Nuclear Physics Flashcards
What is Rutherford’s Alpha Scattering Experiment?
An experiment used to show that the atom is largely empty space and that the majority of mass is in the positively charged nucleus
What happens to the Alpha Particles in Rutherford’s scattering experiment?
Most α is observed to pass straight through.
Some α is observed to be deflected by a small angle.
Very few α is observed to have been scattered by large angles.
How is Rutherford’s Alpha Scattering experiment conducted?
A slit focuses the beam of α towards a thin gold foil. in a Vacuum (as otherwise α will be ionised)
What are the conclusions of Rutherford’s Alpha Scattering Experiment?
Majority pass straight through ∴ largey empty space and distance too great for EM to have an effect.
Some deflect by small angles ∴ atoms have a positively charge nucleus and the positive charge of α is repeled by it.
Very few are deflected by large angles. ∴ most mass is in the nucleus, as the there is no recoil in the gold foil.
How do you calculate an upper limit for the size of a Gold nucleus?
Ek of α will entirly convert to electric potential when it is at its closest to the nucleus.
Ek = Ep
What does an Electron Diffraction pattern look like?
A large double width central maxima. Decreasing down to several non zero minima
How can an Electron Diffraction pattern be used to find the sizze of the nucleus?
The angle of the first minima and the De Broglie Wavelength into the Nλ = d x Sinθ
Why does an Electron Diffraction pattern have a non zero minima?
Because the “Fuzzy” nature of the edge of the nucleus.
“Fuzzy is exam board terminology”
What is the equation for the Radius of the Nucleus?
R = r0 x A^1/3 R = Radius of the nucleus / m r0 = Radius of a single Nucleon / m A = Atomic Mass (nucleon number)
How do you proove that Nucleus Density is Constant?
R = r0 x A^1/3 R ∝ A^1/3 R^3 ∝ A (R^3)/A = Constant Volume / Mass = Constant It is assumed that the Nucleus is spherical
Why do atoms have different densities when nuclei have the same densities?
Because of the presence of electron shells.
High mass atoms have a relatively small radius electron shells compared to low mass due to more charged protons and electrons.
What are the main causes of background radiation?
Natural:
Radon from the ground. (higher in rocks like granite)
Food and drink. Animals eat plants which have absorbed isotopes.
Cosmic Rays(very high energy photons)
Artificial:
Medical (eg x-rays)
What is Corrected Count Rate?
CCR
The actual count rate after background radiation has been factured into the measurement.
What is the equation for the Corrected Count Rate?
CCR = CR - BCR CCR = Corrected Count Rate / s^-1 (or min^-1) CR = Count Rate / s^-1 (or min^-1) BCR = Background Count Rate / s^-1 (or min^-1)
How does a Geiger Muller tube work?
A 450V DC supply would be connected to a central wire (positive electrode) which is surrounded by a Al tube (negative electrode). Between the two there is an inert gas (eg He, Ne or Ar). Radiation will react with the gass allowing for the current to pass. the number of times the current passes is counted.
What are the Properties of Alpha Radiation?
4u mass ≈ 6.68 x 10^-27 kg \+2 charge = +3.2 x 10^-19 C <10cm range in air Can be stopped by a thin piece of paper Very ionising 1 - 10 MeV (mono-energetic as each isotope gives a different energy)
What are the Properties of Beta Radiation?
5.5 x 10^-4 u ≈ 9.11 x 10^-31 kg
-1 charge = -1.6 x 10^-19 C
<2m range in air
Can be stopped by a few mm of Al
Moderatly ionising
0.1 - 2 MeV (continuous range of energy)
What are the Properties of Gamma Radiation?
No mass No charge "infinite" range in air Can be stopped by several inches of Pb Very low ionising potential 0.1 - 10 MeV ( discrete energy levels)
How is Alpha Radiation effected by B and E fields?
E-Field:
Deflected in direction of the field by small amount (due to Q/m and large mass)
B-Field:
Deflection obeys FLHR, deflected by small amount due to Q/m and large mass)
How is Beta Radiation effected by B and E fields?
E-Field:
Deflected in opposite direction of the field by large amount (due to Q/m and smallmass)
B-Field:
Deflection travels in the opposite direction to FLHR due to -Q, deflected by large amount due to Q/m and small mass)
How is Gamma Radiation effected by B and E fields?
It isn’t effected by either.
When a Nucleus is in a Excited State how does it return to ground state?
It emits a Photon (γ ray)
After the decay the nucleus has the same charge and mass, but has less potential energy.
What is the equation for the intensity of Gamma Radiation?
I = k / x² I = Intensity k = Constant X = Distance form source
How can the Intensity of Gamma Radiation be used to calculate the count rate at different distances?
I = k / x² I ∝ 1/x² CCR ∝ 1/x² x²CCR = 1 x(1)²CCR(1) = x(2)²CCR(2)
What are uses of Gamma Radiation?
Tracer in blood
eg. Technetium-99m (“m” mean meta-stable)
As can esily penetrate body, has a short half life and very low ionising.
What are the types of decay caused by the weak nuclear force.
Alpha Decay: unstable nucleus ejects a helium nucleus
Beta Minus Decay: Neutron in an unstable nucleus decays into a proton and an electron, which is ejected.
Beta Plus Decay: Proton in an unstable nucleus decays into a neutron and a positron, which is ejected.
Electron Capture: Electron in a shell is captured by a proton in the nucleus. Proton turns into a Neutron.
How are the four decay types observed?
Alpha: Ionises particle
Beta minus: Ionises particles
Beta plus: Annihilation with electron producing photons.
Electron Capture: X-ray photon is produced
What are the Symbols for Proton, Neutron and Nucleon numbers?
Proton = Z Neutron = N Nucleon = A
What is a Decay Series?
The path which an unstable isotope takes to reach stability.
They can have a single path or can branch including a range of different isotopes and elements.
How do you calculate the number of α and β decays in a Decay Series?
Calculate the difference in mass.
Divide the difference in mass by 4 as this will show the number of α’s (as only they change the mass).
Take away from the charge of the isotope 2x the number of α’s (this will show the difference between the product and initial isotope).
The difference is the number of β (as they increase charge).
What is the N-Z Graph?
It is a graph that plots proton number (x axis) and Neutron number (y axis). It shows what isotopes will undergo what type of decay.
Roughly what is the shape of the N-Z Graph?
The region of stability follows Y=X from x=0 to x=20 then gradient increases so that the area will pass through (80,120).
Just above for the length of the graph is the area containing β- decay isotopes.
Just above for the length of the graph is the area containing β+ decay and e- capture isotopes.
From 60-80 under the graph is the area which under goes α decay?
Which direction do Isotopes move on the N-Z Graph?
β- : down 1 and right 1 β+ : up 1 and left 1 e- capture : up 1 and right 1 α : down 2 and left 2 γ : no change
What is the Radioactive Decay Constant?
The probability that an unstable nuclide will decay in ONE SECOND
What is the Symbol and Units for Radioactive Decay Constant?
Symbol: λ
Units: s^-1
What is the equation for the Radioactive Decay Constant?
ΔN / Δt = -λN
N = The number of unstable nuclides after a given t
λ = The radioactive decay constant (probability it will decay in 1 second)
ΔN / Δt = The rate of change of N
What is Activity?
How many decays occur in 1 second
What is the Symbol and Units of Activity?
Symbol: A
Units: Bq (becquerel) or s^-1
What is the equation for Activity?
A = -ΔN / Δt
A = Activity
N = Nuclide number
t=time
What is the releationship between A and N?
A =λN
What is the equation for the number of Unstable Nuclei as a function of time?
N = N(0) e^(-λt) N = number of nuclei at that time N(0) = Initial number of unstable nuclei λ = Radioactive decay constant t = time
What is the equation for Activity as a function of time?
A = A(0) e^(-λt) A = Activity at that time A(0) = Initial amount of activity λ = Radioactive decay constant t = time
What is an alternative way of writing the equations for the number of unstable nuclei and activity?
N = N(0) x (0.5)^n A = A(0) x (0.5)^n N = Number of unstable nuclei at that time N(0) = Initial number of nuclei A = Activity at that time A(0) = Initial amount of activity n = number of half lives
What shape are the graphs for Number of Unstable Nuclei and Activity as a function of time?
Exponential decay from N(0) and A(0) respectively.
3 Half Lives should be measured to find if it is exponential.(dont have to be consecutive)
What is the shape of Ln N and Ln A graphs?
Straight lines from Ln N(0) and Ln A(0) respectively.
-λt is the gradient
What is a Half Life?
The time taken for the number of unstable nuclides (or activity of a source) to halve for a given isotope.
Can vary from less than a second to billions of years
How are Half Life and Decay Constant linked?
T(1/2) = ln2 / λ T(1/2) = Half Life λ = DEcay Constant
What is the Symbol and Units for Half Life?
Symbol: T(1/2)
Units: seconds
What is the equations for moles?
Mole = Mass / Mr Mole = Number of atoms / Avagadro Constant
What is an Atomic Mass Unit?
The mass of 1/12 of a Carbon-12 nucleus.
What is the value and symbol of the Atomic Mass Unit?
Symbol is u
1u = 931.5 MeV = 1.661 x10^-27 kg
Why is the mass of the Constituent Nucleons greater than the mass of the Nucleus?
Work is done against the strong nuclear force to break apart a nucleus. However once beyond the limit of the strong force the work done can no longer be stored as potential (as it is effectivly at infinity). Therefore the energy transfers to mass to conserve mass-energy.
What is Mass Defect?
The difference in mass between the Constituent nucleons and the nucleus.
What is the Symbol and Units for the Mass Defect?
Symbol: Δm
Units: kg or u
What is Binding Energy?
The work done in seperating a nucleus into its constituent nucleons.
What is the Symbol and Units for Binding Energy?
Symbol: BE
Units: MeV
What is the Binding Energy Per Nucleon?
The average energy required to remove an individual nucleon from a nucleus
What is the equation for Binding Energy Per Nucleon?
BE / A = Binding Energy Per Nucleon
BE = Binding Energy
A = Number of Nucleons
How is Binding Energy calculated?
Mass of Constituent nucleons - Mass of nucleus = Δm
Δm x 931.5MeV = Binding Energy
How is Binding Energy Per Nucleon calculated?
Mass of Constituent nucleons - Mass of nucleus = Δm
Δm x 931.5MeV = BE
BE / A = Binding Energy Per Nucleon
What does a greater Binding Energy Per Nucleon mean?
That the nucleus is more stable as more energy is needed to break it apart.
What is the Graph of Binding Energy per Nucleon against Nucleon Number?
A graph which plots the Binding energy per nucleon against nucleon number.
It effectively show the stability of isotopes.
What shape is the Graph of Binding Energy per Nucleon against Nucleon Number?
Starts at (0,0). Concave curve up to (56,8.8 MeV) as this is BE/A for Fe-56 (the turning point as it is the most stable iostope). It slowly tales of in a shallow curve passing roughly through (250,7.4 MeV).
It DOES NOT drop beneath 7 MeV after Fe-56
X axis is from 0 to ≈ 250. Y axis is from 0 to 9
Where does Fission and Fusion occur on the Graph of Binding Energy per Nucleon against Nucleon Number?
Fission travels up from the right towards Fe-56.
Fusion travels up from the left to towards Fe-56
What is meant by Nuclear Fusion?
The joining of two small nuclei to produce a larger nucleus
What is meant by Nuclear Fission?
The splitting of a Large nucleus to produce two smaller nuclei.
What happens in Nuclear Fusion?
The joining of two small nuclei to produce a larger nucleus.
The products have a greater binding energy per nucleon.
Thus causing a release in energy.
The energy is released as Kinetic energy of Particles, neutrinos and photons.
This energy is Yield
What happens in Nuclear Fission?
The splitting of a large nuclues to produce two smaller nuclei.
The products have a greater binding energy per nucleon.
Thus causing a release in energy.
The energy is released as Kinetic energy of Particles, neutrinos and photons.
This energy is Yield
What is the Proton Proton Chain?
The Main Fusion system in stars.
6 p → He-4 + 2 p + 2 e+ + νe
Simplifies to
4 p → He-4 + 2e+ + 2νe
What is the process of the Proton Proton Chain?
1) p + p → D+ e+ + νe Δm = 0.00046u
2) D + p → He-3 Δm = 0.00646u
Repeat steps 1 and 2 twice
3) He-3 + He-3 → He-4 + 2 p Δm = 0.01158
Total Yield is 2(0.00046 + 0.00646)+0.01158 = 0.02542
0.02542 x 931.5 =23.67873 MeV
How is the yield of Fission calculated?
Mass of (Fissile Nucleus + Fission Neutron) - (Fission Fragments) = Mass Defect Mass Defect x 931.5 = Yield
What are Daughter Products?
The two new nuclei formed from the breaking apert of the Fissile Nucleus
What is a Chain Reaction
When at least one fission neutron goes on to create another fission event.
(More neutrons out than in)
Why does a Chain Reaction occur?
Because there are enough Fission nuetrons being released that the chance of it colliding with another nucleus and causing a fission event is greater than 1
What is a Thermal Neutron?
A neutron which has been slowed down, so that it behaves in the manor of the thermal gas model
What slows Fission Neutron down for it to become a Thermal Neutron?
Water
The neutron crashes into the molecule transfering some of its kinetic energy to it.
What is Critical Mass?
The Minimum mass fo a Fissile material such that it will undergo a chain reaction.
Assume the material to be Spherical, due to smallest surface area to volume ratio
Why does Critical Mass assume the material is spherical?
Spheres have the smallest surface area to volume ratio.
Therefore reducing the number of fission neutrons leaving the material
What is a Moderator?
It is to slow down the fission neutrons to make them thermal neutrons.
Generally Water
What are Control Rods?
They are Boron rod that absorb thermal neutrons to control the rate of reaction.
What is Coolant?
it is used to transfer thermal energy from the core to the turbine water.
What are the Safety Aspects to do with the fuel being used?
It should be below critical mass.
It is generally in small pellets
What are the Safety Aspects to do with the Shielding?
Thick concrete shielding to prevent the escape of ionising radiation
What are the Safety Aspects to do with the Emergency Shut-down?
The control rods are held up with fail-safe electro magnets.
(the clamp holding them opens when no electricity is put through, causing th default position to be open, thus droping the control rod.
How is Radioactive Waste Produced, Handled and Disposed of?
It is produced by the daughter product as they are also unstable.
It is handled remotely, eg(using robots)
It is stored in glass containors due to the longevity than metal or concrete
How are Spent Fuel Rods Reprocessed?
1) Stored in Cooling ponds.
2) Removed to reprocessing plant.
3) Stored in Cooling ponds.
4) Dissolved in Acid
5) Chemical seperated from other elements.
