nuclear physics Flashcards
atomic mass unit
1/12 mass of Carbon-12 atom which is equal to 1.661x10-27 kg
conservation of mass units to energy
using Einstein’s equation, E = mc², the equivalent energy of 1u can be determined, which is 931.5 MeV.
calculate energy released in nuclear changes
- add up total mass of nuclei before change in terms of u and add up the total mass of nuclei after change in terms of u
- calculate the mass difference in terms of u
- convert the mass difference into equivalent energy using conversion factor from formula sheet
mass difference
difference in mass between a nucleus and the sum of the mass of its nucleons. total mass of individual nucleons is greater than mass of nucleus
mass defect
the difference between the mass of the nucleus and the mass of its constituent parts.
as nucleons join together, their total mass decreases because some of their mass is converted into energy and released
binding energy
the energy required to separate the nucleus up into its constituents protons and neutrons. It is equivalent to the mass defect
binding energy per nucleon
the average energy per nucleon to remove all of the nucleons from a nucleus
what produces binding energy
the attractive strong force which holds the nucleons together
graph of average binding energy per nucleon against nucleon number
- rapid increase up to iron
- peak at iron
- decreases gradually after iron
explain how energy is released in fission and fusion
- energy is released/ made available when binding energy per nucleon is increased
- in fission, a large nucleus splits and in fusion nuclei join
- the most stable nuclei are at a peak
- fusion occurs to the left of peak binding energy per nucleon and fission to the right
fission process
- neutrons are released
- fission is usually brought about by neutron bombardment
fission equation
the daughter isotopes can be a range of different elements. The total nucleon number on the left of the equation equals the total nucleon number on the right
fusion process
- two small or light nuclei combine
- electrostatic repulsion has to be overcome
- nuclei have to be given kinetic energy for them to meet
advantages of fusion over fission
- supply of fuel is almost unlimited
- fewer waste or radioactivity or environmental problems
- energy released per unit mass is generally greater
what is enriched uranium
proportion of uranium - 235 is greater than is found in naturally occurring Uranium
definition of thermal neutrons
neutrons that have low energies or speeds
induced fission by thermal neutrons
splitting of nucleus into two smaller nuclei, brought about by bombardment with (thermal) neutrons
definition of a chain reaction
- fission reaction is induced by neutron bombardment]
- fission releases neutrons
- released neutrons cause more fission
definition of critical mass
- minimum mass of fissile material
- for a self-sustaining reaction to be maintained
what do control rods do in the reactor
- control involves limiting the number of neutrons, released from the fission of a nucleus, that can go on and cause fission in other nuclei
- excess neutrons are observed by control rods
- control rods inserted into reactor slows reaction rate
- for a steady state of fission, only one neutron per fission is required to go on to produce further fission
- each fission produces two or three neutrons on average
- some neutrons escape
examples of suitable control rods and their properties
- suitable control rod material is boron or cadmium
- control rod materials must be good at absorbing neutrons
what do moderators do in the reactor
- neutrons from fission are fast (high energy)
- fission most favourable with low energy neutrons
- moderation involves slowing down neutrons by collision with moderator atoms
- large number of collisions required
- collision are elastic so KE is transferred to the atoms
Examples of suitable moderators and their properties
Suitable moderator material is graphite or water
* Moderator must not absorb neutrons and the moderator atoms should have (relatively) low mass
what does coolant do in the reactor
- transfers thermal energy from core to a heat exchanger where water in a secondary cooling system is turned into steam
examples of coolants and their properties
Suitable coolants are water or carbon dioxide
- coolants need to flow easily so they can be pumped around the reactor core
- coolants need to have large specific heat capacities so a lot of thermal energy can be transferred with a smaller volume of coolant
how is thermal energy obtained from nuclear fission
- fission fragments repel each other and collide with other atoms in the fuel rod
- high energy fission neutrons enter moderator [or collide with moderator atoms]
- atoms in moderator and fuel rods gain kinetic energy due to collisions
- temperature depends on the average kinetic energy of vibrating atoms
what are fuel rods
they are rods containing enriched uranium fuel which are inserted into the reactor
why do fuel rods become less effective for power production after they have been used for a while
- the amount of fissionable uranium-235 in fuel rod decreases
- fission fragments absorb neutrons
why are spent fuel rods more dangerous than unused fuel rods
-uranium is an alpha emitter
- it is easy to stay out of range or easy to contain a source
- fission fragments are more radioactive with short half lives or high activities
- they emit mostly beta - and gamma radiation which have a greater range
why are beta - emitting isotopes produced when fuel rods are in the reactor
- fission nuclei are neutron-rich and therefore unstable
- neutron-proton ration is much higher than for a stable nucleus of the same charge or mass
- particle is emitted when a neutron changes to a proton
how is reactor shielded
the reactor is shielded with concrete in order to contain gamma radiation and neutrons
how are spent fuel rods handled and processed
- spent fuel rods are removed and handled by remote control
- they are placed in cooling ponds for several months
- they are transported in specially designed flasks that are resistant to impact
- any uranium-235 that hasn’t fissioned is separated from the active waste
how are radioactive waste materials stored
- the high level waste is stored
- spent fuel rods are buried deep underground at a geologically stable site
- special storage precautions are required
- some of the waste can be stored within relatively inert glass (vitrification)
what is an emergency shut down
where control rose are dropped into reactor to slow down and stop rate of fission as quickly as possible
definition of an isotope
different forms of same element, with same number of protons and different number of neutrons
properties of alpha radiation ie composition, speed, charge, ionizing power, stopped by , path in uniform field
composition: 2 protons, 2 neutrons
speed: 10 % speed of light
charge: +2e
ionizing: most ionizing
stopped by: few cm of air or skin path across
uniform field: slightly towards negative
properties of beta radiation ie composition, speed, charge, ionizing power, stopped by , path in uniform field
fast moving electron
90% speed of light
-1e
less ionizing
stopped by few mm aluminium
moves strongly towards positive
properties of gamma radiation
ie composition, speed, charge, ionizing power, stopped by , path in uniform field
high energy & high frequency photon
speed of light
+- 0
least ionizing
stopped by few cm of lead
straight through field
definition alpha emission
In nucleus 2p and 2 n are ejected (emitted by large nuclei)
definition beta minus emission
fast moving electron emitted when neutron turns into proton in neutron rich nucleus
definition beta plus emission
positron emitted when proton decays to neutron in proton rich nucleus
definition electron capture
proton in nucleus captures electron from inner shell, and decays into neutron in proton rich nucleus.
X ray photon emitted after due to electron from atomic electron shell falls to fill vacancy left by inner shell electron, releasing energy as x-ray photon
definition gamma radiation
high energy photon produced when excited nucleus de-excites, releasing energy as gamma photon
Identifying alpha, beta and gamma radiation
Put the detector within a few cm of the source and put some paper between the source and the detector. If the count rate drops significantly, then the source is alpha.
If the count rate doesn’t change, remove the paper and replace it with a few mm of Aluminium. If the count rate drops significantly, then the source is beta. If the count rate doesn’t change, then the source is gamma.
applications of alpha beta and gamma radiation
alpha- smoke detectors
beta - thickness measurement of cardboard (in a paper mill)
gamma- detecting leaking pipes / medical tracer
Safe handling of radioactive sources in a laboratory
- handle with (long) (30 cm) tweezers because the radiation intensity decreases with distance
- store in a lead box (immediately) when not in use to avoid unnecessary exposure to radiation
Examples of background radiation
- Cosmic rays
- Ground, rocks and buildings
- Radon (in atmosphere)
- Nuclear fallout (from weapons testing/nuclear accidents)
- Discharge/waste from Nuclear power
Experimental verification of inverse square law for gamma rays
- Count rate measured by GM tube from a gamma source (gamma rays not stopped by air)
- Measured count rate equals counts from source PLUS background counts
- Measure background count rate and subtract this from the measured rate with the source present. This gives the corrected count rate (counts just from the source).
- Vary the distance of the GM tube from the source and plot a graph of corrected count rate against 1/(distance)2 to establish an inverse square relationship between intensity and distance.
What is meant by random nature of radioactive decay
- there is equal probability of any nucleus decaying,
it cannot be known which particular nucleus will decay next. - it cannot be known at what time a particular nucleus will decay.
- the rate of decay is unaffected by the surrounding conditions.
Definition of decay constant
the probability of (a nucleus) decay per unit time (usually per second).
Definition of activity
The number of nuclei of an isotope that decay each second.
(remember each decay produces one radioactive particle that can then be detected with a Geiger Muller tube)
Units of activity
Bq (Becquerel) - number of decays per second.
Definition half life
Time taken for half the nuclei of a particular isotope present to decay OR time taken for the activity of a particular isotope to half
Decay curves
ln (activity) - halflife = ln(2)/-G
Decay constant from a log graph
decay constant = - gradient
Existence of nuclear excited states within nucleus
- Nuclei can be in excited states (eg following radioactive decay).
- Nuclei can de-excite (and lose energy) by emitting a photon.
- As energy levels differences are really big in nuclei, the photons have very large energies.
- And hence high frequencies and short wavelengths (gamma part of spectrum).
- Gamma emission is therefore often associated with alpha and beta decay.
Why is beta emission associated with gamma rays of discrete frequencies
- Following decay the nucleus is in an excited state
- Which are at discrete energies
- And emit rays when they de-excite/fall down to lower states
- Reference to E=hf and stating rays (or drop in energy level) have discrete energies.
Why is the gamma source technicium-99 used in medical diagnosis.
- It only emits gamma rays
- gamma rays can be detected outside the body/are weakly ionising and cause little damage
- It has a short enough half-life and will not remain active in the body after use
- It has a long enough half-life to remain active during diagnosis
- The substance has a toxicity that can be tolerated by the body
- It may be prepared on site (at hospital)
Features of Rutherford scattering
Experimental set-up
* Air must be removed (vacuum) because alpha particles only travel short distances in air due to collisions with air molecules.
* Gold foil must be thin so that alpha particles are not absorbed by the foil (have more than one collision).
Observations
* Majority of alpha particles pass straight through (without any deflection).
* A small number of alpha particles are scattered through very large angles, some even come back towards the alpha source (scattered through 180 degrees).
* Conclusions about structure of atom
* The atom is mostly empty space because most alpha particles do not pass close enough to the nucleus to be deflected.
* The nucleus is very small and positively charged to provide necessary electric field strength to repel alpha particle.
* Nucleus contains most of the mass (of the atom) because the alpha particles are scattered through very large angles
* Nucleus is much smaller compared to the separation between nuclei (and hence to the size of the atom itself).
Maximum size of nuclear radius from estimate of closest approach
conversion of initial ke (of alpha particle) to electrical potential energy at point of closest approach.
Ek = 1/2mv² = 1/4πEo x QaQn/r
where Qa is charge on alpha particle, Qn is charge on nucleus, and r is effectively the distance of closest approach to nucleus
Why are other methods for measuring the nuclear radius other than alpha scattering used?
- strong force acting between alpha particle and nucleus complicates results
- scattering is produced by the distribution of protons, not the whole nucleon distribution
- alpha particles are relatively massive, causing recoil of nucleus which complicates results
Advantage of using electrons to measure nuclear radius
- electrons are not subject to the strong force so, electron scattering patterns are easier to interpret.
- electrons give greater resolution (or are more accurate) because they get closer to the nucleus and alpha particles cannot get so close to the nucleus due to electrostatic repulsion so only provide information on the closest distance of approach, not radius.
- electrons produce less recoil in nucleus because electrons are much less massive (than nucleus).
- high energy electrons are easier to produce because electrons have a lower specific charge so are easier to accelerate.
Experimental method for determining size of nucleus
Electron scattering
Typical size of nuclear radius
1x10-15 m (1 fm)
Information that can be gained about the nucleus using alpha particles
- maximum diameter of the nucleus
- proton number and nuclear charge
- that the mass of the nucleus is most of the mass of the atom
Information that can be gained about the nucleus using high energy electrons
- Nuclear radius (diameter)
- Nuclear density
Determination of nuclear radius from electron scattering
intensity /scattering angle graph
interference effect - electrons behaving as waves and being diffracted by nucleus
Derivation of radius from experimental data
straight line graph R -radius of nucleus / A¹/₃- nucleon number
gradient = r
calculation of nuclear density
- Considering the nucleus as a sphere with a radius R, the volume of nucleus: V= ⁴/₃πR³
- As , R = roA^¹/₃, V= ⁴/₃ π (roA^1/3)³= 4/3πro³A = AxVn (where is the volume of one nucleon, is the mass of one nucleon and A is the number of nucleons).
- Density of nucleus mass/volume = Axm/AxV =m/V
- This is the density of a single nucleon, so the density of nuclear matter is independent of the particular isotope being considered
