2. Number of neutrons
Is there an appropriate number of neutrons for that number of protons?

3. Configuration/arrangement
How are those protons and neutrons arranged within the nucleus?

How to determne if an element is stable?

1. Is the N:P ratio reasonable?

Small Nucleus: N=P 1:1 (first 20 elements)

Large Nucleus: N>P 1.6:1 (elements above atomic number 20)
↓
2. Are there magic numbers?

If a nucleus has one of these numbers of protons OR neutrons it gets extra stability.

(2, 8, 20, 28, 50, 82, 126)
↓
3. Even-even nuclei tend to have extra stability.

Especially stable: Even protons + even neutrons

Less stable: Odd protons + odd neutrons

Isomeric Transition

The nucleus has the correct number of protons and neutrons, but it has TOO MUCH ENERGY. It gets rid of that extra energy by emitting a gamma ray. Number of Protons and Neutrons DOES NOT change only the energy state of the nucleus changes.

SAME nucleus, LOWER energy state, gamma emitted

Tc-99m → Tc-99 + γ

What is a metastable state?

The nucleus is relatvely stable but still has extra energy that it wants to get rid of. Written as m ex Tc-99m excited/metastable nuclear state

Decay Types

Decay	What changes?	What is emitted?
Isomeric transition	Energy state only	Gamma
Beta minus	Neutron → proton	β⁻ + antineutrino
Beta plus	Proton → neutron	β⁺ + neutrino
Alpha	Protons AND neutrons decrease	α particle

Mass energy relationship and equation

Mass and energy are two forms of the same thing and can be converted into one another. E=mc²

• E = energy

• m = rest mass

• c = speed of light

• Mass and energy are interchangeable

• Small amounts of mass can represent large amounts of energy

Mass difference → Energy

And that energy can appear as things like:

• Gamma radiation

• Kinetic energy of particles

• Other forms of radiation/energy

Mass Defect

The difference between the combined mass of the individual nucleons and the actual mass of the nucleus. The difference in mass was converted into binding energy

Example:

If you calculate the mass of the protons and neutrons separately, let's pretend you get:

4.10 amu

But the actual nucleus has a mass of:

4.00 amu

The difference is:

4.10 − 4.00 = 0.10 amu which is the mass defect

1 amu = 1/12 the mass of a carbon 12 atom

Nuclear Binding Energy

Energy needed to separate the nucleus into its individual nucleons.

What does higher energy mean?

Energy → ↑ penetrating ability → ↑ ability to transfer energy

Electron volt jule conversion

1 eV = 1.602 x 10^-19 J

eV = tiny unit of energy, commonly used for electrons, photons, and radiation

Joule = larger unit of energy

Nuclide

A specific type of atom defined by its number of protons and neutrons.

example:

• Tc-99 → 43 protons + 56 neutrons

• Tc-99m → 43 protons + 56 neutrons, but in a higher energy state

• Tc-98 → 43 protons + 55 neutrons

They are different nuclides because their nuclear configurations are different.

Atomic Mass Number (A)

Number of Protons + Number of Neutrons

Atomic Number (Z)

Number of protons

Isotopes

Atoms that have the SAME atomic number but DIFFERENT atomic mass

Ex.

Carbon-12

• 6 protons

• 6 neutrons

• Mass number = 12

Carbon-14

• 6 protons

• 8 neutrons

• Mass number = 14

They both have 6 protons, so they're both carbon.

Isobars

Atoms that have DIFFERENT atomic numbers but SAME atomic mass

Example:

Carbon-14

• 6 protons

• 8 neutrons

• Mass = 14

Nitrogen-14

• 7 protons

• 7 neutrons

• Mass = 14

They both have a mass number of 14, but different numbers of protons.

Isotones

Atoms that have DIFFERENT atomic number but the SAME number of neutrons

Example:

Carbon-14

• 6 protons

• 8 neutrons

Oxygen-16

• 8 protons

• 8 neutrons

They both have 8 neutrons, so they are isotones.

Isomers

Atoms that have the SAME atomic number and atomic mass but differ in energy

Tc-99m → Tc-99

What is the Radioactive Decay options when there is Excessive Nuclear Mass?

• Alpha Decay

• Fission

What is the Radioactive Decay options when theres an Appropriate number of nucleons, but to much energy?

• Gamma Emissions

• Internal Conversion

What is the radioactive decay options when there is an Unstable Neutron to Proton Ratio?

• Too many neutrons

  • Beta Decay

• Too many Protons

  • Beta Plus/Positron Decay

  • Electron Capture

Excessive Nuclear Mass: Alpha Decay

Nucleus ejects alpha particle making the nucleus smaller and lighter

Alpha = helium nucleus = 2 protons + 2 neutrons

Ejects 4 total nucleons above

Example:

U-238 → Th-234 + α

Excessive Nuclear Mass: Fission

Nucleus splits into two smaller nuclei

BIG nucleus → smaller nucleus + smaller nucleus + energy

Excessive Energy: Gamma Emission

Nucleus releases extra energy as a gamma photon.

Tc-99m → Tc-99 + γ

Atomic mass and number stay the same

Excessive Energy: Internal Conversion

Nucleus transfers its energy to an orbital electron causing it to leave (ejected electron called a conversion electron) This ejection leaves an empty space in the inner electron shell. An outer-shell electron drops down to fill the inner-shell vacancy, releasing energy. The atom releases this transition energy via one of two competing paths:

• Characteristic X-ray: The energy is emitted as a photon.

• Auger Electron: The energy is transferred to another outer electron, ejecting it from the atom.

Only energy state is changing to become more stable

Atomic mass and number stay the same

Characteristic X ray

Inner-shell electron removed → Causing Inner-shell vacancy → Outer-shell electron falls into vacancy → Energy difference is released as a Characteristic X-ray emitted

Auger Electrons

Inner shell electron removed by incidnet photon or charged particle→ Causing Inner-shell vacancy (photoelectron)→ Outer-shell electron falls into vacancy → Energy is transferred to another orbital electron → Orbital electron is ejected (augar electron) → Two electron vacancies remain (Vacancy 1: electron that left to fill K shell

Vacancy 2: ejected augar electron)→ additional characteristic xray produced or secondary Auger electron may be produced

Unstable N-P Ratio: Beta Minus Decay

Too Many Neutrons in the nucleus so it turns a neutron into a proton.

neutron → proton + electron + antineutrino

The electron that is produced is the beta particle.

Element change occurs due to transmutation

Atomic number Increases by 1.

Unstable N-P Ratio: Beta Plus Decay/Positron Decay

Too many protons in the nucleus so it turns a proton into a neutron

proton → neutron + positron + neutrino

Positron is the positive counterpart of an electron

Element change occurs due to Transmutation

Atomic number decreases by 1

Electron Capture

Also turns a proton into a neutron but instead of producing a positron, the nucleus captures an electron, usually from K or L shell.

proton + electron → neutron + neutrino

Element change occurs due to transmutation

Atom is left ionized with a vacancy

Atomic number deceases by 1

Excitation

Electron gets excited and jumps up, but doesn't leave. Electron raises to higher energy state

Normal electron → Absorbs energy → Electron moves to a higher energy level → Electron is still part of the atom → Eventually returns to a lower energy level

Ionization

Electron gets enough energy to leave the atom, creating ion pairs

Radiation interacts with the electron → Electron absorbs energy → energy > electrons binding energy → electron is completely removed → ion is created

What can charged particles interact with? (Alpha particles (α) → +2 charge, Electrons (β⁻) → −1 charge, Positrons (β⁺) → +1 charge)

Electrons of atoms

Charged particle → interacts with electron → excitation or ionization

Nucleus

Because the nucleus has a positive charge, it can attract or repel the incoming particle depending on its charge. causes charged particle to change dirrection or lose energy

What determines how far the particle travels?

Kinetic Energy of the particle

More kinetic energy → particle can travel further (greater trange in motion)

Less kinetic energy → particle stops sooner

Properties of the material

Density

Higher density = more atoms packed into a given space

More atoms to interact with → particle loses energy faster → shorter range.

High density → more interactions → shorter distance

Atomic number (Z) = number of protons

Higher Z = Stronger interactions with charged particles

Mass number (A) = protons + neutrons

Why does an alpha particle have very high specific ionization?

Alpha = BIG charge + HEAVY + SLOW → LOTS of interactions → many ion pairs in short distance + HIGH ionization + HIGH LET.

heavy mostly straight path

slower alpha greater stopping power

Bragg Peak

The point near the end of a charged particle's range where it deposits a very large amount of energy (The Most) in a short distance.

Start of path
→ relatively lower energy deposition

As it slows down
→ energy deposition increases

Near the end of its range
→ 💥 BRAGG PEAK

Then:
→ particle loses essentially all of its energy and stops.

How is Bragg peak useful for partical therapy?

Radiation can be designed to deposit a large amount of energy at a specific depth in the body. spicifically placing the Bragg peak within the tumor, concentrating dose there while reducing the dose beyond the target.

Why does an beta particle have very low specific ionization?

Beta = SMALL mass + LIGHT + FAST → FEWER interactions → LOW ionization + longer range + LOW LET.

Bremsstrahlung

beta particle slows/deflects near nucleus → loses energy → X-ray photon produced.

Photon Inteactions: Rayleigh (Coherent Scatter)

The photon interacts with the entire atom but does NOT transfer enough energy to ionize it.Causes photon to change direction.

Rayleigh = whole atom interaction → no ionization → photon changes direction → essentially no energy loss.

Photon Inteactions: Photoelectric Effect

Photon gives ALL of its energy to an inner-shell electron, causing that electron to be ejected from the atom. Results in full absorption of photon

Photon → inner electron → photoelectron + vacancy → characteristic X-ray/Auger

Photon Inteactions: Pair Production

When a high-energy photon passes near the nucleus and is converted into an electron + positron pair. Photon must have atleast 1.022 Mev becuase an electron and positron both have a resting mass energy of 0.511 Mev. Results in full absorption of photon.

Pair production = photon ≥ 1.022 MeV → electron + positron.

Positron eventually annihilates with electron → 2 × 0.511 MeV photons.

Photon Inteactions: Compton Scatter

A photon hits an outer shell electron, gives it some of its enery and then continues in a different dirrection with the remaing energy. Cause partial absorption

Photon energy ↑ → Compton interaction probability ↓

Photon energy ↓ → Compton interaction probability ↑

Photo Attenuation

The reduction in the intensity of a photon beam as it travels through matter.

photons enter material → some interact/get absorbed or scattered → fewer photons make it out.

I=I0​e^−μx

Where:

• I = intensity after traveling through the material

• I₀ = original intensity

• μ = linear attenuation coefficient

• x = thickness/distance traveled through the material

• e = mathematical constant (~2.718)

Photon Attenuation Continued:

Half Value Layer

the thickness of material needed to reduce photon intensity to 50% of its original value.

Example:

Start with 100%

1 HVL → 50%

2 HVLs → 25%

3 HVLs → 12.5%

So every additional HVL cuts the remaining intensity in half.

μ ↑ → HVL ↓

μ ↓ → HVL ↑

A material with a high attenuation coefficient doesn't need to be as thick to cut the beam in half.

What are the three processes for the release of energy?

Three distinct processes can occur in the electron structure of the atom to release energy

● Bremsstrahlung Radiation

● Characteristic x-rays

● Auger electrons