Section 12 - Nuclear Physics Flashcards
Describe how ideas about 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.)
To prevent the alpha particles been absorbed by the gold and so that they are only scattered once.
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 fired 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
In R = R₀A^1/3, what is the value of R₀?
About 1.4fm
Relatively speaking, what is the density of the nucleus like?
Huge
How does the volume of protons and neutrons compare?
It is about the same.
Do different nuclei have the same density?
Yes
What evidence shows that density of nuclear matter is constant, regardless of the number of nucleons?
Derive the equation for the density of a nucleus.
- p = mass / volume
- p = A x m(nucleon) / (4/3 x πR³)
- p = A x m(nucleon) / (4/3 x (R₀A^1/3)³)
- p = 3m(nucleon) / 4πR₀³ = Constant
(A = number of nucleons)
What is the equation for the density of a nucleus?
p = 3m(nucleon) / 4πR₀³ = Constant
Where:
• p = Density (kg/m³)
• m(nucleon) = Mass of a nucleon
• R₀ = Constant = 1.4fm
(Note: Not given in exam!)
What is the value of R₀?
1.4fm
What is the value for nuclear density?
1.45 x 10^17 kg/m³
What do we assume when calculating nuclear radius’?
Assume there are no gaps between nucleons.
Assume the nucleons are spherical.
(probably 1 more)
Nuclear density is much greater than atomic density (which is approximately between 10^3 and 10^15 kgm^3), what does this tell us about the structure of an atom?
Most of atom’s mass = in nucleus.
Nucleus = small compared to atom.
Atom = contains lots of empty space.
What type of nuclei are radioactive?
Unstable nuclei
What things can cause a nucleus to be unstable?
- Too many neutrons
- Not enough neutrons
- Too many nucleons altogether
- Too much energy
What is radioactive decay?
When an unstable nucleus releases energy and/or particles until it reaches a stable form.
Why are radioactive emissions also known as ionising radiation?
When a radioactive particle hits an atom, it can knock off electrons, creating an ion.
Is radioactive predictable?
No, it is random.
What are the 4 types of radioactive decay?
- Alpha
- Beta minus
- Beta plus
- Gamma
What makes up alpha radiation?
2 protons and 2 neutrons (helium nucleus)
What makes up beta-minus radiation?
Electron
What makes up beta-plus radiation?
Positron
What makes up gamma radiation?
Short-wavelength, high-frequency EM waves
What is the charge on an alpha particle?
+2
What is the charge on a beta-minus particle?
-1
What is the charge on a beta-plus particle?
+1
What is the charge on gamma radiation?
0
What is the mass of an alpha particle (in atomic mass units)?
4
What is the mass of an beta-minus particle (in atomic mass units)?
Negligible
What is the mass of an beta-plus particle (in atomic mass units)?
Negligible
What is the mass of an gamma radiation (in atomic mass units)?
0
What stops alpha radiation?
Paper, skin or few cm of air.
What stops beta-minus radiation?
3mm aluminium
What stops gamma radiation?
- Many cm of lead
* Several m of concrete
Why don’t beta plus have a range?
They almost immediately annihilate with electrons.
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.
For an alpha particle, describe the ionising power, speed, penetrating power and whether it is affected by a magnetic field.
- Ionising power = Strong
- Speed = Slow
- Penetrating power = Absorbed by paper or a few cm of air
- Affected by magnetic field
For a beta-minus particle, describe the ionising power, speed, penetrating power and whether it is affected by a magnetic field.
- Ionising power = Weak
- Speed = Fast
- Penetrating power = Absorbed by 3mm of aluminium
- Affected by magnetic field
For a beta-plus particle, describe the ionising power, speed, penetrating power and whether it is affected by a magnetic field.
Annihilated by electron - so virtually 0 range.
For a gamma ray, describe the ionising power, speed, penetrating power and whether it is affected by a magnetic field.
- Ionising power = Very weak
- Speed = Speed of light
- Penetrating power = Absorbed by many cm of lead or several m of concrete
- Not affected by magnetic field
How can a magnetic field show you the type of radiation?
Charged particles (alpha and beta) are deflected in a circular path.
Beta deflects more because it is lighter.
Positive charge goes one way, negative goes the other.
Curvature of path can show mass and charge
How can material thickness by controlled using radiation?
- A material is flattened as it is fed through rollers
- Radioactive source is placed on once side of the material and a radioactive detector is placed on the other
- The thicker the material, the more radiation it absorbs and prevents from reaching the detector
- If too much radiation is being absorbed, the rollers move closer together to make the material thinner (and vice versa)
Give a use of alpha particles.
Smoke alarms
Why do alpha particles not travel very far?
They are strongly positive so quickly ionise many atoms and lose their energy to the atom.
Why are alpha particles suitable for use in smoke alarms?
They allow current to flow, but have a short range.
When smoke is present, the alpha particles can’t reach the detector and this sets the alarm off.
When are alpha particles dangerous?
When they are ingested, because they cannot penetrate skin, but quickly ionise body tissues, causing damage.
Give a use of beta radiation.
Controlling the thickness of a material in production.
Compare the speed of alpha and beta particles.
Beta particles are faster
Compare the number of ionisations per mm in air for alpha and beta particles.
- Alpha - 10,000 ionisations per mm
* Beta - 100 ionisations per mm
Compare the danger between alpha and beta
Beta has lower mass and charge than alpha but can still ionise electrons.
Lower number of interactions (100 atoms per mm compared to 10,000 atoms per mm) means beta causes less damage to body tissues.
What are some uses of gamma rays?
- Radioactive tracers
* Treatment of cancerous tumours
Why is gamma used in medicine?
What does it prevent the use of?
Weakly ionising compared to alpha and beta = do less damage to body tissue.
Prevents the need of surgery to help diagnose patients.
How can gamma rays be used as a tracer in medicine?
- Radioactive source with a short half-life is injected or eaten by patient
- Detector (e.g. a PET scanner) is then used to detect emitted gamma rays
Why is a short half life important?
Prevents prolonged radiation exposure - can’t effect other patients when the diagnosis is over
How can gamma rays be used to treat cancerous tumours in medicine?
- Rotating beam of gamma rays is used to kill tumour cells.
* This lessens the effect of the radiation on healthy cells nearby the tumour.
What are some short and long term effects of exposure to gamma radiation?
SHORT: • Tiredness • Reddening of skin • Soreness of skin LONG: • Infertility
Why do medical staff use shielding (for example staff leaving the room)?
To keep exposure time to a minimum - to reduce the risks of radioactive source
In experiments, how is background radiation accounted for?
Measure background radiation (3 readings with a Geiger counter, then find average) separately and subtract it from your measurements.
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
Why is the air a source of background radiation?
- It contains radon gas released from rocks
* Radon is an alpha emitter
Why is the ground and buildings a source of background radiation?
All rock contains radioactive isotopes
Why is cosmic radiation a source of background radiation?
- Cosmic rays are particles from space
* When they collide with the upper atmosphere, they produce nuclear radiation
Why are living things a source of background radiation?
- All plants and animals may contain C14
* They also contain other radioactive materials
Why is man-made radiation a source of background radiation?
Medical and industrial sources give off some radiation.
medical e.g. x-rays, internal e.g. food, nuclear waste, fallout, air travel
Why type of radiation does radon gas emit?
Alpha particles
What are cosmic rays?
Particles (mostly high-energy protons) from space
How does the intensity of gamma radiation change with distance from the source?
- It decreases by the square of the distance from the source
* I = k / x²
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)
What sort of equation is the equation that relates the intensity of gamma radiation at a given distance from the source?
Inverse square law
Does the inverse square law apply for all radioactive sources?
Yes
How can the inverse square law for radioactive source be applied to safety?
The radioactive source becomes significantly more dangerous the closer you hold it to your body, so keeping a large distance from the source is important.
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.
When investigating the inverse square law for a radioactive source, what is it important to remember?
Correct each reading for background radiation.
What does the graph for corrected count rate from a radioactive source against distance look like?
1/x² graph
What precautions should you take when investigating a gamma source?
Hold source away from body (more dangerous = closer = inverse square law) when transporting.
Use long handling tongs to minimize radiation absorbed by the body.
Don’t use for too long - put away straight after use.
Put a sign on the door to warn people who are pregnant or at risk or just not involved in the experiment to stay away.
Do different isotopes decay at different rates?
Yes
Describe the randomness of radioactive decay?
Completely random
How can you find patterns in nuclear behavior?
Take a very large number of nuclei.
Will different samples of a particular isotope decay at different rates?
No, the same proportion of atomic nuclei will decay in a given time for isotopes (have different number neutrons and same protons).
Each unstable nucleus in the isotope has the same constant decay probability.
What is the activity of a radioactive sample?
The number of nuclei that decay per second.
Does the size of a radioactive sample affect its activity?
Yes - the activity is proportional to the size of the sample.
What is the difference between the rate of decay and the activity of a sample?
- Rate of decay - Proportion of atomic nuclei that decay in a given time
- Activity - Number of nuclei that decay each second
What is the unit for radioactive activity?
Becquerels (Bq)
What is 1 becquerel?
1 decay per second
What is the decay constant?
The probability of a given nucleus decaying per second.
What are the units for decay constant?
s^-1
A large value for the decay constant shows a … rate of decay.
Fast
In decay equations, what is N?
The number of unstable nuclei.
In decay equations, what is λ?
The decay constant
In decay equations, what is A?
The activity of the sample
What equation relates the activity of a sample to the number of nuclei?
A = λN
Where:
• A = Activity (Bq)
• λ = Decay constant (s^-1)
• N = Number of unstable nuclei
What is the equation for the rate of change of the number of unstable nuclei?
ΔN/Δt = -λN
Where:
• ΔN/Δt = Rate of change of the number of unstable nuclei (s^-1)
• λ = Decay constant (s^-1)
• N = Number of unstable nuclei
Derive ΔN/Δt = -λN.
- A = λN
- A is the rate of change of N, so A = ΔN/Δt, therefore:
- ΔN/Δt = -λN
- There is a negative sign because the number of atoms left is always decreasing.
Define the half-life of an isotope.
The average time it takes for the number of unstable nuclei to halve.
What is the symbol for the half-life of an isotope?
T(1/2)
Where 1/2 is subscript
Put simply, how is the half-life of an isotope measured?
Measuring the time for the activity to halve.
How does an isotope’s half-life relate to how long it is radioactive for?
The longer the half-life, the longer it stays radioactive.
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.
Instead of a N against t graph for radioactive decay, what are you more likely to see and why?
• A against t, which is the same graph.
• This is because A is easier to record than N.
The graph is also the same for count rate.
How can the graph of N against t for radioactive decay be made linear?
- Plot ln(N) against t.
* This should be a straight line of negative gradient.
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 can the half-life of a radioactive isotope be found from the ln(N) against t graph (or ln(A) against t)?
Gradient = -λ
On an N against t graph for radioactive decay, what is the y intercept?
N₀
On an ln(N) against t graph for radioactive decay, what is the gradient equal to?
-λ
Remember to practise drawing out the graphs for:
• N against t
• ln(N) against t
Pg 162 of revision guide
What is the equation for the half-life of a radioactive sample?
T(1/2) = ln2 / λ (= 0.693/λ)
Where:
• T(1/2) = Half-life (s)
• λ = Decay constant (s^-1)
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 is the equation for the number of unstable nuclei remaining in a radioactive sample?
N = N₀e^(-λt)
Where:
• N = Number of unstable nuclei remaining
• N₀ = Original number of unstable nuclei
• λ = Decay constant (s^-1)
• t = Time (s)
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?
What is molar mass?
The mass that 1 mole of a substance would have (grams per mole, gmol^-1).
It is equal to its relative atomic or relative molecular mass.
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 is the equation for the activity remaining in a radioactive sample over time?
A = A₀e^(-λt)
Where: • A = Activity remaining (Bq) • A₀ = Original activity (Bq) • λ = Decay constant (s^-1) • t = Time (s)
What does a graph of activity against time look like?
Same as N-t
Give some uses of radioactive substances.
- Dating organic material
- Diagnosing medical problems
- Sterilising food
- Smoke alarms
What isotope is used in the radioactive dating of objects?
Carbon-14
How does radioactive dating of objects work?
• Living plants take in carbon dioxide for photosynthesis, including the radioactive isotope carbon-14
• When they die, the activity of the C-14 starts to fall, with a half life of 5730 years
• Materials that were once living can be tested to find the current amount of C-14 in them, and date them
It is the ratio of carbon when they are dead compared to when they were dead.
What is the half-life of carbon-14?
5730 years
When can it be difficult to get a reliable age from carbon dating
What type of radiation is best for use in radioactive tracers?
Gamma
Give an example of a radioactive tracer and why it is used.
• Technetium-99m
(Radioactive tracer is injected or swallowed and then moves to the area of interest in the body.
Radiation is recorded and an image appears)
• It is a gamma emitter, has a half-life of 6 hrs and decays to a much more stable isotope
Half life is long enough to record data but short enough to be at an acceptable level and it won’t be in the body after the diagnosis.
What is the problem with a long half-life?
It can be dangerous, because the isotope stays radioactive for a long time.
Why must radioactive waste be stored for hundreds of years?
Uranium decays into several different isotopes with different half life’s emitting alpha, beta and gamma.
Must be stored for hundreds of years until activity has fallen to a safe level.
It has a long half so it stays radioactive for a long time.
Describe how standard notation of elements works.
- Symbol for the element is written in large text
- Mass number is in the top left
- Atomic number is in the bottom left
What is the symbol for mass number?
A
What are the two main forces acting on a nucleus? What does each do?
- Strong nuclear force - Holds the nucleus together
* Electromagnetic force - Pushing protons apart
What is plotted on the axis of a stability graph for isotopes?
Number of neutrons (N) against number of protons (Z)
When will a nucleus be unstable?
If it has:
1) Too many neutrons
2) Too few neutrons
3) Too many nucleons altogether
4) Too much energy
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.
What is the line of stability on a stability graph?
The line (and surrounding region), in which stable nuclei may be found.
When will the number of neutrons overtake the number of protons in an atoms
After 20 neutrons/protons in the atom
Remember to practise drawing out the stability graph for nuclei.
Pg 164 of revision guide
What is the symbol for atomic number?
Z
In what nuclei does alpha emission happen and why?
- Very heavy nuclei
* These nuclei are too massive to be stable, so losing nucleons makes them more stable
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?
In what nuclei does β⁻-emission happen and why?
- Neutron rich nuclei
* This converts a neutron into a proton, so the nucleus becomes more stable
When an beta-minus particle is emitted, what happens to the nucleon number and proton number?
- Nucleon number -> Stays the same
* Proton number -> Increases by 1
What happens in β⁻ decay?
A proton is changed into a neutron, while an electron and an electron antineutrino are emitted from the nucleus.
How is a β⁻ particle symbolised using standard notation?
0
β
-1
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?
In what nuclei does gamma-emission happen and why?
- Nuclei with too much energy
* Losing a gamma ray helps lower the energy, making the nucleus more stable
When might a nucleus have too much energy so that a gamma ray is released?
- After alpha or beta decay.
* After a nucleus captures one of its own electrons (electron capture).
What do particles emit after decay?
gamma photons
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
When a gamma ray is emitted, what happens to the nucleon number and proton number?
There is no change to either, just a decrease in energy.
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
Molybdenum-99 undergoes beta minus to form Technetium-99m.
It then emits a gamma photon as it transitions to the ground state.
Half life = 6 hours.
Why is Technetium good in medicine?
(Technetium)
Only emits gamma = less ionising = causes less damage.
Short half life = won’t be in body after diagnostic, but long enough to detect during diagnostic
What is electron capture?
Proton rich nuclei.
Nucleus absorbs one of it’s inner orbital electrons.
This results in a proton changing into an neutron and emitting an electron neutrino.
An outer orbital electron transitions to replace the absorbed electron, resulting in an emission of an X-ray photon.
What is the equation for electron capture?
p + e -> n + ve + γ
Note: The gamma ray isn’t always included.
What is the general equation of electron capture?
Describe when each type of radioactive emission may occur.
• α - Heavy nuclei • β⁻ - Neutron-rich nuclei β+ - Proton-rich nuclei Electron capture - proton-rich nuclei • γ - Nuclei with too much energy
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 is nuclear fission?
When a large, unstable nucleus splits into two smaller nuclei and 2/3 neutrons, while releasing energy.
What are the two smaller nuclei called in fission?
Fission fragments
Why is energy released during nuclear fission?
Because new, smaller nuclei have a higher average binding energy per nucleon
Higher binding energy per nucleon = …?
More stable nucleus
Why are large nuclei more likely to spontaneously fission?
Larger nucleus = more unstable
What does spontaneous fission limit the number of?
Limits the number of nucleons that a nucleus can contain - it limits the number of possible elemets
What nuclei can undergo nuclear fission?
Large nuclei (at least 83 protons)
What are the two types of nuclear fission?
- Spontaneous
* Induced
How can nuclear fission be induced?
Making a low energy neutron enter a U-235 nucleus.
What sort of neutron is required in order to induce nuclear fission and why?
- Low energy neutrons (a.k.a. thermal neutrons)
* Only these can be captured
What is another name for the low energy neutrons used in inducing nuclear fission?
Thermal neutrons
Why is energy released in nuclear fission?
The new, smaller nuclei have higher binding energy per nucleon.
What happens when making a low energy neutron enter a U-235 nucleus?
How does a nucleus’ size impact it’s stability?
The larger the nucleus, the more unstable it will be.
How many protons are needed in a nucleus in order for it to undergo fission?
At least 83
Which nuclei are most likely to undergo spontaneous nuclear fission and why?
Very large ones, because they are unstable.
What limits the number of possible elements?
Nuclear fission
Aside from two smaller nuclei, what is produced in induced nuclear fission?
2 or 3 neutrons
How can we harness the energy released during nuclear fission?
Using a thermal nuclear reactor.
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
Name all of the parts of a nuclear reactor.
- Control rods
- Fuel rods
- Moderator (water)
- Pump
- Heat exchanger
- Concrete case
Remember to practise drawing out a diagram of a nuclear reactor.
Pg 166 of revision guide or pg 397 of textbook
What fuel do nuclear reactors use?
Uranium-235 (and some U-238, but this doesn’t undergo fission)
How are fuel rods inserted into a nuclear reactor?
Remotely, which keep workers as far away from the radiation as possible.
How does the chain reaction in a fission reactor work?
- Fission reactions produce more neutrons
* These then induce other nuclei to fission
What does the moderator do and why?
- Slows down neutrons -> To allow them to be captured by the uranium nuclei
- Absorb neutrons -> To control the rate of reactions
What is the name for neutrons that have been slowed down by the moderator?
Thermal neutrons
What is the moderator in nuclear reactors?
Water
How does a moderator work?
Elastic collisions with the nuclei of the moderator material slow down the neutrons
What type of collisions are involved when neutrons collide with the moderator
What is conserved?
Elastic (kinetic energy is conserved)
Why is water used as a moderator in nuclear reactors?
- Collisions with particles of a similar mass are most efficient at slowing down neutrons
- Water contains hydrogen
- So it fits this condition
What two assumptions do we make about the collisions between the neutron and moderator material?
Collision between the particles is perfectly elastic - Kinetic energy and momentum is conserved.
The moderator particle is stationary before the collision.
If the mass of the neutron is roughly the same as the mass of the moderator particle:
After the neutron collides with the moderator particle, what is the neutrons velocity?
Final velocity of the neutron is 0 ms^-1
If the mass of the neutron is roughly the same as the mass of the moderator particle, which two quantities are transferred from the neutron to the moderator particle?
Kinetic energy and momentum
Why is it important for the mass of neutron to be similar to mass of moderator particle?
More similar mass = more kinetic energy and momentum transferred to the to the moderator particle from the neutron.
We need to slow down the neutron (to around 2200ms^-1) a lot so transferring most of its KE and momentum slows it down.
What do we not want to do to neutrons?
Stop them.
What is the perfect amount of fuel for a steady fission reaction called?
Critical mass
What happens if the fuel is less than the critical mass?
The reaction will just peter out.
What mass of fuel do nuclear reactors use?
- Supercritical (more than is needed for a steady reaction)
* Control rods are used to control the rate of fission
How do control rods work?
Limit neutrons: They absorb neutrons so that the rate of fission is controlled.
Further you push in the control rods…
…the more neutrons they absorb
Give an example of a material that control rods can be made from.
Boron or Cadmium
How does an emergency shutdown of a nuclear reactor work?
The control rods are lowered fully into the reactor, which slows down the reaction as quickly as possible.
How does a nuclear reactor generate energy?
The coolant sent around the reactor removes heat, that was produced by fission.
The heat from the reactor is then used to make steam for powering an electricity-generating turbine.
What is the role of the thick concrete case in a nuclear reactor?
Prevents radiation escaping and reaching people who work in the power station
Why are the waste products of nuclear fission reactor still unstable and radioactive?
Spent fuel rods are dangerous, since fission waste products have a larger proportion of neutrons than nuclei of a similar atomic number = unstable and radioactive
What do fission waste products emit?
beta and gamma = strongly penetrating
Do the radioactive products of nuclear reactors have any uses?
The less radioactive ones can be used as tracers in medicine, etc.
Describe what happens to high-level radioactive waste from a nuclear reactor.
- Placed in cooling ponds (remotely - to limit the exposure to workers) as it is very hot initially
- Stored in sealed containers until the activity has fallen sufficiently, thick concrete walls are used to protect operators
What happens to intermediate-level waste?
Encapsulated in cement in steel drums, requires thick concrete walls
What is low-level waste?
contaminated clothing - doesn’t generate heat - low levels of radioactivity.
What are the benefits to nuclear power?
Nuclear power can be used for centuries to keep generating electricity, unlike fossil fuels.
Doesn’t release greenhouse gases - affects atmosphere.
It is efficient (energy produced per unit mass of fuel). Generates many thousands times more electrical energy per kg of nuclear fuel than per kg of fossil fuel.
How are greenhouse gases still produced even if fission itself doesn’t produce it?
The process produces greenhouse gases e.g. transporting uranium fuel rods to the power station
What factors are taken into account for the risks of nuclear reactors?
They are built extremely carefully to reduce danger of nuclear disaster.
How we deal with waste products is a risk effecting people and the environment.
What is nuclear fusion?
The joining of two light nuclei to give a larger nucleus.
Why is a lot of energy released during nuclear fusion?
The new, heavier nuclei has a much higher binding energy per nucleon.
What is the nuclear fusion reaction that happens in the Sun?
Hydrogen nuclei fuse in a series of reactions to form helium.
Give the chemical equation for nuclear fusion in the Sun.
2H1 + 1H1 -> 3He2 + Energy
Why is nuclear fusion difficult to achieve?
It requires a lot of energy to start it.
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.
Why does nuclear fusion need high temperatures?
Needs to be really fast to overcome electrostatic force.
(speed is proportional to temperature).
(1/2mv^2 is proportional to temperature)
How much kinetic energy is required to make nuclei fuse together?
About 1 MeV = a lot of energy
How does the mass of a nucleus compare to the mass of its constituent parts?
The mass of a nucleus is LESS than the mass of its constituent parts.
What is mass defect?
The difference between the mass of a nucleus and the mass of its constituent nucleons.
What has less mass?
Nucleus or it’s constituent nucleons
Mass of nucleus is less than the mass of it’s constituent nucleons
When a nucleus decays, energy is released. In what form?
Gamma photons (radiation) and kinetic energy of the decay products.
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:
What is larger? The mass of a nucleus or the mass of the sum of individual particles within the nucleus
Mass of individual particles added together.
Why is the sum of the mass of individual particles larger than the mass of nucleus?
Because energy is lost binding them together to form the nucleus. Mass and energy can be converted.
What happens in terms of energy when two small nuclei join?
The total mass decreases, so the lost mass is converted to energy and released.
What is the amount of energy released (when two nucleons join together and the total mass decreases + lost mass is converted to energy) equivalent to?
The amount of energy released is equivalent to the mass defect.
The energy of pulling a nucleus apart is equal to the energy….
….released when the nucleus formed.
Define binding energy.
The energy required to separate all of the nucleons in a nucleus.
How can you visualise binding energy
What is the unit for binding energy?
MeV
How does binding energy compare to the mass defect?
Binding energy is the energy equivalent of mass defect.
Estimate the binding energy in eV of the nucleus of a lithium atom 6Li3, given that its mass defect is 0.0343 u.
1) Convert the mass defect into kg.
• Mass defect = 0.0343 x (1.661 x 10^-27) = 5.697 x 10^-29
2) Use E = mc².
• E = (5.697 x 10^-29) x (3.00 x 10^8)² = 5.127 x 10^-12 J
• E = 32.0 MeV
What is u equal to?
1 u = 1.661 x 10^-27 kg
What is the energy equivalent of 1 u?
931.5 MeV
When finding the binding energy where should you look on the data sheet and what should you try to avoid?
Use proton rest mass = 1.00728 and neutron rest mass = 1.00867.
Try to avoid using proton (or neutron) rest mass = 1.67x10^-27 kg, then converting to u with 1.661x10^-27.
It does work but it might be easier to do the u version instead of kg method.
What is a useful way of comparing the binding energies of different nuclei?
Looking at the average binding energy per nucleon.
What is the equation for average binding energy per nucleon?
Average binding energy per nucleon = B / A
Where:
• Average binding energy per nucleon is in MeV
• B = Binding energy (MeV)
• A = Nucleon number
(Note: Not given in exam!)
What graph is typically plotted with binding energies?
Average binding energy per nucleon against nucleon number.
What does a high binding energy mean?
A large amount of energy is required to remove nucleons from the nucleus.
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
The higher the average binding energy…
..the more stable the nucleus (as it takes more energy to remove nucleons)
Where are the most stable nuclei on a graph of average binding energy per nucleon against nucleon number?
The maximum point on the graph (at Fe-56).
What does Fe-56 have the highest?
Highest binding energy per nucleon
Where is the peak on a graph of binding energy per nucleon against nucleon number?
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 dos the change in binding energy give you?
Energy released
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
Which usually releases more energy: fusion or fission?
Fusion, because there is a greater change in average binding energy per nucleon (steeper gradient on graph).
Remember to practise drawing out the graph of average binding energy per nucleon vs nucleon number.
Pg 168 + 169 of revision guide
Remember to practise doing the binding energy calculations on pg 169 of revision guide.
Do it
What do particles emit after decay?
gamma photons
What is electron capture?
Proton rich nuclei.
