Section 12- Nuclear Physics Flashcards
What did the alpha particle scattering experiment enable?
The calculation of the size of the nucleus
What was the set-up for the alpha scattering experiment?
- monoenergetic alpha particles were fired at a thin gold foil
- zinc sulphide screen flashed when alpha particles hit it
- vacuum
What was the screen in the scattering experiment made out of?
Zinc sulphide
What were the paths of the particles in the scattering experiment?
- most passed straight through
- some displayed a small deflection
- 1 in 10000 were deflected by angles > 90°
What did the results from the alpha scattering experiment show?
The atom must contain a small concentrated positive charge with mass
What charge do alpha particles in the scattering experiment have?
Positive
In nuclear physics, what can Coulomb’s law be used to calculate?
The distance between two particles when they have an electrostatic force
In the scattering experiment, at what point will an alpha particle scatter back?
When its kinetic energy equals its electric potential energy
What law can be used to find the distance between two charged particles?
Coulomb’s law f= (8.99X10 9 ) q1q2/r 2
What does 1u mean?
One atomic mass unit
Does the strong force only affect adjacent nucleons?
Yes
Approximately, how many times bigger is the diameter of a uranium atom than its nucleus?
23,000 x
Approximately, how many times bigger is the diameter of a hydrogen atom than its nucleus?
145,000 x
What does it mean, that radioactive decay is spontaneous?
The rate cannot be changed by heating/cooling, dissolving in acid etc.
What will NOT change the rate of radioactive decay?
- heating/cooling
- dissolving in acid
- applying pressure
- applying a magnetic or electric field
Is radioactive decay continuous?
No
What happens in alpha decay?
A nuclei decays into a new nuclei and emits an alpha particle
What happens in beta minus decay?
A nuclei decays into a new nuclei by changing a neutron into a proton and electron
What happens in gamma decay?
After alpha or beta decay, surplus energy is sometimes emitted
Is the atom changed when it emits gamma?
No
What are the properties of gamma radiation?
High frequency, short wavelength. move at 3x10^8 ms. stopped by lead
What is the most ionising type of radiation?
Alpha
Why can alpha only travel a few cm in air?
It is highly ionising
Why do alpha particles from the same source all travel the same distance in air?
They have the same energy if they are from the source, so they travel the same distance before they have lost all their energy
Why do alpha particles ionise air?
To gain the electrons they need to become a helium atom
What can alpha radiation be blocked by?
A sheet of paper or few cm of air
What can beta radiation be blocked by?
A few mm of aluminium
What can gamma radiation be blocked by?
A few cm of lead
Why does each beta particle travel a different distance?
It has a range of energies
Why can gamma rays travel large distances?
They barely interact with air molecules
Why does gamma radiation intensity decrease?
They spread out
intensity ↓ as beam area ↑
What equation shows how the intensity of gamma rays varies with distance?
I = k / x2
Brief outline of an experiment to verify the 3 types of radioactive emission?
- measure activity of background radiation
- place geiger count within 2cm of source then measure count rate again
- deduct backgound count - does reading change when tube is moved to distance of 10cm?
- leave tube at this distance and place aluminium instead - count rate ↓ then beta
- repeat with lead sheet - count rate should drop to background count
What are some sources of background radiation?
- radon gas from ground
- human body and food
- rocks
- cosmic rays
- artificial sources (e.g. medical, nuclear power and weapons)
How should sources of radiation be stored?
In a lead box
What are some steps for safe handling of radioactive sources?
- use handling tool e.g. tongs
- use lowest activity source possible
- keep 2m away from others
What are alpha particles used in?
Smoke alarms
Why are alpha particles used in smoke alarms?
Allow current in air to flow, but don’t travel very far
How do smoke alarms work?
- alpha particles ionise many atoms and lose energy quickly
- allow current to flow
- when smoke present, alpha particles can’t reach detector and this sets alarm off
What is beta radiation used in?
Control thickness of sheets of material e.g. paper, Al foil or steel
What is gamma radiation used in?
- radioactive tracers - help diagnose patients without need for surgery
- treatment of cancerous tumours
What law does gamma follow?
Inverse square
What is the activity of a source?
The average number of undecayed nuclei which decay per second
If a source has one nucleus decay per second, what is its activity?
1 Bq
What is the unit for activity?
Bq = Becquerels
What is the symbol for activity?
A
What is the decay constant?
The probability of a given nucleus decaying in the next second
What is the symbol for the decay constant?
λ
the equation for activity is found on the data sheet. what do the symbols stand for?
A=λN
A=λN
a= activity (bq^-1)
λ= decay constant
N= number of nuceli
What does A stand for in A=λN?
Activity (Bq)
What does λ stand for in A=λN?
Decay constant (s-1)
What does N stand for in A=λN?
Number of undecayed nuclei
What is half life?
The time taken for half of the radioactive nuclei to decay into other nuclei
Graphically, what does radioactive decay look like?
An exponential curve
The radioactive decay equations are given on the data sheet. what do the symbols stand for?
N = N₀e^-λt A = A₀e^-λt
N = N₀e^-λt and A = A₀e^-λt N=number of molecules A= activity t= time seconds decay constant
What does N₀ mean in N = N₀e^-λt?
Initial number of radioactive nuclei present
What does N mean in N = N₀e^-λt?
Number of radioactive nuclei remaining at time t
What does A₀ mean in A = A₀e^-λt?
The initial activity of the sample
What does A mean in A = A₀e^-λt?
The activity at time t
What is Avogadro’s constant used for?
To calculate the number of atoms/nuclei that are present in a known mass of an element
What is the equation using Avogadro’s constant?
N = mNₐ / M
How is the equation for half life (T₁/₂ = ln2/λ)?
A = A₀e^-λt
at half life, A = A₀/2
A₀/2 = A₀e^-λt₁/₂
1/2 = e^-λt₁/₂
take natural logs: ln2 = λt₁/₂
How does carbon dating work?
- whilst living, plants take in CO2
- small fraction of carbon atoms is radioactive C-14
- ratio of C-14 to C-12 increases with time
- enables age of plant to be calculated
What does C-14 decay to in B- decay?
N-14, electron and an anti-neutrino
What does C-14 decay to in B+ decay?
N-16, positron and a neutrino
Equation for electron capture of C-14?
C-14 + e- → B-14 + neutrino
What counts as ‘light’ isotopes?
With proton number from 0-20
For light isotopes on the N-Z (neutron-proton) graph, what pattern do they follow?
Follow the straight line N=Z
What happens to stable nuclei as Z number increases beyond about 20?
They have more neutrons than protons
Why do larger nuclei have more neutrons than protons?
Extra neutrons help to bind nucleons together without introducing the repulsive electrostatic forces than protons would
What type of nuclei are often alpha emitters?
With proton number beyond about 60 (but most with > 80p and 120n)
Why are very large nuclei, with more neutrons than protons, often unstable?
Strong nuclear force between nucleons is unable to overcome the electrostatic force of repulsion between the protons
In a N-Z graph, where do B- emitters lie?
To the left of the stability belt
Why, on an N-Z graph, do B- emitters lie to the left of the stability belt?
These isotopes are neutron rich
How do the nuclei to the left of the stability belt on an N-Z graph become more stable?
Neutron rich, so they convert a neutron to a proton and electron- beta - decay
In a N-Z graph, where do B+ emitters lie?
To the right of the stability belt
Why, on an N-Z graph, do B+ emitters lie to the left of the stability belt?
These isotopes are proton rich
How do the nuclei to the right of the stability belt on an N-Z graph become more stable?
Proton rich, so they convert a proton to a neutron and positron
On an N-Z graph, which region does electron capture take place in?
To the right of the stability belt
On an N-Z graph, what does electron capture lie in the same region as?
B+ emission
On an N-Z graph, where does a nucleus that emits an alpha particle move to?
Moves diagonally downwards to the left
On an N-Z graph, where does a nucleus that emits a B+ particle move to?
Moves diagonally upwards, left
On an N-Z graph, where does a nucleus that captures an electron move to?
Moves diagonally upwards
On an N-Z graph, where does a nucleus that emits a B- particle move to?
Moves diagonally downwards, right
What is the technetium generator used for?
In hospitals, to produce a source which emits gamma radiation only
What is a metastable state?
A long-lived excited state in radioactive nuclei
In the technetium generator, how is Tc-99 formed?
- Tc-99 forms in an excited state after alpha/beta emission
- it stays in the excited state long enough to be separated from its parent isotope
- decays to ground state by gamma emission
What is the half life of Technetium-99?
6h
Is the Tc-99 used in technetium generators in the ground state?
No
What state is the Tc-99 used in technetium generators?
Metastable
What are the uses of Tc-99 in the metastable state?
Diagnosis;
- monitoring blood flow
- gamma camera - image internal organs and bones
When might an unstable nucleus emit gamma radiation?
When the ‘daughter’ nuclei is formed in an excited state after it emits an alpha or beta particle or undergoes electron capture
What is binding energy?
The energy required to separate an atom into its constituent parts
How can it be shown that Ca has binding energy?
- 20p, 20e, 20n
- total mass of protons, neutrons and electrons is 40.34u
- however Ca has a mass of 39.96u
- use E=mc² to calculate binding energy
How would you calculate the binding energy of an atom?
- add up masses of constituent parts
- take away mass on periodic table
- multiply mass difference by unified mass constant
- E=mc² in J
- change to MeV
What does a graph of binding energy per nucleon against nucleon number reveal?
The stability of the elements
On a graph of binding energy per nucleon against nucleon number, which are the most stable elements?
Those with a nucleon number around 56 Fe
Which type of elements release energy from fusion versus fission?
- smaller nucleon number - fusion
* high nucleon number - fission
Why do we know energy is released in fusion?
Binding energy per nucleon increases. Mass defect is greater. Energy has been released
Why do we know energy is released in fission?
As a heavy nucleus split binding energy of each fragment is greater. Mass defect is greater therefore energy has been released
What is fusion?
The process by which light nuclei join together forming heavier nuclei
Where does fusion happen?
In stars
What temperatures are required for fusion?
Above 8 million K
At 8 million K for fusion, how will positive nuclei be?
In a plasma, moving at very high speeds
When, in fusion, will nuclei fuse?
When they overcome the electrostatic repulsion
What happens, in fusion, after nuclei overcome the electrostatic repulsion?
The strong nuclear force holds them together
What is induced nuclear fission?
The process by which energy is released when a radioactive isotope is forced to split
What is used in induced nuclear fission and why?
Uranium 235 - long half life and abundance mean it is found in large quantities
How is nuclear fission undergone?
The radioactive nucleus absorbs a slow neutron, causing it to become unstable and split
Why is energy released in induced nuclear fission?
Due to change in mass
What does the chain reaction that is nuclear fission consist of?
- when a nucleus is split, more neutrons are released
- these can then split other uranium nuclei
- the process keeps going
In induced nuclear fission, why do neutrons need to be slowed down?
Or they will bounce off the (uranium) nuclei
In induced nuclear fission, what are neutrons slowed down using?
A moderator
In induced nuclear fission, why do extra neutrons need to be absorbed?
So the reaction stays at a constant rate
In induced nuclear fission, how are extra neutrons absorbed?
Using control rods
What is the critical mass of a fuel?
The minimum mass required to establish a self-sustaining chain reaction
What does the reactor core contain?
- fuel rods
- control rods
- coolant
What is the coolant in a nuclear reactor?
Water at high pressure
What is the reactor core connected to in a nuclear reactor?
A heat exchanger, via steel pipes
What is function of the control rods?
To absorb neutrons
What does the depth of the control rods control?
The number of neutrons in the core
What happens if the control rods are pushed in further?
They absorb more neutrons so that the number of fission events per second is reduced
What condition must be true, in a nuclear reactor, for a chain reaction to occur?
The mass of the fissile material (e.g. U-235) must be greater than a minimum mass (the critical mass)
Why does the mass of the fissile material need to be greater than the critical mass for a chain reaction to occur?
- some fission neutrons escape form the fissile material without causing fission
- if mass of fissile material < critical mass, too many fission neutrons escape as SA to mass ratio is too high
What are the safety features of nuclear reactors?
- reactor core is a thin steel vessel
- core is in a building with thick concrete walls
- every reactor has an emergency shut down system
- the sealed fuel rods are inserted and removed from the reactor by remote handling devices
How is the reactor core being a thick steel vessel a safety feature?
- to withstand high pressure and temperatures in the core
* absorbs beta emission and some gamma radiation and neutrons from the core
How is the reactor core being in a building with thick concrete walls a safety feature?
Absorb neutrons and gamma radiation that escape from the reactor vessel
How is every reactor having an emergency shut-down system a safety feature?
Control rods are inserted completely into the core to stop fission when needs be
How is radioactive waste categorised?
High, intermediate or low level, depending on its activity
Example of high level radioactive waste?
Spent fuel rods
How are spend fuel rods stored (high level waste)?
- stored underwater in cooling ponds for a year as they continue to release heat
- then stored in sealed containers in deep trenches in Sellafield
How is intermediate level radioactive waste stored?
Sealed in drums that are encased in concrete then stored in special buildings with walls of reinforced concrete
How is low level radioactive waste stored?
Sealed in metal drums and buried in large trenches
Examples of low level radioactive waste?
Lab equipment and protective clothing
What does 1 u equal in MeV?
931.5 MeV
Describe how ideas atoms have changed over time.
- The idea of atoms has been around since the time of Ancient Greeks -> Proposed by Democritus
- In 1804, John Dalton suggested that atoms couldn’t be broken up and each element was made of a different type of atom
- Nearly 100 years later, JJ Thomson showed that electrons could be removed from atoms
- Thomson suggested that that atoms were spheres of positive charge with negative electrons in them like a plum pudding
- Rutherford suggested the idea of a nucleus - that atoms did not have uniformly distributed charge and density
What was the original model for atom structure?
Plum pudding model
Describe the plum pudding model.
Atoms are made of positive charge with electrons stuck in them like plum pudding.
Who suggested an alternative to the plum pudding model?
Rutherford (and Marsden)
Which experiment showed the existence of a nucleus in atoms?
Rutherford scattering
Describe the Rutherford scattering experiment.
- Beam of alpha particles from radioactive source is fired at thin gold foil.
- Circular, fluorescent defector screen surrounding gold foil (and the alpha source) was used to detect alpha particles deflected at any angle.
- Most of the alpha particles went straight through the foil, but a small proportion were deflected by a large angle (up to 90°).
Why is the foil used very thin?
Ideally 1 atom thin.
Since the gold foil was very thin, it was thought that the alpha particles could pass straight through it, or possibly puncture the foil.
(So it doesn’t have many interactions.)
If the plum pudding model of atomic structure were true, what would you expect to see in the Rutherford scattering experiment?
The flashes on the screen/detector should have been seen within a small angle of the beam.
This is because the alpha particles (positively charged) would be deflected by a small amount by the electrons.
Describe the main conclusions of the Rutherford scattering experiment.
Atoms must have a small, positively-charged nucleus at the centre:
• Most of the atoms must be empty space, since most of the alpha particles passed straight through the foil
• Nucleus must have a large positive charge, since positively-charged alpha particles were repelled and deflected by a large angle
• Nucleus must be small, since most of the alpha particles passed straight through the foil (very few deflected by > 90°)
• Most of the mass must be in the nucleus, since positively-charged alpha particles were repelled and deflected by a large angle by the nucleus.
What does the Rutherford scattering experiment tell us about the empty space in the atom?
Most of the atom must be empty space, since most of the alpha particles passed straight through the foil
What does the Rutherford scattering experiment tell us about the charge of the nucleus?
Nucleus must have a large positive charge, since positively-charged alpha particles were repelled and deflected by a large angle
What does the Rutherford scattering experiment tell us about the size of the nucleus?
The nucleus is small, since most of the alpha particles passed straight through the foil
What does the Rutherford scattering experiment tell us about the distribution of mass in the atom?
Most of the mass must be in the nucleus, since positively-charged alpha particles were repelled and deflected by a large angle
How did Rutherford and Kay discover EVIDENCE for the existence of a neutron?
Fired high energy alpha particles at different gases.
Thought there was only protons in the nucleus.
If there was only protons, you’d expect high mass (massive) nuclei to have very high charges (compared to lower mass nuclei).
But the charges observed were lower than expected.
Must be another part in the nucleus: he called in “proton-electron doublet” - it was actually the neutron.
When an alpha particle is fired at a nucleus, what can be assumed at the point at which it’s direction of travel is reversed?
Initial kinetic energy = Electric potential energy
(This is because all of the initial kinetic energy that the alpha particle was fire with has been converted into potential energy)
What does an alpha particle reaching it’s closest approach to the nucleus look like?
What is r?
R = shortest distance between nucleus and alpha particle
Describe how you can estimate the closest approach of a scattered particle to a nucleus, given the initial kinetic energy.
- Equate the initial kinetic energy that the particle was fired with with the potential energy of the particle at the turning point. This is from Coulombs law.
- Initial kinetic energy = Electric potential energy
- Ek = Qgold x Qalpha / 4πε₀r
- Calculate r
Give the equation used to find the closest approach of an alpha particle to the a gold nucleus.
Ek = Qgold x Qalpha / 4πε₀r
Where:
• Ek = Kinetic energy (J)
• Qgold = Charge of the gold nucleus (C)
• Qalpha = Charge of the alpha particle (C)
• ε₀ = 8.85 x 10^-12 F/m
• r = Distance from centre of nucleus or Distance of closest approach (m)
(NOTE: Not given in exam)
What is the charge of a nucleus?
+Ze
Where:
• Z = Proton number (Number of Protons)
• e = Size of charge of an electron
How can the radius of a nucleus be estimated using scattered particles?
- Calculate an estimate for the closest approach of an alpha particle to the nucleus
- This is the maximum possible radius
An alpha particle with initial kinetic energy of 6.0MeV is fired at a gold nucleus. Estimate the radius of the nucleus by finding the closest approach of the alpha particle to the nucleus.
- Initial kinetic energy = 6.0 x 10^6 MeV = 9.6 x 10^-13 J
- This equals electric potential energy, so:
- 9.6 x 10^-13 = Qgold x Qalpha / 4πε₀r
- 9.6 x 10^-13 = (79 x 1.60 x 10^-19) x (2 x 1.60 x 10^-19) / 4π x 8.85 x 10^-12 x r
- r = 3.8 x 10^-14 m
- This is a maximum estimate for the radius.
What are the two methods of estimating nuclear radius and which is better?
- Closest approach of scattered particle
- Electron diffraction
Electron diffraction gives more accurate values.
Why are electrons used to estimate nuclear radius?
They are leptons, so they do not interact with the strong nuclear force.
We know very little about the strong nuclear force.
Why can electron beams be diffracted?
Like other particles, they show wave-particle duality and have a de Broglie wavelength.
They are also used because they are lighter = better to accelerate
What is the equation for the de Broglie wavelength of electrons AT HIGH SPEEDS?
λ ≃ hc / E
Where: • λ = de Broglie wavelength (m) • h = Planck constant = 6.63 x 10^-34 • c = Speed of light in a vacuum (m/s) • E = Electron energy (J)
(Note: Not given in exam, but can be derived!)
Derive the equation for the de Broglie wavelength of electrons at high speeds.
• The speed of high-energy electrons is almost the speed of light, c. • So λ = h / mv = h / mc • Since E = mc²: • λ = hc / E (can't it just be E=hf??)
In order to use electron diffraction to determine nuclear radius, what must the electrons’ energy be and why?
High, because the wavelength must be very small in order for diffraction to be observed due to the tiny nucleus.
In order to use electron diffraction to determine nuclear radius, of what order must the electrons’ wavelength be?
10^-15
When a beam of high-energy electrons is directed onto a thin film of material, what is seen?
A diffraction pattern on a screen behind it.
What is the equation for the first minimum on the diffraction pattern caused by high-energy electron diffraction?
sinθ ≃ 1.22λ / 2R
Where:
• θ = Angle from normal (°) or scattering angle
• λ = de Broglie wavelength
• R = Radius of nucleus the electrons have been scattered by (m)
(Note: Not given in exam and can’t be derived!)
Or Rsinθ ≃ 0.61λ
Describe how electron diffraction can be used to estimate nuclear radius.
- Beam of high-energy electrons is directed at a thin film in front of a screen
- λ = hc / E
- Diffraction pattern is seen
- Look at the first minimum:
- sinθ = 1.22λ / 2R
A beam of 300 MeV electrons is fired at a piece of thin foil, and produces a diffraction pattern on a fluorescent screen. The first minimum of the diffraction pattern is at angle of 30° from the straight-through position. Estimate the radius of the nuclei the electrons were diffracted by.
- E = 300 MeV = 4.8 x 10^-11 J
- λ = hc / E = 6.63 x 10^-34 x 3.00 x 10^8 / 4.8 x 10^-11 = 4.143 x 10^-15 m
- R = 1.22λ / 2sinθ = 1.22 x 4.143 x 10^-15 / 2sin(30) = 5.055 x 10^-15 m = 5 fm
Describe the diffraction pattern for a beam of high-energy electrons directed at a thin foil.
Similar to light source shining through circular aperture:
• Central bright maximum (circle)
• Surrounded by other dimmer maxima (rings)
• Intensity of maxima decreases as angle of diffraction increases
This shows intensity for each maximum:
Remember to practise drawing out the graph for relative intensity against the angle of diffraction for electron diffraction.
Pg 156 of revision guide
What is the approximate radius of an atom?
0.05nm
5 x 10^-11 m
What is the radius of the smallest nucleus?
1fm
1 x 10^-15 m
What are nucleons?
Protons and neutrons
What is the symbol for nucleon number?
A
How do we estimate the size of a molecule
Number of atoms x size of one atom
Describe the graph of radius of nucleus against nucleon number.
• Starts at origin
• Curve, starting with strep gradient and then becoming shallower
As more nucleons are added, the nucleus gets bigger
What equation relates nucleon number to atomic radius?
R = R₀A^1/3
Where:
• R = Radius of nucleus
• R₀ = Constant = 1.4fm
• A = Nucleon number
If R is radius of nucleus and A is amount of nucleons, what is R₀?
radius of 1 nucleon
What is A when talking about radius of a nucleus?
A = Nucleon number
Not actvity
How can the relationship between radius of nucleus and nucleon number be demonstrated?
- Plot R against A^1/3
- This gives a straight line
- So R ∝ A^1/3
Describe the graph of R (radius of nucleus) against A^1/3 (nucleon number).
- Straight line with positive gradient
* Goes through origin
What evidence shows that density of nuclear matter is constant, regardless of the number of nucleons?
What stops gamma radiation?
- Many cm of lead
* Several m of concrete
Describe how you can investigate the penetrating power of different radiation types.
1) Record the background radiation count rate when no source is present.
2) Place an unknown source near to a Geiger counter and record the count rate.
3) Place a sheet of paper between the source and Geiger counter. Record the count rate.
4) Repeat step 2 replacing the paper with 3mm thick aluminium.
5) Count rate - background rate = corrected count rate
6) Look at when the corrected count rate significantly decreased. From this, work out what kind of radiation is emitted.
What are some sources of background radiation?
1) The air - radioactive radon gas from rocks (alpha)
2) Ground and buildings
3) Cosmic radiation
4) Living things
5) Man-made radiation - medical e.g. x-rays, internal e.g. food, nuclear waste, fallout, air travel
What is the equation for the intensity of gamma radiation at a given distance from the source?
I = k / x²
Where:
• I = Intensity (counts/sec)
• k = Constant
• x = Distance from the source (m)
How can you investigate the inverse square law for radioactive sources?
1) Set up a Geiger counter with the tube at the end of a metre ruler.
2) Turn on the Geiger counter and take a reading of the background radiation count rate (in counts/sec). Do this 3 times and take an average.
3) Place the radioactive source at a distance d from the Geiger tube.
4) Record the count rate at that distance. Do this 3 times and take an average.
5) Repeat this at distances 2d (doubles), 3d (triples etc), 4d, etc.
6) Put away the source immediately afterwards.
7) Correct each average reading for background radiation. Plot a graph of corrected count rate against distance of the counter from the source. You should see that as the distance doubles, the corrected count rate drops to a quarter.
What does the graph for corrected count rate from a radioactive source against distance look like?
1/x² graph
Describe the graph for N against t (for a radioactive source).
(Also A against t)
- Starts at a positive y-intercept
- The gradient becomes gradually less negative
- The x-axis is an asymptote
- Exponential decay, so the time to halve N is always the same
How can you show that a graph is exponential decay?
• Find the time for the first y value (y-intercept when t=0) to halve.
• Draw a horizontal line from this point to the curve, then draw down to the x-axis.
Repeat this for a quarter of the first y value, then an 8th if you can.
The distance between each line you draw is the half life.
• If they are the same, then this is exponential decay.
How can the half-life of a radioactive isotope be found from the N against t graph (or A against t)?
- Read of the count rate when t = 0
- Go to half the original value and draw a horizontal line to the curve then down to the x-axis
- Read off the t value at this point
- Repeat these steps for a quarter of the original value
How do you derive the equation for half life?
when t =T(1/2), the number of undecayed nuclei has halved, so N=(1/2)N₀.
The N equation becomes (1/2)N₀ = N₀e^(-λT(1/2))
then….
What does a graph of: Number of unstable nuclei remaining, N, against time, t, look like?
What does a graph of ln(Number of unstable nuclei remaining) against time look like?
What is the Y intercept?
How can you form a straight line equation from N = N₀e^(-λt)?
Describe the practical you would use to represent nuclear decay with dice?
How can you find the number of atoms with the molar mass and total mass?
Total mass / molar mass = number of moles
Number of moles x Avogadro’s constant = number of atoms
What does a graph of activity against time look like?
Same as N-t
When can it be difficult to get a reliable age from carbon dating
Describe the stability graph for nuclei.
- Number of neutrons (N) is plotted against number of protons (Z)
- N = Z dotted line is added for reference. It goes diagonally to the top right, through the origin.
- Line of stability starts along the N = Z line, then curves upwards away from it.
- Area above line of stability is β⁻-emitters. It gets gradually wider.
- Area below line of stability is first β⁺-emitters and then α-emitters. It gets gradually wider. The α-emitter area starts at earlier on the lower side of the area.
When will the number of neutrons overtake the number of protons in an atoms
After 20 neutrons/protons in the atom
When an alpha particle is emitted, what happens to the nucleon number and proton number?
- Nucleon number -> Decreases by 4
* Proton number -> Decreases by 2
What is the general equation for an alpha decay?
What happens in β⁻ decay?
A proton is changed into a neutron, while an electron and an electron antineutrino are emitted from the nucleus.
What is the general equation for Beta minus decay?
What happens in beta plus decay?
Proton rich isotopes.
Proton changes into a neutron.
(Proton number decreases by 1, nucleon number = same).
A nucleus ejects a beta plus particle.
Electron neutrino emited
What is the general equation for beta plus decay?
What do gamma photons being able to emit two POSSIBLE energies show?
Two possible gamma photon energies proves that the nucleus can exist in at least two excited states
What 6 things can you acknowledge from this?
- 8% of time it forms to the ground state (Radon).
- 2% of the time it forms to the excited state.
Emits alpha decay.
Radium-226 is unstable.
Emits gamma to de-excite.
Decays to Radon-222
What is the general equation of electron capture?
What is the symbol for beta plus particle (with Z and A number)?
What is the symbol for beta minus particle (with Z and A number)?
Describe the energy level diagram for an alpha emission.
- Horizontal line for the unstable isotope
- Arrow going to the bottom right, with a shallow gradient (labelled alpha with the change in energy)
- Horizontal line with the product
Describe the energy level diagram for a beta emission followed by a gamma emission.
- Horizontal line for the unstable isotope
- Arrow going to the bottom right, with a steep gradient (labelled beta with change in energy)
- From this, an arrow going vertically down (labelled gamma with change in energy)
- Horizontal lone with the product
What quantities are conserved in nuclear reactions?
- Energy
- Momentum
- Charge
- Nucleon number
What happens when making a low energy neutron enter a U-235 nucleus?
Describe the structure of a nuclear reactor.
- Fuel rods in centre
- Control rods are inserted partly between the fuel rods
- Moderator (water) surrounds fuel and control rods (closed system)
- Pump pushes water through pipes in a heat exchanger
- Cool water is pumped into the heat exchanger and steam is pumped out (to a turbine)
- Concrete case surrounds everything
Remember to practise drawing out a diagram of a nuclear reactor.
Pg 166 of revision guide or pg 397 of textbook
What is the nuclear fusion reaction that happens in the Sun?
Hydrogen nuclei fuse in a series of reactions to form helium.
Why does nuclear fusion require a lot of energy to achieve?
- All nuclei are positively charged, so there is an electrostatic force of repulsion between them.
- A large amount of energy is required to overcome this repulsion so that the nuclei get close enough for the strong interaction to hold the nuclei together.
Given energy is released in a nuclear decay, what can we say about the mass before the decay compared to after the decay?
Mass after decay is ALWAYS less.
What does Einstein’s equation state?
Mass and energy are equivalent:
How can you visualise binding energy
Describe the graph of average binding energy per nucleon against nucleon number.
- Starts at nucleon of 2 (hydrogen) and a very small average binding energy
- Increases rapidly and then begins to plateau
- Peak is at Fe-56
Describe why fusion and fission release energy in terms of binding energy.
In both, the average binding energy per nucleon increases, so energy must have been released.
On the graph, the peak is where binding energy per nucleon is the highest. From left of this, fusion occurs to gain a higher binding energy per nucleon. From the right of the peak, fission occurs to gain a higher binding energy per nucleon.
In fusion and fission, mass is converted into energy so mass of the the product is less than the reactant, what increases in the product?
The product will always have a higher binding energy per nucleon.
Where does fusion happen on a graph of average binding energy per nucleon against nucleon number?
To the left of Fe-56.
Where does fission happen on a graph of average binding energy per nucleon against nucleon number?
To the right of Fe-56.
What can the average binding energy per nucleon graph be used for
To estimate the energy released in nuclear reactions.
How can you find the difference in mass with E=mc^2
