SRS Unit 1.2 ATAR Physics - Ionising Radiation & Nuclear Reactionc

WIP - til Decay Series

Bohr’s Atomic Model

• The nuclear model where protons and neutrons are contained in a nucleus and electrons are orbiting it in shells

Proton

Charge:

• + 1.602×10⁻¹⁹ 𝐶

• +1 𝑒

Location:

• Nucleus

Mass:

• 1.6726 ×10⁻²⁷ 𝑘𝑔

• 1.007276 𝑎𝑚𝑢

Neutron

Charge:

• 0C

• 0 e

Location:

• Nucleus

Mass:

• 1.6749 ×10⁻²⁷ 𝑘𝑔

• 1.008665 𝑎𝑚𝑢

Electron

Charge:

• −1.602×10−19 𝐶

• −1 𝑒

Location:

• Outside nucleus

Mass:

• 9.1094 ×10−31 𝑘𝑔

• 0.000549 𝑎𝑚𝑢

Nucleons

• A collective term for protons and neutrons found in the nucleus.

Nuclides

• The range of atomic nuclei associated with a particular atom, which is defined by the atomic number and the various isotopes of that atom as identified by the mass number.

Isotopes

• Two or more types of atoms that have the same atomic number and position in the periodic table but different number of neutrons.

Atomic Number (Z)

• The number of protons that defines the element

Atomic Mass Number

• The total mass of protons (Z) and neutrons (N) of an atom in Atomic Mass Units (amu)

Neutron Number (N)

• Atomic Mass Number (rounded) - Atomic Number

Electrostatic Force (EF)

• An attractive and repulsive force between particles caused by their electric charges

• Like charges repel, opposites attract

• Also referred to as Coulomb’s force

Strong Nuclear Force (SNF)

• The “glue” holding protons and electrons together in the nucleus together

• Exists within quarks, which form protons and neutrons

SNF > EF

• If the Strong Nuclear Force is stronger than the Electrostatic Force, nuclei will be stable

• However, if this delicate balance is interfered with, nuclei will become unstable and decay

Stable nuclide

• A nuclide that will never (or close to never) decay

Unstable nuclide

• A nuclide that will decay

• It will keep decaying until the balance of protons and neutrons is stable

Radioactive decay

• The process by which an unstable atomic nucleus loses energy by radiation and the emission of subatomic particles

Radioisotope

• A radioactive isotope

Beta Positive/Plus Decay (β⁺)

• Occurs when the nucleus has too many protons

• Therefore the Electrostatic Force overpowers the Strong Nuclear Force

• The proton decays into a neutron to release excess EF and stabilise the nucleus

• Due to this, the nucleus emits a positron (anti-electron) known as a Beta Positive Particle along with a neutrino

Beta Negative/Minus Decay (β^-)

• Occurs when the nucleus has too many neutrons

• Therefore the Strong Nuclear Force overpowers the Electrostatic Force

• The neutron decays into a proton to gain additional EF and stabilise the nucleus

• Due to this, the nucleus emits an electron known as a Beta Negative Particle along with an anti-neutrino

Alpha Decay (α)

• Occurs when the nucleus is too heavy to naturally be stable (every element above Bismuth)

• The nucleus releases two protons and two neutrons at the same time - an Alpha Particle

• An Alpha Particle is the same as a Helium-4 nucleus

Gamma Decay (γ)

• Occurs when nucleus has excess energy but the correct ratio of protons to neutrons

• The nucleus emits energy Gamma Radiation - gamma waves

Segre Plot

• A graph/visualisation of the stability in nuclei showing all known isotopes of each element and their radioactivity/stability

• y axis is number of neutrons (N), x axis is number of protons (Z)

• Beyond element 82 (Lead) there are no more stable isotopes

• The number of radioactive isotopes for each element exceeds the number of stable ones

Penetrating ability

• How well radiation can pierce through matter

Ionisation ability

• How well radiation can ionise atoms

• Ionisation is the process by which an atom loses or gains an electron, thus resulting in a net positive or negative charge

Alpha Particle (α)

Mass:

• 4.001 506 u

Charge:

• +2e

Penetrating Ability:

• Low

Ionisation Ability:

• High

Beta Positive/Plus Particle (positron) (β⁺)

Mass:

• 0.000549 u

Charge:

• +1e

Penetrating Ability:

• Medium

Ionisation Ability:

• Medium

Beta Negative/Minus Particle (electron) (β^-)

Mass:

• 0.000549 u

Charge:

• -1e

Penetrating Ability:

• Medium

Ionisation Ability:

• Medium

Gamma Particle (γ)

• High energy light/electromagnetic wave

Mass:

• 0 u

Charge:

• 0e

Penetrating Ability:

• High

Ionisation Ability:

• Low

• Can only ionise atoms if it strikes an electron directly and knocks it loose

Nuclear Equation formats

• LHS → RHS

• Reactants → Products

• Parent Nucleus → Daughter Nucleus + decay particles + energy

Alpha Decay Equation

PN → DN + α + energy

Beta Positive/Plus Decay Equation

PN → DN + β⁺ + v_e + energy

Beta Negative/Minus Decay Equation

PN → DN + β^- + v_e + energy

Gamma Decay Equation

PN* → PN + γ + energy

Decay Series

• A graph visualising the different decays an isotope undergoes to achieve stability

• Each isotope has their own “signature” sequence

• y-axis: mass number

• x-axis: atomic number

• Diagonal line → alpha decay

• Horizontal line → beta decay

• Series stops at Lead-206

Half-life (t_1/2)

• The time required for a substance to decay to half its initial size

• Graphically, its trend line is mathematical exponential decay

Equation for half-life

N = N₀ × (1/2)ⁿ

• N = Final amount of substance / no. of remaining atoms

• N₀ = Initial amount of substance / no. of remaining atoms

• n is the number of half-lives that have elapsed

• n = (time elapsed)/(time of half-life) = t/t_1/2

Equation for number of half-lives elapsed

n = t/t_1/2

• n = number of half-lives elapsed

• t = time elapsed

• t_1/2 = time of half-life

Atomic Mass Unit

• Defined as 1/12 of the mass of a Carbon-12 nucleus

• 1u = 1.66054 × 10^-27kg

Electron volts

• The preferred units of Energy on the atomic scale

• Equal to the energy gained by an electron when passing a potential difference of 1 Volt

• 1eV = 1.602 × 10^-19J

• 1J = 6.242 × 10¹⁸eV

• 1 megaelectron volt is 1,000,000 eV

Equation for Mass-Energy Equivalence

E = mc²

• E = energy (J or eV)

• m = mass (kg or u)

• c = the speed of light (299 792 458 m/s)

• 1u = 931.6 MeV

Mass Defect

• Mass of nucleons together < mass of nucleons apart

• Mass defect (∆m) is usually measured in atomic mass units (u)

• ∆m = mass of nucleons − total mass of individual nucleons

• This mass is converted into binding energy

Binding Energy

• The mass of individual nucleons that is converted in energy to keep them together

• Binding Energy = ∆m × 931.6

Calculating energy released from Alpha Decay

Calculating energy released from Beta Plus Decay

• The value of 0.0010972 is twice the mass of an electron and is due to the mass of the positron released by the parent nucleus and the one fewer electron in the daughter isotope

Calculating energy released from Beta Minus Decay

Binding Energy Per Nucleon

• A measurement of stability in the nucleus

• The higher the value, the more stable the nucleus will be