Physics: Module 6 - NUCLEAR & PARTICLE PHYSICS

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why had they initially proposed that the electron must exist within a nucleus

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1

why had they initially proposed that the electron must exist within a nucleus

  • it was the only other fundamental particle we knew about

  • it had been observed in certain radioactive decays that electrons are emitted from the nucleus

    • huge conflicts with this and Heisenberg Uncertainty Principle

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strong nuclear force

  • acts over a very small distance (about 3fm/3x10^-15m)

  • independent of charge (acts on both protons and neutrons)

  • stronger than the electromagnetic force in the nucleus (but on by about 2 order)

  • can be repulsive and attractive (below 0.5fm = 0.5x10^-15m)

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<p>what does this graph show?</p>

what does this graph show?

  • resultant force on proton (e.g. the combines effect of electromagnetic and strong nuclear force)

  • electric force dominates at large separations

  • strong nuclear force dominates at small separations

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why must there be more neutrons than protons in a large nuclei?

  • outer protons become increasingly far apart

  • strong nuclear force becomes less dominant

    • need to increase as EM repulsion could cause them to fly apart

  • add more neutrons to increase strong nuclear force without increasing EM repulsion

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equation relating nuclear density to nuclear number

  • V is prop to m, therefore V is prop to R^3, so R^3 is prop to m

  • mass of nucleus is determined by m = AMp

    • A = nuclear number, Mp = mass of proton

    • note: mass of proton and neutron are the same

R^3 is prop. to AMp

R^3 = cAMp

  • c = constant

R = (CAMp)^1/3

R = (CMp)^1/3 * A^1/3

  • (CMp)^1/3 is pre calculated as r(o) = 1.2x10^-15

R = r(o) * A^1/3

  • where R = radius of nucleus, A = nucleus number

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matter and antimatter

  • every fundamental particle that exists has an anti-particle

  • these have the same rest mass but opposite charge

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what happens if a particle meets its anti-particle?

they will annihilate to produce a pair of high energy photons

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sub-atomic particles

  • what are the two main families of particles?

  • What are their characteristics?

Leptons:

  • fundamental particles

  • can’t be broken down further, not made up of different particles

Hadrons:

  • any particle made up of quarks which feels the strong force

  • has two groups:

    • baryons (heavy) and mesons (middle)

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Define the two groups of hadrons

Baryons:

Quarks can combine in triplets (all quarks or antiquarks) to form a Baryon

Mesons:

Quarks can also combine in quark - antiquark pairs to form a meson

  • note: anything that is a baryon has a baryon number of 1

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state the baryon number, strangeness, and lepton number of fundamental particles (hadron only)

up (u)

  • B# = 1/3

  • S = 0

  • L# = 0

anti-up (u with a line on top)

  • B# = -1/3

  • S = 0

  • L# = 0

down (d)

  • B# = 1/3

  • S = 0

  • L# = 0

anti-down (d with a line on top)

  • B# = -1/3

  • S = 0

  • L# = 0

strange (s)

  • B# = 1/3

  • S = -1

  • L# = 0

anti-strange (s with a line on top)

  • B# = -1/3

  • S = 1

  • L# = 0

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state the baryon number, strangeness, and lepton number of fundamental particles (lepton only)

electron (e-)

  • B# = 0

  • S = 0

  • L# = 1

positron (e+)

  • B# = 0

  • S = 0

  • L# = -1

electron neutrino (curly Ve)

  • B# = 0

  • S = 0

  • L# = 1

antielectron neutrino (curly Ve with a line on top)

  • B# = 0

  • S = 0

  • L# = -1

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  • gravitational force acts on …

  • electromagnetic force acts on …

  • strong force acts on …

  • weak force acts on …

  • anything with mass

  • charged objects

  • hadrons (quarks, baryons, and mesons) only

  • hadrons and leptons

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force mediators:

  • electromagnetic force is carried by …

  • strong force is carried by …

  • weak force is carried by …

  • the photon

  • the gluon

  • the gauge bosons (W+, W-, Z^0)

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conservation laws

  • in all interactions, the following must be conserved:

  • mass-energy

  • charge

  • momentum

  • spin

  • baryon number

  • lepton number

  • strangeness

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what are weak interaction responsible for?

beta decay

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what is the equation for beta-minus decay in terms of quarks

d → u + e- +Ve (curly V with a line on top)

or

d → u + beta- +Ve (curly V with a line on top)

  • when a neutron becomes a proton, a down quark turns into an up quark

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what’s happening in beta-minus decay?

  • the weak interaction causes a down quark to turn into an up quark by emitting W- boson

  • this almost immediately decays into an electron and anti-electron neutrino (Ve - curly V with line on top)

    • W- gauge boson emitted

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beta-minus decay equation

n → p+ + e- + Ve (curly V with line on top)

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outside the nucleus, neutrons are … . They decay after …

unstable, about 15 minutes via this weak interaction

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beta plus decay and beta plus decay in terms of quarks

  • what is emitted?

p+ → n + e+ + Ve (curly V)

  • u → d + e+ + Ve

OR

  • u → d + beta+ + Ve

    • W+ gauge boson is emitted

  • up quark turns into a down quark

    • electron neutrino is added due to conservation laws

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binding energy

the energy required to separate a nucleus into its constituent parts

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why is there a difference between the mass of the separate particles and of the whole atom?

because work has to be done to separate the particles

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what does a higher binding energy mean?

more stable

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  • light nuclei have … binding energy

  • Fe- has the … binding energy per nucleon making it …

  • for isotopes with A>20 there’s …

  • He - 4 is an anomaly which is …

  • low

  • greatest, the most stable nucleus

  • little variation in binding energy

  • unusually stable

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<p>from which point is fusion and fission occurring?</p>

from which point is fusion and fission occurring?

the cutoff line is approx. at Fe

<p>the cutoff line is approx. at Fe</p>
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nuclear fusion

  • for some lighter isotopes its energetically favourable to fuse together

  • in these cases, the final particle will have less mass than the parent particles

  • the final particle is more tightly bound than the parent particles and therefore more stable

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nuclear fission

for some heavy nuclei, it’s energetically favourable for them to split into lighter nuclei:

  • a massive nucleus which is neutron-rich is unstable

    • it’s held together by the strong force

  • the nucleus distorts, if sufficiently distorted, the electrostatic repulsion between the protons may be strong enough to separate them

    • greater distance from distortion

  • two highly excited fission products are formed

    • called daughter products

  • the product nuclei become more stable by emitting neutrons

<p>for some heavy nuclei, it’s energetically favourable for them to split into lighter nuclei:</p><ul><li><p>a massive nucleus which is neutron-rich is unstable</p><ul><li><p>it’s held together by the strong force</p></li></ul></li><li><p>the nucleus distorts, if sufficiently distorted, the electrostatic repulsion between the protons may be strong enough to separate them</p><ul><li><p>greater distance from distortion</p></li></ul></li><li><p>two highly excited fission products are formed</p><ul><li><p>called daughter products</p></li></ul></li><li><p>the product nuclei become more stable by emitting neutrons</p></li></ul>
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what is a thermal neutron?

slow neutron - roughly a few km/s

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induced nuclear fission

  • a thermal neutron is absorbed by the nucleus of a fissile atom (e.g. uranium-235)

  • 2 to 5 high-speed neutrons are released - if slowed, these could go on to be absorbed by other nuclei causing further fission reactions - a chain reaction

<ul><li><p>a thermal neutron is absorbed by the nucleus of a fissile atom (e.g. uranium-235)</p></li><li><p>2 to 5 high-speed neutrons are released - if slowed, these could go on to be absorbed by other nuclei causing further fission reactions - a chain reaction</p></li></ul>
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what are common nuclear fuels

uranium, plutonium, thorium

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what is one of the best fissile material?

what is its half life?

  • uranium-235

  • 710 million years

    • only 0.7% of uranium is U-235

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what is the most abundant uranium isotope?

uranium-238

  • half life of 4500 million years

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problems with a nuclear fission reactor

  • the neutrons are travelling too quickly to be absorbed

  • the neutrons are absorbed by U-238 nuclei

  • some neutrons absorbed by materials in the reactor cause these materials to become radioactive

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control rods

  • control the rate of fission within the reactor with rods of boron that can be raised or lowered between the fuel rods

  • these control rods will absorb the neutrons and prevent further fission from being induced

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moderator

  • a material such as graphite or heavy water surrounds the individual fuel rods

  • neutrons leaving the fuel rods undergo collisions with the atoms which acts to slow them down

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nuclear fusion in the sun

  • hydrogen nuclei (NOT ATOMS) fuse to produce Helium nuclei

  • there’s electrostatic repulsion between nuclei and so they need very high temperatures (high velocities) to get close enough

  • there must also be a very high density (and therefore pressure) to allow enough collisions to take place so that some do fuse

  • there’s an overall decrease in mass which releases energy in the form of KE and photons

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advantages of fusion

  • no radioactive waste products are directly formed

  • almost unlimited supply of raw materials

  • possible energy source for up to 1 million years

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disadvantages of fusion

  • need temperatures in excess of 100 million K

  • at the moment we have to supply more energy that we get out

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  • basic equation of fusion

  • where is deuterium found

  • where is tritium found and what does it do

  • tritium + deuterium → helium + neutron

  • found naturally in seawater

  • tritium is created

    • lithium could surround the core

    • this would absorb neutrons to become tritium

    • lithium + neutron → tritium + helium

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radioactive decay

is spontaneous (unaffected by heat, pressure, pH, magnetic or electric fields) and is random (no way to predict when a certain nucleus will decay)

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alpha emission

alpha: 2 neutrons, 2 protons

Pu → U + alpha + energy

  • the numbers all add up!! conservation laws

  • Pu - parent nucleus

  • U - daughter nucleus (outcome)

  • energy due to a decrease in mass - energy=mc^2

    • Pu > U + alpha

<p>alpha: 2 neutrons,  2 protons</p><p>Pu → U + alpha + energy</p><ul><li><p>the numbers all add up!! conservation laws</p></li><li><p>Pu - parent nucleus</p></li><li><p>U - daughter nucleus (outcome)</p></li><li><p>energy due to a decrease in mass - energy=mc^2</p><ul><li><p>Pu &gt; U + alpha</p></li></ul></li></ul>
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beta emission

  • beta+ decay

  • beta- decay

beta: fast-moving electron

beta-

  • C → N + beta + antielectron neutrino

    • Ve- used to conserve lepton number conservation

beta+

  • F → O + beta + energy + electron neutrino

<p>beta: fast-moving electron</p><p>beta-</p><ul><li><p>C → N + beta + antielectron neutrino</p><ul><li><p>Ve- used to conserve lepton number conservation</p></li></ul></li></ul><p>beta+</p><ul><li><p>F → O + beta + energy + electron neutrino</p></li></ul>
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gamma emission

gamma: high energy electromagnetic wave (lander<10^-13)

Co → Co + gamma

<p>gamma: high energy electromagnetic wave (lander&lt;10^-13)</p><p>Co → Co + gamma</p>
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when is gamma emitted

  • as the nucleus settles into a lower energy state

  • also emitted in alpha and beta decay

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neutron emission

neutron is emitted from the nucleus

  • Be → Be (isotope) + n

<p>neutron is emitted from the nucleus</p><ul><li><p>Be → Be (isotope) + n</p></li></ul>
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electron capture

proton-rich nuclide absorbs an electron from a low orbit, this turns a proton → neutron

  • Al + e- → Mg + energy + electron neutrino

<p>proton-rich nuclide absorbs an electron from a low orbit, this turns a proton → neutron</p><ul><li><p>Al + e- → Mg + energy + electron neutrino</p></li></ul>
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alpha, beta, gamma:

  • charge

  • how ionising

  • how penetrating

  • absorbed by

  • change in parent nucleus

  • mass

  • typical speed of emission

apha:

  • +2, highly, weakly, paper/5cm air, loses 2 neutrons and 2 protons, 4.00151u, 1x10^6 m/s

beta:

  • moderately, moderately, thin sheet of foil or 1m of air, 1 extra proton and 1 less neutron as neutron→proton, 0.00055u, 1x10^8 m/s

gamma:

  • weakly, highly, 5cm lead, none, 0, c = 3x10^8 m/s

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<p>what does it mean if the value is…</p><ul><li><p>above the line</p></li><li><p>below the line</p></li></ul><p>what is the curve called?</p><p>when does alpha emission occur?</p><p>as you get a larger nucleus …</p>

what does it mean if the value is…

  • above the line

  • below the line

what is the curve called?

when does alpha emission occur?

as you get a larger nucleus …

  • above the line - too many neutrons to be stable: beta- emission (neutron → proton)

  • below the line - too many protons to be stable: beta+ emission (proton → neutron)

N-Z stability curve (N=#neutrons , z=#protons)

if Z>82 - too many protons and neutrons: alpha emission

the proportion of neutrons increase: repulsive electrostatic force increases therefore you require more strong force

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activity (A)

the rate at which nuclei in a source decay and emit radioactive particles

  • measured in Becquerels (Bq)

  • 1 Bq = 1 decay/second

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count rate

number of detected particles per second

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main equations in radioactive deacy

  • A = lander*N

  • N = No*e^(-lander*t)

  • A = Ao*e^(-lander*t)

  • lander*t1/2 = ln2 (t1/2 = half life)

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decay constant

  • the probability of radioactive decay of a nucleus per unit time

  • units: s^-1 when activity is in Bq

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how to check if its exponential decay?

see if the half life remains constant from the graph (halves in equal times)

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half life

  • the mean time taken for the activity of the source to decrease by one half

  • also the mean time taken for the # of radioactive nuclei to decrease by one half

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  • where is carbon-14 made?

  • how does it decay?

  • radiocarbon dating process?

  • in the upper atmosphere by neutron capture

  • decays elsewhere at the same rate - so there’s approximately a fixed quantity in the atmosphere

  • living organisms take in the radioactive C-14 in the CO2 (plants) and glucose (animals) they absorb

  • when the organism dies, they stop taking in the CO2 and so the amount of C-14 inside them starts decreasing as it radioactively decays (beta emission) into N-14

    • its half-life is 5700 years

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why can’t carbon dating be used on artefacts older than 100,000 years?

the activity would be so low that it could not be differentiated from the background

  • proportion of C-14 to C-12 nuclei in dead and living objects and by comparing them it can be dated using N=No*e^(-lander*t)

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limitations of carbon dating

assumes the ratio of C-14 atoms to C-12 atoms has remained constant

  • increased emission of CO2 may have reduced this ratio as would volcanic eruptions

  • solar flares and the testing of nuclear weapons may also affect the ratio

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