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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<10^-13)
Co → Co + gamma
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
Note 
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