Physics: Module 6 - NUCLEAR & PARTICLE PHYSICS

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

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)

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

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

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

matter and antimatter

* every fundamental particle that exists has an anti-particle
* these have the same rest mass but opposite charge

what happens if a particle meets its anti-particle?

they will annihilate to produce a pair of high energy photons

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)

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

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

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

* 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

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)

conservation laws

* in all interactions, the following must be conserved:

* mass-energy
* charge
* momentum
* spin
* baryon number
* lepton number
* strangeness

what are weak interaction responsible for?

beta decay

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

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

beta-minus decay equation

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

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

unstable, about 15 minutes via this weak interaction

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

binding energy

the energy required to separate a nucleus into its constituent parts

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

what does a higher binding energy mean?

more stable

* 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

from which point is fusion and fission occurring?

the cutoff line is approx. at Fe

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

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

what is a thermal neutron?

slow neutron - roughly a few km/s

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

what are common nuclear fuels

uranium, plutonium, thorium

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

what is the most abundant uranium isotope?

uranium-238

* half life of 4500 million years

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

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

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

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

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

disadvantages of fusion

* need temperatures in excess of 100 million K
* at the moment we have to supply more energy that we get out

* 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

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)

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

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

gamma emission

gamma: high energy electromagnetic wave (lander

when is gamma emitted

* as the nucleus settles into a lower energy state
* also emitted in alpha and beta decay

neutron emission

neutron is emitted from the nucleus

* Be → Be (isotope) + n

electron capture

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

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

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

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

activity (A)

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

* measured in Becquerels (Bq)
* 1 Bq = 1 decay/second

count rate

number of detected particles per second

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)

decay constant

* the probability of radioactive decay of a nucleus per unit time
* units: s^-1 when activity is in Bq

how to check if its exponential decay?

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

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

* 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

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)

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