Nuclear Flashcards
What is the equipment used in a Rutherford scattering experiment?
A source of alpha particles in a lead container. A thin sheet of gold foil. A movable detector. An evacuated chamber.
What were the results of the Rutherford scattering experiment?
Majority of alpha particles fired at a thin sheet of gold leaf passed straight through. Some of the particles passed through the leaf with a small angle of deflection and very few were deflected at very large angles. (Back scattered)
What is the interpretation of the results of the Rutherford scattering experiment?
All the positive charge inside an atom is concentrated only on a small part inside the nucleus which is present at the centre of the atom along with the neutrons.
With negative charge scattered around the outside in shells. Radius of the nucleus = 1/10,000 radius of the atom.
How did the data from the Rutherford scattering experiment lead to a change in our understanding of the atomic structure?
Most alpha particles passed straight through the gold foil, which implied that atoms are mostly composed of open space. Some alpha particles were deflected, suggesting interactions with other positively charged particles within the atom. If they followed the plum pudding model, all should have passed through.
Order α, β and γ by least to most penetrating.
alpha, beta and then gamma.
What can be used to shield from α, β and γ radiation?
A sheet of paper, A few mm of aluminum foil and a block of lead.
What are the relative ionising powers of α, β and γ radiation?
alpha is most ionising; beta has middling strength ionisation and gamma is the least ionising.
What are some applications of α, β and γ radiation?
α- Smoke detectors (alpha particles emitted from americium ionise the nitrogen and oxygen allowing a current to flow)
β- Determining and regulating the thickness of a sheet of metal. Medical tracers.
γ- Treatment of cancers and sterilising medical equipment.
Why is technetium-99m a suitable radioisotope for medical uses?
Half life is short enough that the patient has not got a radioactive isotope inside them for too long (limit exposure). Half life is long enough that the isotope undergoes decay for long enough to arrive too the relevant part of the body and be measured.
What are the properties of a radioisotope that could be used for medical purposes?
Short half lives to keep doses low, Long enough for procedures and easy enough to store.
Why does the intensity of γ radiation obey an inverse square law relationship?
Without a limit to its range
The intensity of the influence at any given radius (r) is the source power divided by the area of the sphere.
Gamma radiation is not absorbed by matter easily, whereas alpha and beta are absorbed quickly before they can spread out.
What is background radiation, and what are some sources of it?
The natural radiation that is always present in the environment. Air (radon gas), building materials, Rocks and cosmic rays.
Higher exposure when flying or working in the medical field. Or, where you live.
What is the count rate, background count rate and corrected count rate?
Corrected count rate = Count rate - Background count rate
Count rate- how much radioactivity you are detecting every second.
What is the relationship between the activity of a source, the measured corrected count rate, the distance between the source and the detector, and the size of the detector’s window?
(corrected count rate)/ (Area of detector window) = no. decays per sec per unit area at distance d = (total no. decays per sec)/(4pi d^2)
4pi d^2 = surface area of a sphere with radius d
What is the Activity?
Decays per second
What is meant when radioactive decay is described as a random and spontaneous process?
Randomness -It is impossible to predict when a particular radioactive nucleus will decay. Spontaneity - you cannot cause or influence the decay
What is the decay constant of a radioactive source?
𝜆 the probability of an individual nucleus decaying per second. Its unit is s-1.
What is the half-life of a radioactive source?
The time for the number of nuclei in a pure sample of a radioactive isotope too halve.
t/2 = ln(2) / 𝜆
where 𝜆 = decay constant
What is the derivation of the equation for half life?
N(t) = N0 . e^( -𝜆t)
Time for the N0 too half
N(t/2) = N0/2
N0 .e^( -𝜆t/2)
rearrange for t/2
What are the relationships between the molar mass, total mass of sample and atomic mass number?
number of moles = mass of sample / molar mass
molar mass ≈ mass number
How can the molar mass be estimated from the sample’s isotope notation?
molar mass ≈ atomic mass
What are the equations for how the activity, number of nuclei, mass and number of moles change over time?
A(t) = A0. e^ (–𝜆t)
N(t) = N0. e^( -𝜆t)
M(t) = M0. e^( -𝜆t)
n(t) = n0. e^( -𝜆t)
Why does carbon dating work?
A small percentage of all naturally occurring carbon is radioactive C-14. When living organisms die, no longer take new C from atmosphere. % of C-14 then decreases.
When is carbon dating used?
Requires organic material and much older objects. Not too old as the Activity would be too low; not modern objects because of carbons half life.
Why does argon dating work?
Potassium 40 is a naturally occurring isotope with an effective half life. Two decay modes. Potassium decays too argon, which is a noble gas, and so unreactive, therefore, if its is found it must be produced from potassium decay. Or, decays too calcium.
How does potassium decay too argon?
Electron capture
Activity, Number of nuclei, Mass or number of moles against time graph
Exponential decay- will always decrease by the same proportion for a given time.
Negative exponential
For what reason is the model of activity against similar too the model of number of nuclei (N) against time?
The graph of x against time is modelled as the same exponential decay for any quantity proportional too the number of nuclei in a decay
What is the equation relating activity, the number of nuclei and the decay constant?
A = N. λ
If activity is equal too the rate of decay, what equation would represent this?
A = dN/ dt (differential equation)
Name and describe three safety techniques when handling radioactive Isotopes
Limit exposure by storing the source in a led lined container and removing from the room straight after use.
Maximise distance by handling with tongs and observing from a distance.
Use a suitable radiation shield like a lead apron or screen (BE SPECIFIC)
School sources are often directed.
What is good practice when concerning safety in handling radio isotopes?
Putting up relevant signage and checking local rules regarding handling sources.
What is radioactive decay?
Less stable isotopes become more stable by losing energy in the form of radiation.
Why do products from beta minus decay have a range of kinetic energies?
The energy must be shared between the B- particle and electron anti neutrino.
What determines the stability of a nucleus?
The stability is determined by the balance between the strong nuclear force holding it together and electrostatic repulsion.
How do the forces acting on the subatomic particles change with N and Z (the number of protons and neutrons)
As Z and N increase, the separation increases beyond the range of the strong force and it stops acting. More neutrons are required than protons too hold them together too balance the forces.
What type of nuclei typically undergo alpha decay?
Heavy nuclei with a neutron number of around 80 (when the graph stops at 80,126)
What type of nuclei undergo beta minus decay?
Neutron rich nuclei (as a neutron decays too a proton)
What type of nuclei undergo beta plus decay? (or electron capture)
proton rich nuclei (as a proton decays too a neutron)
What type of nuclei undergo gamma decay?
An excited nucleus
How are nuclear energy levels related too gamma decay?
Excited particles emit energy as they drop to lower energy levels. The nucleus will deexcite by emitting a more energetic electromagnetic wave called a
gamma ray.
On an N/Z graph what section is linear?
from (0,0) to (20,20)
What area on the N/Z graph represents the beta minus decay?
The area above the line of stable nuclei
What area on the N/Z graph represents the beta plus decay?
The area below the line of stable nuclei
How do you plot the different decay modes on an N/Z graph
Beta plus = N+1, Z-1
Beta minus = N-1, Z+1
Alpha = N-2, Z-2
How can the radius of the nucleus be estimated from data from a scattering experiment?
For one layer:
P(Back scattering) = Area of nucleus / Area of atom
Overall:
P(Back scatrering) =no. layers * (rN^2 / rA^2)
Pi cancels and rearrange
What is the distance of closest approach?
The alpha particle slows down too rest as it approaches the like charged Au as all of the kinetic energy is transferred to the electric potential energy.
How can the radius of the nucleus be estimated from electron diffraction data?
The DeBrogile wavelength is comparable too the nuclear diameter. Plot the angles of diffraction of a high speed electron through a grating/crystal . Only one clear minimum and intensity is never 0. can calculate D/r using the minimum angle.
What is the relationship between the nuclear radius and mass number?
nuclear radius = some constant * (mass number)^1/3
r = r0 * (A)^1/3
where mass number = P+N
can plot using linear regression log(r) against log(A) where the gradient is equal too 1/3
What is an empirical law?
A law based upon data and not theory
How does R = R0 A1/3 imply that the density of nuclear matter is constant?
The nuclear density is the mass per unit volume of the nucleus.
3u / (4πr0^3) where u and r0 are constant
Mass of nucleus = Atomic mass number * Atomic mass unit = A*u
Volume of the nucleus = Volume of a sphere 4/3πr^3
If you substitute the equation in place of r, the density is equal too 3u / (4πr0^3)
What is the equation for nuclear density?
3u / (4πr0^3) where u= atomic mass unit and r0 is some constant
What is the mass defect of a nucleus?
Δm = Total initial mass - final mass
The energy released in a radioactive decay comes from the mass products being very slightly less than the mass of the start nucleus.
What is the binding energy?
The amount of energy required to split a nuclei’s constituents infinitely far apart from each other. (Protons and neutrons)
How do you calculate the binding energy?
mass defect = The total mass of the individual nucleus (calculated using the N and Z) - mass of the nucleus (normally given)
BE = mass defect * c^2
Energy of a decay
E= Δmc^2
What is the atomic mass unit?
1/12th of the mass of a carbon 12
What is the mass of the neutrino equal too?
Always taken as 0
What does it mean when the decay has a negative mass defect?
The Δenergy will be negative and so the atom requires energy to undergo its decay.
What happens too the binding energy if the atomic mass of the nucleus increases?
The binding energy increases
Describe the binding energy per nucleon too nucleon number graph
The graph increases too and levels out at 8.5 MeV for the heaviest naturally occurring elements (Fe 56 or Ni 62) then decreases back down too 7 MeV. The region with a nucleon number less than Fe 56, before it, undergoes fusion due too their lower BE’s and electrostatic forces repelling one another. The region above Fe 56 tends too undergo fission due too it requiring more energy (stable).
What is nuclear fission?
Splitting of a heavy nucleus into two lighter daughter nuclei. Typically A> 220. Can be spontaneous, though rare, or induced.
What is nuclear fusion?
Two small light nuclei fuse together too form a heavier nucleus. Requires extreme pressures and temperatures too overcome the repulsive forces.
Where does most nuclear fusion occur?
Stars
Analysing a BE against Atomic number graph
Fission of a heavy nucleus produces nuclei with higher BE per nucleon and is more stable. Stops around iron as otherwise fission requires energy and doesn’t emit any. 130-230 A
Fusion of two small nuclei results in the formation of daughter nuclei with a higher BE per nucleon. 0-60 A
What is a fissile material?
Material that can sustain a chain reaction of fission.
What is a thermal neutron?
A neutron in thermal equilibrium with its environment and is slow moving.
What is induced fission?
A stable nucleus splits into small nuclei due to the absorption of a slow-moving neutron.
What is a chain reaction and how is it sustained?
During fission, neutrons are ejected from the nucleus, which in turn, can collide with other nuclei which triggers a cascade effect
This leads to a chain reaction which lasts until all of the material has undergone fission, or the reaction is halted by a moderator. The average number of neutrons released in each chain is enough too sustain any others going forward.
What is the critical mass?
Mass required to sustain a chain reaction
What are the fuel rods made of?
Enriched uranium
What is “Enriched” uranium?
The percentage of uranium 235 in naturally occurring uranium is artificially increased.
What is the purpose of control rods and what are they made of?
Control rods absorb neutrons and the further they are lowered into the reactor, more neutrons are absorbed and the rate of fission decreases. Made of Boron.
What is the purpose of a moderator, What are they made from?
Slow the neutrons produced in fission events, made from graphite, heavy water or water.
How do moderators work?
The fast moving neutrons collide with the moderator molecules and some of the KE of the neutrons is transferred which can be modelled as an elastic collision. The kinetic energy is conserved.
Why do molecules with Lower A’s make better moderators?
The collision is elastic and by modelling this collision. (A-1)/(A+1) * u = Vneutron
Describe the process of nuclear waste treatment
Leave spent fuel rods in cooling ponds for (months/years) to absorb excess heat and block all beta minus and some gamma.
Recycle any unused fissile material.
Vitrify waste (liquid –> glass)
Stored by placing in steel or lead containers deep underground (block gamma)
Name three safety features of a nuclear reactor
Thick steel vessels around the core blocking beta minus
Concrete shields blocking gamma
Control rods can be lowered completely too stop all further fission
What is the most stable/Heavy element?
Iron
Where do the fission fragments appear on a BE per nucleon / A graph?
Symmetrical around half of the nucleon number of the fission fuel (parent nucleus) so that the sum their nucleon numbers = the parents nucleon number.
Artificial radioactive nuclides are manufactured by placing naturally-occurring nuclides in a
nuclear reactor. They are made radioactive in the reactor as a consequence of bombardment by…
Neutrons
What is a radioactive isotope?
An isotope that releases energy in the form of particles (mass) or EM radiation to become more stable
