1. Radioactivity Flashcards by Hannah Emery

What is the typical order of nuclear sizes?

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Nuclear time scales have a _____ range.

Vast

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What are nuclear energies typically measured in?

MeV

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State the conversion between eV and J

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What are nuclear masses typically measured in?

Unified atomic mass units (u)

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State the conversion between u and MeV/c²

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Convert the following constant to MeV fm

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Convert the following constant to MeV fm

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A nucleus consists of _______ (positively charged) and ________ (neutral).

Protons
Neutrons

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Isotopes have different numbers of ________.

Neutrons

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What is the mass number, A?

Number of protons + number of neutrons

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What is the atomic number, Z?

Number of protons

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What is alpha decay?

Decay in which a helium nucleus (alpha particle) containing 2 protons and 2 neutrons is emitted.

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State 5 properties of an alpha particle (He nucleus)

Strongly ionising
Heavy
Large charge
Very damaging inside the body
Stopped by skin/paper

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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.

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State 4 properties of a beta particle (electron/positron)

Less ionising than alpha
Much faster speed
Lower charge
Stopped by a sheet of aluminium

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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).

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State 4 properties of a gamma ray photon

Very energetic
Interacts weakly with matter
Uncharged
Stopped by a thick sheet of lead

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Why do larger nuclei have more neutrons?

Because neutrons have no repulsive forces so this is how they keep themselves together.

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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.

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There are no stable nuclei with an atomic number, Z, above __.

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Give the equation for the rate of decay

dN/dt = rate of decay
N = number of atoms which can decay
λ = decay constant

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State the decay law

N = number of atoms which can decay
N_0 = initial number of atoms
λ = decay constant
t = time

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Describe the shape of a linear decay plot

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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.