chap 3

How can we predict the products in a nuclear reaction"?

• conservation “rules”

  • properties of a system that do not change are said to be conserved

• conserved properties;

  • mass (in nucleus, P+N)

  • energy

Forms of energy

• potential energy

  • stored energy

  • ex. radioactive decay, held by mass inside nucleus

• kinetic energy

  • mass of particles

• radiation energy

  • light, gamma rays (electromagnetic energy)

• excitation energy

• thermal energy

  • heat

Potential energy

• the stored ability to do work

• ex.

  • compressed spring

  • 2 magnets held apart

  • raised pendulum or swing

  • mass (inside nucleus, P+N)

Kinetic energy

• energy of motion

• ex

  • a child swinging

  • car in motion

  • thrown football

  • decay products/particles carry __ __ away from the nucleus

Radioactive decay

• spontaneous transformation of 1 isotope into another through the emission of 1 (or more) particles AND release of energy

Where des the energy in radioactive decay come from?

• the mass of the particles

• for energy to be released, mass must be converted to energy

  • potential → kinetic

  • energy can also be released by photons, or electromagnetic radiation

Change in __ is the energy released

• mass

  • bc thats where its stored

Q value

• energy released by a nuclear reaction

• also called

  • transition energy

  • reaction energy

  • decay energy

• Q > 0 means energy is released

• Q < 0 means energy is needed

• change in mass = (mass of reactants) - (mass of products)

• Q = [(mass of parent) - (mass of daughter + mass of emissions*)] x c²

• Q = [MP - (Md + Me*)] x c²

• Q = [MP - Md - Me*] x c²

• the answer for _ in decay events will always be positive

Electron Volts (eV)

• 1 eV = kinetic energy of an electron accelerated through a 1V potential

Converting mass to energy

• E = mc²

• 1 amu = 931.5 MeV/c²

  • so if we convert 1 amu to energy, we get 931.5 MeV

  • its a conversion factor, basically like saying 1 lb = 2.2 kg

How to calculate Q for a nuclear reaction

1. start w the complete reaction

2. calculate mass of reacting particles (parents)

3. calculate mass of products (daughter, *)

4. determine the difference of step 2 - step 3, then multiply by c²

5. convert to energy (931.5 MeV/c² per u)

C²

• speed of light squared

• mass unit to energy unit

Ways to help predict the outcome of a decay event

1. atomic notation

2. chart of nuclides

3. nuclear equations & conservation/balancing

4. energy calculations/estimations

5. decay schemes

6. decay modes

Decay modes

• The specific way an unstable atomic nucleus (radionuclide) or subatomic particle spontaneously transforms into a more stable state, emitting particles and/or energy in the process

• types

  • alpha decay

  • beta decay (isobaric transitions, 3 forms)

    • same mass, diff atomic #

  • gamma decay (isomeric transitions, 2 forms)

    • same atoms, arranged differently

Decay Schematic

• graphical representation of decay scheme

• common conventions

• set up is on a standard graph

  • Z is represented on the X-axis

    • moving RIGHT → INCREASES Z protons

  • instead of N, a decay scheme displays energy

  • energy is represented on the Y-axis

    • moving DOWN the scheme RELEASES (or decreases) energy

• at least in this course, __ __ will always point down

  
  

Notation

• horizontal lines = energy state of nucleus

• diagonal lines = particle emission (a, B)

• vertical lines = gamma emissions (y)

Horizontal lines =

• energy states of nucleus

Diagonal lines

• particle emissions (a, B)

Vertical lines

• gamma emissions (y)

What specific info is on a decay scheme?

• possible decay modes

  • “what” and “how many” decay reactions are possible?

• energy info

  • energy of the emitted particles

    • alpha energy or maximum beta energy

    • gamma energy

  • Q value

    • energy difference between ground states

• branching ratio

  • probability (%) of decay mode

  • mode 1, mode 2, mode 3

Branching ratio

• probability (%) of a given decay mode

• mode 1, mode 2, mode 3

Gamma decay

• isomeric transitions (same atoms, arranged differently)

• __ __

• Internal conversion - IC

Other decay modes

• spontaneous fission

• neutron emission

Beta-plus

• Z-1 (loss of proton)

• + release of energy

Alpha decay

• spontaneous emission of an alpha particle + release of energy

• 4^He²+ ion (+2 charge, no electrons)

  • 2 protons, 2 neutrons

• in the daughter…

  • A-4

  • Z-2 (loss of 2 protons)

  • N-2

• only observed for heavy nuclei

  • lead (Z=82) & higher

  • bc its the fastest way to loose mass

• typical energy release (Q) = 3-7 Mev

  • can also produce a gamma ray

• parent decays by producing an _ particle

• is mono-energetic

  • for a given transition, the __ will ALWAYS have the same energy

Alpha decay Diagrammatic Repressentation

1. start heavy nucleus

2. radioactively decaying by emission of 2 protons + 2 neutrons

balancing is

“conservation of nucleons”

How is the energy divided up? (alpha decay)

• gamma energy first

  • subtract any gamma emissions from Q

• remainder is kinetic energy

  • alpha gets approx 98%

  • daughter gets the remainder

    • recoil energy

• alpha decay is mono-energetic

  • for a given transition, the alpha will ALWAYS have the same energy

Alpha decay is __-energetic

• mono

• for a given transition, the alpha will ALWAYS have the same energy

  • every alpha particle emitted from a specific radioactive decay process has the exact same amount of kinetic energy

  • only the alpha particle carries the energy from the decay event

• chart displays the energy spectrum for alpha decay

  • for a single release of energy of a alpha decay

Conservation of momentum (alpha decay)

• before the decay - nothing is moving

• after the decay - movement

• movement is energy

  • and it must be conserved

    • alpha & daughter must have same momentum

    • opposite directions

Beta decay

• isobaric transitions

  • isotopes w same atomic mass, diff atomic # & diff neutrons

• Modes

  • • Beta Minus Decay (β-) – called Beta Decay or “Negatron” Emission/decay

    • Beta Plus Decay (β+) – called Beta Plus Decay or “Positron” Emission/decay

    • Electron Capture - EC

• can occur w light or heavy isotopes

  • neutron-RICH isotopes: B-decay

  • neutron-POOR isotopes: B+ or ec

Neutron rich isotopes will undergo

• B - decay

Neutron poor isotopes will undergo

• B + decay or ec

Beta (-) Decay / Negatron emission

• emission of an beta particle (negatron) & anti-neutrino

  • anti-neutrino helps balance momentum of equation

• the emitted electron (e-): identical to the atomic electron

  • except it is emitted from the nucleus

• only observed for neutron-RICH isotopes

• typical energy range: 0.1 to 2 MeV

  • can also produce a gamma ray

• in the daughter…

  • A = unchanged (isobaric)

  • Z + 1 (move up)

  • N - 1 (move left)

• neutron spontaneously transforms into a proton

  • gains proton bc if one neutron is loss, then a proton needs to be added to maintain mass

negatron

• negative electron

• compensates for the change in charge

  • when a neutron → proton

anti-neutrino

• small mass

• electrically neutral and has a net charge of 0

• helps balance momentum of equation

Beta (-) Decay / Negatron emission Diagrammatic representation

1. start w neutron rich nucleus, neutron spontaneously transforms to proton

2a. emission of anti-neutrino

2. emission of negatron (negative electron)

How is the energy divided up? (beta - decay)

• gamma energy first

  • subtract any gamma emissions from Q

• remainder is kinetic energy

  • beta & anti-neutrino SHARE the emission energy

  • daughter gets the remainder

• so the energy from this decay is shared by

  • the beta (negatron), the antineutrino, & the daughter

• Beta decay is POLY energetic

Beta - decay is __ energetic

• poly

• chart displays the energy spectrum for beta - decay

  • for a single release of energy of a beta - decay

• maximum beta energy = Q

• average beta energy = 1/3 Q

Conservation of momentum (beta - decay)

• similar to alpha decay, except we have 3 particles now

• electron & anti neutrino are much lighter than the recoil

  • recall, mass of an electron is abt 2000X smaller than a proton

• conservation of energy & momentum

  • almost all (>99.9%) of energy goes to small particles

  • divided randomly between e- & anti-neutrio

    • not evenly, average beta energy is 1/3 Q

Nuclides near the top right part of the Chart of Nuclides are typically

• decay by alpha decay

• unstable

• heavy nuclei

when calculating q for beta - decay why is electron mass not accounted for

Standard mass tables list the masses of neutral atoms (nuclei plus their surrounding electrons), not bare nuclei. In \(\beta ^{-}\) decay, the parent atom turns into a daughter atom with one extra proton, meaning the daughter atom naturally needs one more orbital electron to remain neutral. The mass difference between the neutral parent atom and the neutral daughter atom automatically accounts for the newly created beta particle (electron)

the electron's mass naturally balances out on both sides of the equation because the daughter atom gains an extra orbital electron to match its new, higher atomic number

Nuclides to below and to the right of the Line of Stability are typically

• decay by negatron / B - decay

• light to heavy nuclei

• unstable

what does m final represent in the equation for Q

• emission particles

• daughter nuclides