1. Radioactivity Flashcards
What is the typical order of nuclear sizes?
Nuclear time scales have a _____ range.
Vast
What are nuclear energies typically measured in?
MeV
State the conversion between eV and J
What are nuclear masses typically measured in?
Unified atomic mass units (u)
State the conversion between u and MeV/c²
Convert the following constant to MeV fm
Convert the following constant to MeV fm
A nucleus consists of _______ (positively charged) and ________ (neutral).
Protons
Neutrons
Isotopes have different numbers of ________.
Neutrons
What is the mass number, A?
Number of protons + number of neutrons
What is the atomic number, Z?
Number of protons
What is alpha decay?
Decay in which a helium nucleus (alpha particle) containing 2 protons and 2 neutrons is emitted.
State 5 properties of an alpha particle (He nucleus)
- Strongly ionising
- Heavy
- Large charge
- Very damaging inside the body
- Stopped by skin/paper
What is beta decay?
Decay in which a high energy electron (or positron) and an anti-neutrino (or neutrino) are emitted from the nucleus.
In the case of an electron, a neutron in the parent nucleus decays into a proton, an electron, and an anti-neutrino. The proton remains in the nucleus.
State 4 properties of a beta particle (electron/positron)
- Less ionising than alpha
- Much faster speed
- Lower charge
- Stopped by a sheet of aluminium
What is gamma decay?
Decay in which a nucleus de-excites and emits a gamma ray photon (like electron transitions leading to photons in atoms).
State 4 properties of a gamma ray photon
- Very energetic
- Interacts weakly with matter
- Uncharged
- Stopped by a thick sheet of lead
Why do larger nuclei have more neutrons?
Because neutrons have no repulsive forces so this is how they keep themselves together.
Describe the graph of the number of neutrons, N, against the number of protons, Z, in nuclides
Stability valley = line of stable nuclides
Stability valley moves away from N=Z for large Z.
Alpha emitters are heavy nuclides.
Beta- emitters are above the line of stability.
Beta+ emitters are below the line of stability.
There are no stable nuclei with an atomic number, Z, above __.
83
Give the equation for the rate of decay
dN/dt = rate of decay
N = number of atoms which can decay
λ = decay constant
State the decay law
N = number of atoms which can decay
N_0 = initial number of atoms
λ = decay constant
t = time
Describe the shape of a linear decay plot
Define half-life
The time taken for half the atoms in a sample to decay.
Give the equation for half-life
N_0 = initial number of atoms
λ = decay constant
t_1/2 = half-life
Define activity
The rate at which decays occur.
Give the equation for activity
A = activity
λ = decay constant
N = number of atoms which can decay
What are the SI units for activity?
The Becquerel, Bq
1 Bq = 1 decay/second
How does carbon dating work?
Cosmic radiation converts N-14 in the atmosphere to C-14 (with a half-life of 5730 years). It combines with oxygen to form carbon dioxide which plants take up. When the plant dies, the decay of C-14 can be used to determine the age of the artefact.
How do decay sequences impact the rate of decay/production of materials?
In a chain of nuclide production, the rate of decay of an atom determines how quickly it is depleted and the rate of decay of the atom ahead of it in the sequence determines how quickly it is produced.
The first atom in the chain only decays.
The final atom in the chain is only produced.
Describe the differential equations for the decay sequence of 3 nuclei: A, B, and C
State the decay equation for alpha decay
Alpha decay results in a nuclei of a _________ ___________ as Z has changed.
Different element
How much energy is released by one alpha decay?
~5 MeV
How is the energy release due to a decay calculated?
By comparing the difference in mass between reactants and products.
Give the equation for the energy release due to a decay
Q = energy release
M_reactants = nuclear mass of reactants
M_products = nuclear mass of products
c = speed of light
Energy release must be ________ for decay to be possible.
Positive
State the conversion between nuclear mass and atomic mass
M_N = nuclear mass
M_A = atomic mass
Z = atomic number
m_e = electron mass
What is the Geiger-Nuttall rule?
The relationship between the half-life and energy release for alpha decay, explained by quantum tunneling. It assumes that the alpha particle is pre-formed inside the nucleus and moves in the spherical potential well.
Describe the shape of the potential for alpha decay
r = distance between the alpha particle and the daughter nucleus
Q = alpha particle energy
Region 1 (r < a): the alpha particle is classically confined to this region
Region 2 (a < r < b): the barrier region where the potential is greater than Q
Region (b < r): classically permitted region
Give the equation for the Coulomb potential energy between two nuclei
V = potential energy
Q = charge
ε0 = vacuum permittivity
r = separation distance
Z = atomic number
e = electron charge
State the time-independent Schrodinger equation
What are the solutions to the time-independent Schrodinger equation when E > V_c?
Oscillatory solutions
What are the solutions to the time-independent Schrodinger equation when E < V_c?
Exponential solutions
What is the coulomb potential for alpha decay approximated as?
A step potential
What is the transmission probability?
The probability of a particle tunnelling through a barrier.
The decay constant is the product of the transmission _________ and the _________ at which a particle of velocity, v, hits the barrier
Probability
Frequency
λ = fP
State the decay equation for beta- decay
State the decay equation for beta+ decay
State the decay equation for orbital electron capture
A positron is the ____________ of an electron.
Anti-particle
An anti-particle has the same ____ but equal and opposite ______.
Mass
Charge
Is beta decay a strong or weak interaction?
Weak interaction
What does the electron neutrino/electron anti-neutrino add to beta decay?
They conserve lepton numbers
Where does beta decay occur?
Inside the nucleus
Give the nuclear equation for beta- decay
Give the nuclear equation for beta+ decay
Give the nuclear equation for orbital electron capture
Why do electrons/positrons have a range of energies in beta decay?
Because the neutrinos also carry some of the energy released.
What is the other name for orbital electron capture?
Inverse beta decay
Where does orbital electron capture occur?
In proton-rich nuclei
Briefly describe the process of orbital electron capture
The nucleus captures an orbiting inner electron so the outer shell electron replaces this, causing one of the protons to be converted into a neutron and a photon to be emitted.
