Download Atomic and Nuclear Physics

Atomic and Nuclear Physics
9th of January 2014
7.1 ATOMIC STRUCTURE
Simple model of an atom
• Electrons kept in orbit around the nucleus as a
result of the electrostatic attraction between
the electrons and the nucleus (small + dense)
The Plum-Pudding Model
• The atom was imagined to be a sphere of
positive charge with negatively charged
electrons dotted around inside
• Rutherford designed an experiment to test the
plum pudding model. It was carried out by his
assistants Geiger and Marsden.
Evidence that supports a nuclear
model of the atom:
Geiger and Marsden’s Experiment
• A beam of alpha particles was aimed at very
thin gold foil (only few atoms thick) and their
passage through the foil detected.
• Expected the alpha particles to pass straight
through the foil but something else also
happened.
Rutherford’s Scattering Experiment
1. Most undeflected alpha particles show –
atoms are mostly empty space;
2. Small deflections show – a repulsive force
exists;
3. Deflections show - same charge as the alpha
rays (positive);
4. Only SOME deflections: hence the nuclei are
a small target;
Rutherford’s Scattering Experiment
5. Large Deflections show: nuclei have enough
mass of alphas to bounce back;
6. Mass of nucleus is more than the mass of an
alpha particle;
7. High density as it has a large mass and a small
size ;
Why must it be done in a Vacuum?
1. To avoid/ reduce absorption of alpha
particles
2. To avoid/ reduce chances of collisions
between air molecules and alpha particles
3. Allow sufficient range for alpha particles (so
it reaches the gold foil)
(Limitations of )Rutherford’s Nuclear
Model
• Electrons orbit a central nucleus (small, dense)
• HOWEVER: ^ does not explain the stability of an
atom – the electron accelerate around the
nucleus, they would therefore never lose energy
causing them to don’t spiral into the nucleus but
in reality they should spiral into the nucleus but
they don’t as there is a force that opposes it
• Electron accelerate and give off energy
Existence of atomic energy levels –
SEE CHEMISTRY
• Students should be familiar with emission
and absorption spectra, but the details of
atomic models are not required. Students
should understand that light is not a
continuous wave but is emitted as “packets”
or “photons” of energy, each of energy hf.
7.2 NUCLEAR STRUCTURE
Nuclide, Isotopes and Nucleon
• Nuclide: a specific combination of a distinct #
of protons and # of neutrons that form a
nucleus
• Isotopes: nuclei with the same number of
protons but different number of neutrons
• Nucleon: particles of the nucleus (proton or
neutron)
Atomic Number and Mass Number
• Nucleon Number A = Proton # + Neutron # =
(mass of the atom)
• Proton Number Z = Atomic Number
• Neutron number N = Neutron # atom
Interactions in a Nucleus
• Coulomb repulsion (electromagnetic force) long range between
protons splits the nucleus
• Strong, short-range nuclear interaction between nucleons (p and n)
binds the nucleons
• Overall balance must be correct and more neutrons needed
• Strong force is very strong, short range and the same for all
nucleons (as nuclei all have the same density)
• Adding more neutrons (compared to protons) contributes to
binding and does not add to tendency to split the nucleus / a
proton repels every other proton (in the nucleus) so extra neutrons
are needed for binding
7.2 RADIOACTIVE DECAY RADIOATIVITY
Natural Radioactive Decay
• Unstable nuclei change spontaneously/rando
mly/emit energy;
• by the emission of alpha particles and
electrons and gamma rays
• The inclusion of the antineutrino in β− decay
is required.
Alpha Particle, α
• Range depends: the charge of the alpha
particle, the kinetic energy of the alpha
particle, the density of the air
2 protons and 2 neutrons = Helium Nucleus
Charge
2+
Energy
5 MeV
Range in Air
> 5cm
Penetration
Low, Stopped by air
Ionising Ability
Very High
Detection
GM tube, cloud chamber,
photographic paper
Alpha Energy
• Alike an explosion:
• Momentum conserved;
• so different speeds as different masses;
• opposite directions because momentum
was zero initially;
Alpha Decay
• Original Atom loses 2 Protons and 2 Neutrons
- loses 4 from its Atomic Mass, loses 2 from
Atomic Number
• Changes into a different element
Beta Particle, βFast moving electron
Charge
-
Energy
___ MeV
Range in Air
> 30cm
Penetration
Moderate, about 1mm Aluminium
Ionising Ability
Very High
Detection
GM tube, cloud chamber, photographic paper
• Most deflected by a magnetic field
Beta Minus Decay
• One neutron splits into one electron and one
proton – Atomic number goes up by one and
Atomic Mass remains unchanged
• Electron emitted from the nucleus;
antineutrino also emitted – reason for beta
particles with different energy values
Beta Plus Decay
• One neutron splits into one positron and one
proton – Atomic number goes down by one
and Atomic Mass remains unchanged
• Positron (antielectron as an electron) emitted
from the nucleus; neutrino also emitted –
reason for beta particles with different energy
values
Gamma Ray, γ
•
•
•
•
•
•
Light – high speed 300,000,000 m/s
High Energy Electromagnetic Radiation
No Charge
Large Range, High Penetration
Stopped by think block of lead
Low ionizing ability – loses some energy
• Gamma radiation is often released as surplus
energy; the energy difference as a gamma photon
Comparing range of Beta and Alpha
Decay
• Beta have smaller mass / smaller / have greate
r speed than alpha;
• beta have smaller charge than alpha;
• therefore less likely to interact with air molecu
les;
Nuclear radiation and health
• To ionise an atom, it requires about 10eV
• Very high dose: affect central nervous system,
leading to loss of coordination and death within
2-3 days
• Medium dose: can damage the stomach and
intestine, resulting in sickness and diarrhoea
• Low dose: loss of hair, bleeding and diarrhoea
• Safe dose: all ionising radiation is potentially
harmful so there is no point below which it
becomes totally safe – however at low levels the
risk is small and outweighed by the benefits
Long Term Biological Effects of Ionising
Radiation
• Increased probability of getting cancer or
having a child with a genetic mutation
• Mutations in living organisms
• Damage to cell and tissue
• Problems arising the disposal of radioactive
waste – difficult to dispose hence ^^
• How associated risks can be reduced – using
thick sheets of lead/ thick lead container
Protection against radiation
• Distance - as alpha and beta have very short
range in air
• Number of gamma decreases proportional to
1
- hence the further you are, the safer you
2
𝑟
will be
• Shielding – thick lead shielding
Detecting Ionising Radiation
• G-M (Geiger Muller) Tube – amplified passed on to a scaler (shows the total
number) or ratemeter (shows the rate in
‘counts per second’ with a loudspeaker clicks
each time a ray from the source passes
through the tube)
• Photographic Film – blackened/ gets darker
Sources of Background Radiation
• Cosmic Rays – From Outer Space
• Rocks – Radon Gas from the Ground
• Food – Naturally from animals, plants who
absorb radiation from the soil – passes up
through the food chain
• Medical – X-Rays, Equipment
• Fallouts – Nuclear Waste
Why some nuclei are stable and others
unstable
• An explanation in terms of relative numbers of
protons and neutrons and the forces involved
is all that is required.
• Increase proton number = increase coulomb
force, to counter that neutrons needed to
increase strong force
7.2 RADIOACTIVE DECAY – HALFLIFE
Radioactive Decay
• Unstable nuclei change spontaneously/randomly/
emit energy
by the emission of alpha particles and
electrons and gamma rays
• Rate of decay decreases exponentially with time
• Any quantity that reduces to half its initial value
in a constant time decays exponentially
• The nature of the decay is independent of the
initial amount.
Radioactive Half-life
• Radioactive Half-life: Time taken for half of
the nuclei in a sample to decay OR time taken
for activity of a radioactive sample to halve –
each half life is equal
• Most ‘stable’ isotopes are the ones with the
LONGEST half-life as it takes longer for the
unstable nuclei to emit Alpha, Beta and
Gamma as it randomly decays
Activity
• This activity is measured in becquerels
• 1 becquerel = 1 nucleus decaying per second
• Bodies are slightly radioactive with an activity
of 4000 Bq
Half Life
• REMEMBER TO TAKE ACCOUNT BACKGROUND
RADIATION – TAKE IT AWAY! Minus it! It isn’t zero
so you need to take it into account!
7.3 NUCLEAR REACTIONS
Artificial induced transmutation
• Change of an atom from one element to
another – this can be artificially initiated
bombarding a target material with highenergy particles
• 1 amu = 931.5 Mev
Unified Nuclear Mass
• 1/12 of the mass of a Carbon-12 atom
• students must be familiar with the units MeV
c −2 and GeV c −2 for mass
Binding Energy
𝐸 = 𝑚𝑣 2
• Mass Defect
• Binding Energy = energy released when nuclides
form constituent OR the energy required to
separate nucleus into separate nucleons
• Binding Energy per nucleon =
• Atomic mass + mass defect/ binding energy =
total mass of protons + total mass of neutrons
Nucleon number of the binding
energy per nucleon Graph
Explaining increases in binding energy
• energy is released in the decay of K40 / energy released is the
• difference in binding energies / decay is spont
aneous / A40
• is more stable than K40;
7.3 FISSION AND FUSION
Nuclear Fission
• Large nuclei are induced to break up into
smaller nuclei and release energy in the
process.
• Used in nuclear reactors and atomic bombs
• Single reaction - bombarding a Uranium
nucleus with a neutron
• Chain reaction as it results in production of 3
neutrons
Nuclear Fusion
• Main source of the sun’s energy – fuels all
suns: fusion of 2 different isotopes of
Hydrogen to produce Helium
• Small nuclei are induced to join together into
large nuclei and release energy in the process
Fusion v. Fission
• nuclear fusion waste much less active than
fission waste;
fusion fuel much more abundant than fission
fuel;
fusion fuel has higher energy density than
fission;
radiation/pollution from plant lower for
fusion;
13.2 NUCLEAR PHYSICS
13.2 RADIOACTIVE DECAY
Beta positive Decay
• Students should know that β energy spectra
are continuous, and that the neutrino was
postulated to account for these spectra.
Equations for Exponential Decay
(given)
• 𝑁 = 𝑁0 𝑒 −𝜆𝑡 - exponential decay equation
• ^ activity can substitute here too
• Rate of decay is proportional to the no. of undecayed nuclei
𝑑𝑁
• 𝐷𝑒𝑐𝑎𝑦 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 =
= 𝜆 – how quickly the material will decay
𝑑𝑡
(s¯¹) proportionality between the number of nuclei and the rate of
decay
• 𝐴 (𝐵𝑞 − 𝑑𝑒𝑐𝑎𝑦 𝑝𝑒𝑟 𝑠𝑒𝑐) = −
• 𝑇1 =
2
ln 2
𝜆
Δ𝑁
Δ𝑡
= −𝜆𝑁= 𝜆 𝑁0 𝑒 −𝜆𝑡
Outline methods for measuring the
long half-life of an isotope
• If a large amount of radioactive substance is used
then a significant number of decays will occur per
unit time, the activity can be measured
• GM tube before sample, count the no. of decays
• Plot of decays against time will produce a nice
exponential curve.
• The half-life can be calculated from the decay
curve. However a problem arises if the half-life is
very short or very long.
Outline methods for measuring the
short half-life of an isotope
• Some nuclei have such short half-lives that
transporting the sample to a detector is
virtually impossible,
• i.e. the substance decays before you get it to
the detector. In such cases the sample must
be created (Artificial Transmutation) in or very
near a detector.
NEEDED? Uses of Radioactivity
• Works by injecting a radioisotope, then
detecting it with a G.M counter – chosen
isotope must have a short half-life but remains
long enough to be detected
1. Radioactive Tracers – finding leaks from a
pipeline, Fertiliser,
2. Medical Radioactive Tracers – to find kidney
blocks
NEEDED? Uses of Radioactivity
3. Sterilising – kill bacteria, moulds and insects
in food – prolongs shelf life; sterilizes medical
equipment (eg. Plastic Syringes)
4. Radiotherapy – careful usage kills cancer cells
5. Radioactive dating – archaeological
specimens and rocks; by finding out how
much uranium has changed into lead –
possible to calculate the age of the rock
NEEDED? Uses of Radioactivity
6. Quality Control – measuring how much
ionizing radiation passes through then
adjusting the thickness accordingly
7. Smoke Detection – Weak source emits alpha
particles which ionizes the air and conducts
electricity and a small current flows; when
there is smoke, it absorbs the alpha particles,
current reduces and the alarm sounds
Radioactive Potassium- Argon Dating
• K-40 decays to Ar-40 with a half-life of 1.26 x 10⁹
• When rock containing K is molten, any Ar that is
formed will bubble up to the surface and leave
the rock, but when the rock solidifies the argon is
trapped
• If a rock sample is heated the Ar atoms are
released and can be counted with a mass
spectrometer – if you count the K nuclei you can
calculate the age of the rock
Radioactive Carbon-14 Dating
• Only used for organic material up to about 60000 years
old
• (living things contain) carbon (14)
• C14 is a radioactive isotope / beta emitter
• (radio)activity decreases (over time)
• (estimate) half-lives (since material was alive)
• compare activity (of sample now with living tissue) /
ratio of C14 to C 12 is fixed in living material
% 𝑛𝑜𝑤 = % 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑥 𝑒 −𝜆𝑡
Original is 10^-10 %
7.8 NUCLEAR REACTIONS
Problems with using fission as an
energy source
• initial activity is very high;
• it is still highly radioactive after 70 years;
• thereby posing a severe health risk / causing
problems of disposal / OWTTE;
Nuclear Fission (splitting)
• Nucleus of Uranium-235 splits by collision
with a neutron to produce 2 daughter nuclei
and a small number of neutrons (3)
• This process releases energy in the form of
kinetic energy (= thermal energy) of the 2
nuclei (fission products)
• The neutrons produced by one fission can
strike other U-235 nuclei creating a chain
reaction
Nuclear Fission (splitting)
Chain Reaction?
• Neutrons (about 3) are emitted which can
collide with/hit other uranium nuclei;
• Start new fission processes which in turn will
lead to more and so on;
Nuclear Reactor
Outer Shell - Lead
• When fission process
is used as an energy
source to generate
electricity – the chain
reaction must be
controlled:
Fuel Rods – Uranium
Control Rods
– Boron
Moderator – Graphite
Control Rods
•
•
•
•
Made of boron
Placed between rods of nuclear fuel
Absorbs some of the neutrons
Moveable, adjustable – so there are just
enough neutrons to keep the chain reaction
going
• Lowered = decreased rate of reaction
• Raised = increased rate of reaction
Moderator
• Usually made out of water, Graphite or heavy
water (water with heavier isotopes)
• Reduces the speed of neutrons, so the Control
Rods have enough time to absorb it – can
sustain a chain reaction involving U-235