Nuclear Flashcards

(186 cards)

1
Q

What was the Rutherford scattering experiment?

A
  • Rutherford passed beams of alpha particles through a thin sheet of gold to experiment:
  • The different angles of deflection of the alpha particles
  • The number of alpha particles that were deflected at each angle
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Why was a lead container used in the Rutherford scattering experiment?

A
  • The source was placed in a lead container as alpha particles are emitted in all directions
  • The lead container helped produce a collimated beam of alpha particles (alpha particles travelled parallel to eachother)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Why was the Rutherford scattering experiment carried out in a vacuum?

A
  • Alpha particles are highly ionising, meaning they can only travel ~5cm before interacting with air molecules
  • The vacuum helped ensure that the alpha particles didn’t collide with any other particles on their way to the thin gold sheet
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What were the three observations found in the Rutherford scattering experiment?

A
  • The majority of alpha particles passed straight through the gold sheet unaffected
  • Some alpha particles deflected through small angles of < 10°
  • Only a small number of alpha particles deflected straight back at angles of > 90°
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What was the conclusion of the Rutherford scattering experiment?

A
  • Atoms consist of a small, dense positively charged nucleus surrounded by negatively charged electrons
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

How has the model of the nucleus changed over time?

A
  • John Dalton: all matter is made up of atoms
  • JJ Thomson: plum pudding model (ball of positive charge with negative electrons embedded)
  • Rutherford scattering experiment
  • Niels Bohr: discovered electrons orbit in shells
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is an unstable nucleus and what happens to it?

A
  • Some isotopes are unstable due to an imbalance in the protons and neutrons within the nucleus
  • To become more stable, a nucleus can emit particles or radiation by the process of radioactive decay
  • The 3 main types of radioactive emission is: alpha, beta and gamma
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What is an alpha particle and when is it emitted?

A
  • An alpha particle is a high-energy helium nucleus (2 protons and 2 neutrons)
  • They are usually emitted from nuclei that are too large
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Characteristics of alpha particles

A
  • They are the most ionising type of radiation (have the highest charge of +2e)
  • They are the least penetrating type of radiation
  • Have a range of 3-7cm in air
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What is a beta particle and when is it emitted?

A
  • A beta-minus particle is a high-energy electron. They are emitted from nuclei that have too many neutrons
  • A beta-plus particle is a high-energy positron. They are emitted from nuclei that have too many protons
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Characteristics of beta particles

A
  • Moderately ionising (have a charge of ±1e)
  • Moderately penetrating (have a range of 20cm to 3m in air)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What is gamma radiation and when is it emitted?

A
  • Gamma rays are a type of high-energy electromagnetic radiation
  • They are emitted by nuclei that need to lose some energy
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Characteristics of gamma radiation

A
  • The least ionising type of radiation (photon has no charge)
  • The most penetrating type of radiation (has an infinite range and follows the inverse square law)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is each type of radiation absorbed by?

A
  • Alpha: paper
  • Beta: aluminium foil ~3cm
  • Gamma: thick lead or concrete
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What is ionising ability?

A
  • The number of ion pairs a type of radiation produces per cm of air
  • Alpha particles are the most ionising type of radiation
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What happens to different types of radiation in an electric and magnetic field?

A
  • Alpha particles are deflected slightly towards the negative plate
  • Beta particles are deflected strongly towards the positive plate
  • Gamma particles are unaffected
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

How is radiation used in thickness control?

A
  • Beta radiation can be used to determine the thickness of aluminium foil, paper, plastic and steel
  • The thickness can be controlled by measuring how much beta radiation passes through the material to a Geiger counter
  • Beta radiation must be used as alpha would be absorbed and gamma would always pass straight through
  • The Geiger counter then adjusts the pressure of the rollers to maintain the correct thickness
  • A source with a long half-life must be chosen so it doesn’t need to be replaced
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is the inverse square law for gamma radiation?

A
  • I = k / x^2
  • I = intensity of the gamma radiation (W/m2)
  • x = distance from the source (m2)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

What is background radiation?

A
  • The ionising radiation present in the environment
  • Can be separated into natural and artificial sources
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

What are some natural sources of background radiation?

A
  • Airborne radon gas comes from rocks in the ground, as well as building materials
  • This is due to the presence of radioactive elements, such as uranium, which occur naturally in small amounts in all rocks and soils
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

What are some artificial sources of background radiation?

A
  • Nuclear waste: it can be dangerous for people handling it
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

How do we record background radiation?

A
  • Use a Geiger counter to measure the radiation when no source is present
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What is done to minimise the radiation dose of a sample?

A
  • Short-lived isotopes are preferred to long-lived ones
  • The smaller the sample of radioactive material, the better
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

What precautions are taken against radiation?

A
  • Keep radioactive sources shielded when not in use, e.g: in a lead box
  • Wearing protective clothing to prevent the body from becoming contaminated
  • Limiting exposure time
  • Handling radioactive sources with long tongs
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
How is radiation used in medicine?
- Radiation therapy - Gamma radiation is used to destroy cancerous cells. They are directed at the cancerous cells from different angles so only they receive the full radiation and healthy cells are less affected
26
Why was a thin gold sheet used in the Rutherford scattering experiment?
- The target material needed to be extremely thin ~10^-6m thick - This is because a thicker foil would stop the alpha particles completely - Gold was chosen due to its malleability, meaning it could easily be hammered into thin sheets
27
What quantities does the inverse square law apply to and what types of radiation?
- Applies to activity, count rate and intensity - ONLY applies to gamma rays, not alpha or beta radiation
28
What is radioactive decay?
- The spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particle
29
What type of process is radioactive decay and what does this mean?
- Radioactive decay is a random process, which means: - There is an equal probability of any nucleus decaying - It cannot be known which particular nucleus will decay next - It cannot be known at what time a particular nucleus will decay - The rate of decay is unaffected by surrounding conditions - It is only possible to estimate the proportion of nuclei decaying in a given time period
30
How can you demonstrate the nature of radioactive decay?
- The random nature of radioactive decay can be demonstrated by observing the count rate of a Geiger-Muller (GM) tube - When a GM tube is placed near a radioactive source, the counts are found to be irregular and cannot be predicted - Each count represents a decay of an unstable nucleus - These fluctuations in count rate on the GM tube provide evidence for the randomness of radioactive decay
31
What is the average decay rate and why is it useful?
- Since radioactive decay is spontaneous and random, it is useful to consider the average number of nuclei that are expected to decay per unit of time - This is known as the average decay rate
32
What is the decay constant?
- The decay constant λ is defined as the probability that an individual nucleus will decay per unit of time - Each radioactive element can be assigned its own decay constant
33
What is the activity of a sample?
- The activity A of a radioactive sample is defined as the average number of nuclei that decay per unit time
34
How can you calculate the activity of a sample?
- A = ΔN / Δt = -λN - ΔN = number of decayed nucleu - N = number of nuclei remaining in a sample - A = activity of sample (Bq)
35
What is the activity of a radioactive sample measured in?
- Becquerels (Bq) - An activity of 1 Bq is equal to one decay per second
36
What does the equation for the activity of a radioactive substance show us?
- The greater the decay constant, the greater the activity of the sample - The activity depends on the number of undecayed nuclei remaining in the sample - The minus sign indicates that the number of nuclei remaining decreases with time
37
What type of decay is radioactive decay and explain the graph
- In radioactive decay, the number of undecayed nuclei falls very rapidly, without ever reaching zero - This is known as exponential decay - Number of undecayed nuclei decreases with time at a decreasing rate
38
How is the decay constant related to the graph of radioactive decay?
- The steeper the slope, the larger the decay constant - The shallower the slope, the smaller the decay constant
39
What is the equation to find the number of undecayed nuclei?
- N = N₀ e^(-λt) - N = number of undecayed nuclei at a certain time t - N₀ = initial number of undecayed nuclei (when time = 0) - λ = decay constant - t = time interval
40
How can we use the equation for number of undecayed nuclei for other quantities?
- The number of nuclei can be substituted for other quantities, such a count rate and activity - A = A₀ e^(-λt) - C = C₀ e^(-λt)
41
What is the molar mass?
- The molar mass, or molecular mass, of a substance is the mass of the substance (in grams) in one mole - Measured in g / mol
42
How can you calculate the number of moles?
- mol = mass (g) / molar mass (g/mol)
43
What is Avogadro's constant?
- Avogadro's constant Nₐ is defined as the number of atoms in one mole of a substance, equal to 6.02 x 10^23
44
How can you find the number of nuclei?
- The number of atoms (hence number of nuclei) can be found using: - number of nuclei = (mass x Nₐ) / molar mass
45
What is half-life?
- Half-life is defined as the average time taken for a given number of nuclei of a particular isotope to halve - Since activity A is proportional to the number of undecayed nuclei N, the activity of the sample also halves
46
What is the equation for the half-life of an isotope and its derivation?
- We know that when t is equal to the half-life t₁⁄₂, the activity of N of the sample will be half of its original value, so N = 1/2N₀ - Therefore, 1/2N₀ = N₀ e^(-λt₁⁄₂) - Cancel out N₀: 1/2 = e^(-λt₁⁄₂) - Take logs: ln(1/2) = -λt₁⁄₂ - Make t₁⁄₂ the subject: t₁⁄₂ = ln2 / λ
47
What does the equation for half-life show us?
- The half-life and the radioactive decay constant λ are inversely proportional - Therefore, the shorter the half-life, the larger the decay constant and the faster the decay
48
How can we use a curved graph to determine the half-life of an isotope?
- Draw a line to the curve at the point where the number of nuclei (or activity) has dropped to half of its original value - Draw a line from the curve to the time axis, this is the half-life
49
How can we show nuclear decay on a straight line graph?
- N = N₀ e^(-λt₁⁄₂) - Take logs of both sides: lnN = lnN₀ - λt₁⁄₂ - Rearrange in y = mx + c form: lnN = - λt₁⁄₂ + lnN₀ - Gradient (m) = -λ - x-axis = t (time) - y-axis = lnN - y-intercept = lnN₀
50
What are the uses of radioactivity?
- Nuclear power - In medicing (radiotherapy, tracers) - Radiocarbon dating for archeological artefacts - Uranium-lead dating of rock samples - Radioisotope power stations
51
How is carbon related to living oraganisms for radioactivity?
- All living organisms absorb carbon-14, but after they die they do not absorb any more - The proportion of carbon-14 is constant in living organisms as carbon is constantly being replaced during the period they are alive
52
What is carbon-14 used for and how is it produced?
- The isotope carbon-14 is commonly used in radioactive dating - It forms as a result of cosmic rays knocking out neutrons from nuclei, which then collide with nitrogen nuclei in the air to form carbon-14 + proton
53
How does radiocarbon dating work?
- All living organisms constantly absorb carbon-14 - When they die, the activity of carbon-14 in the organic matter starts to fall, with a half-life of around 5730 years - Samples of living materials can be tested by comparing the current amount of carbon-14 in them and compared to the initial amount (based on the ratio of carbon-14 to carbon-12) - Hence, they can be dated
54
When is radiocarbon dating most reliable?
- Carbon dating is highly is highly reliable for estimating the ages of samples between 500 and 60000 years old
55
What happens if the sample you are carbon dating is less than 500 years old?
- The activity of the sample will be too high to measure small changes accurately - Therfore the ratio of carbon-14 to carbon-12 will be too high to determine an accurate age
56
What happens if the sample you are carbon dating is more than 60000 years old?
- The activity will be too low to distinguish between changes in the sample and background radiation - Therefore, the ratio of carbon-14 to carbon-12 will be too small to determine an accurate age
57
What is the age of the Earth and how has it been discovered?
- For many years, scientists could not agree on the age of the Earth - Until recently, the Earth was believed to be only millions of years old - Over the last century, radiometric dating methods have enabled scientists to discover the age of the Earth is many billions of years old - The most critical of these methods is uranium-lead dating
58
How does uranium-lead dating work?
- Initially, there is only uranium in a rock, but over time, the uranium decays via a decay chain which ends with lead-206, which is a stable isotope - Uranium-238 has a half-life of 4.5 billion years - Over time, the raio of lead-206 atoms to uranium-238 atoms increases - The ratio of uranium to lead in a sample of rock can then be used to determine its age
59
How do radioisotope power systems work?
- The decay of an isotope may release energy as heat - Radioisotope power systems are designed to transform this heat into electrical power - Such devices can be used to power space probes and satelites - Typically, plutonium-238 is used as fuel, with 1g generating a power output of about 500 mW
60
What is common between the most common elements in the universe and why?
- The most common elements in the universe all tend to have values of N and Z less than 20 (and iron which has Z=26, N=30) - This is because lighter elements (with less protons) tend to be much more stable than heavier ones
61
What does N, Z and A represent in nuclear physics?
- N = number of neutrons - Z = number of protons - A = number of nucleons
62
Explain the nuclear stability graph
- Plot N (number of neutrons - y-axis) against Z (number of protons - x-axis) - Line of stability: increases with a gradient of 1 until N and Z = 20, then increases with a steeper gradient (N increases faster than Z) - Above the line of stability: β- emitters - Below the line of stability & below N=100: β+ emitters - Below the line of stability & above Z=82: α emitters
63
When will a nucleus be unstable?
- If it has: - Too many neutrons - Too many protons - Too many nucleons (too heavy) - Too much energy
64
What happens to light isotopes for nuclear stability?
- When Z < 20: - All nuclei tend to be very stable - They follow the straight line N=Z
65
What happens to heavy isotopes for nuclear stability?
- When Z > 20: - The neutron - proton ratio increases - Stable nuclei must have more neutrons than protons
66
Why is the neutron-proton ratio significant to the stability of nuclei?
- At short ranges (1-3fm), nucleons are bound by the strong nuclear force - Below 1fm, the strong nuclear force is repulsive in order to prevent the nucleus from collapsing - At longer ranges, the electromagnetic force acts between protons, so more protons cause more instability - Therefore, as more protons are added to the nucleus, more neutrons are needed to add distance between protons to reduce the electrostatic repulsion - Also, the extra neutrons increase the amount of binding force which helps to bind the nucleons together
67
What can we use the graph of stability for?
- It is useful in determining which isotopes will decay via alpha emission, beta-plus emission, beta-minus emission and electron capture
68
What happens during alpha emission and when does it occur?
- Alpha emitters are found below the line of stability when Z>82, where there are too many nucleons in the nucleus (too heavy) - These nuclei have more protons than neutrons, but they are too large to be stable - This is because the strong nuclear force between the nucleons is unable to overcome the electrostatic force of repulsion between the protons - Hence, the nucleus emits an alpha particle (2 protons and 2 neutrons) to become lighter
69
What happens during beta-minus decay and when does it occur?
- Beta-minus emitters are found to the left of the stability line, where the isotopes are neutron-rich compared to stable isotopes (have too many neutrons) - A neutron is converted to a proton and emits a β- particle (electron) and an anti-electron neutrino
70
What happens during beta-plus decay and when does it occur?
- Beta-plus emitters are found to the right of the stability line, where the isotopes are proton-rich compared to stable isotopes (have too many protons) - A proton is converted to a neutron and emits a β+ particle (positron) and an electron neutrino
71
What happens during electron capture and when does it occur?
- Electron capture occurs when a nucleus captures one of its own orbiting electrons - As with β+ decay, a proton in the nucleus is converted into a neutron, releasing a gamma-ray (and an electron neutrino) - Hence, this also occurs to the right of the stability line, where the isotopes are proton-rich compared to stable isotopes
72
What is the decay equation for β- emission?
ᴬZX → ᴬ(Z+1)Y + ⁰₋₁e + ν̅ₑ
73
What happens if a nucleus has too many neutrons?
- Beta-minus decay occurs - One of the neutrons in the nucleus changes into a proton and a β- particle (electron), and an anti-electron neutrino is released - The nucleon number remains constant: neutron number decreases by 1 and proton number increases by 1
74
What is the decay equation for β+ decay?
ᴬZX → ᴬ(Z−1)Y + ⁰₊₁e + νₑ
75
What happens if a nucleus has too many protons?
- β+ emission or electron capture occurs - In β+ emission, a proton changes into a neutron and a β+ particle positron) and an electron neutrino is released - In electron capture, an orbiting electron is taken in by the nucleus and combined with the proton, causing the formation of a neutron and an electron neutrino - In both decays, the nucleon number stays constant: the neutron number increases by 1, and the proton number decreases by 1
76
What is the decay equation for electron capture?
ᴬZX + ⁰₋₁e → ᴬ(Z−1)Y + νₑ
77
What happens if a nucleus has too many nucleons?
- The nucleus is too heavy - Alpha (α) emission occurs - An α particle is a helium nucleus - The nucleon number decreases by 4, and the proton number decreases by 2
78
What is the decay equation for α decay?
ᴬZX → ᴬ⁻⁴(Z−2)Y + ⁴₂α
79
What happens if a nucleus has too much energy?
- Gamma (γ) emission occurs - The gamma particle is a high-energy electromagnetic radiation - This usually occurs after a different type of decay, such as alpha or beta decay - This is because the nucleus becomes excited and has excess energy
80
What is the nucleus excited state?
- A daughter nucleus is in an excited state after a decay - This excited state is usually very short-lived, and the nucleus quickly moves to its ground state - It does this either directly or via one or more lower-energy excited states
81
What happens if a nucleus is in an excited state?
- Once an unstable nucleus has decayed, it may enter an excited state - Here, it will emit any remaining energy in the form of a gamma photon (γ) - The emission of a γ photon does not change the number of protons or neutrons in the nucleus, it only allows the nucleus to lose energy
82
What is technetium-99m?
- Technetium-99m is used as a γ source in medical diagnosis - The "m" stands for metastable which means the nucleus exists in a particularly stable excited state
83
How is technetium-99m found?
- Technetium-99m is the decay product of molybdenum-99 which can be found as a product in nuclear reactors
84
What is the decay equation for molybdenum-99 and technetium-99m?
- ⁹⁹₄₂Mo → ⁹⁹₄₃Tc + ⁰₋₁e + ν̅ₑ - ⁹⁹₄₃ᵐTc → ⁹⁹₄₃Tc + γ
85
How are nucleus excited states used in medicine?
- Molybdenum-99 has a half-life of 66 hours. This is long enough for the sample to be transported to hospitals. Subsequently, the technetium-99m can be separated at the hospital - Technetium-99m has a half-life of 6 hours. This is an adequate timeframe for examining a patient and not too long to cause any damage
86
How are nucleus energy levels shown on a diagram?
- The decay mode (usually alpha or beta) is shown by a diagonal line - The excited state, or states, are generally stacked in descending energy order to the right of the decay - Gamma decay is shown by a vertical downwards arrow
87
How can we calculate nuclear radius?
- Can be calculated experimentally using: - Rutherford scattering: the closest approach method - Electron scattering
88
How does the closest approach method work?
- The Rutherford scattering experiment indicates that there must be an electrostatic repulsion between the alpha particles and the gold nucleus, as some of the alpha particles are found to rebound from the gold foil by 180° - The alpha particle is fired with an initial kinetic energy Ek. At the point of closest approach r, the repulsive force reduces the speed of the alpha particles to zero momentarily - At this point, the initial kinetic energy of the alpha particle is equal to the electric potential energy of the gold nucleus - Ek = Ep (kinetic energy = potential energy) - The closest approach method gives an estimate of the upper limit of the radius of a nucleus
89
What is the equation for closest approach and how is it found?
- At the point of closest approach r, the initial kinetic energy of the alpha particle is equal to the electric potential energy of the nucleus - Ek = Ep - ½mv² = Qq / (4πε₀r) - Q = 2e (charge of an alpha particle) - q = Ze (charge of target nucleus) - Rearrange to find: - r = Ze² / (πε₀mv²) - Z = proton number of target nucleus - e = elementary charge (e) - m = mass of alpha particle - v = initial velocity of alpha particle
90
Advantages of the closest approach method
- Gives a good estimate of the upper limit for a nuclear radius - Alpha particles are scattered only by the protons and not all the nucleons that make up the nucleus
91
Disadvantages of the closest approach method
- Alpha scattering does not give an accurate value for nuclear radius as it will always be an overestimate. This is because it measures the smallest separation between the alpha particle and the nucleus, not its radius - The nucleus will recoil as the alpha particle approaches - Very few alpha particles will rebound at exactly 180° - Alpha particles are hadrons, hence they will be affected by the strong nuclear force, which is not accounted for in the calculations
92
How does the electron scattering method work?
- Electrons accelerated to close to the speed of light are found to have wave-like properties, such as the ability to diffract - When a beam of electrons is directed at a thin target, each electron will diffract around a nucleus. This happens because the de Broglie wavelength of a high-speed electron is similar to the size of a nucleus - The resulting diffraction pattern that forms is a central bright spot with dimmer concentric circles around it - The size of the nucleus can be determined using the angle of the first minimum intensity
93
Why must the electron be close to the speed of light for electron scattering to work?
- For the electrons to diffract around a nucleus, the de Broglie wavelength must be similar to the size of a nucleus - The de Broglie wavelength of an electron is equal to: λ = h / mv - Therefore, to decrease the de Broglie wavelength, we must increase the speed of the electron
94
Advantages of the electron scattering method
- Much more accurate than the closest approach method - Gives a direct measurement of the radius of a nucleus - Electrons are leptons, so they are not affected by the strong nuclear force
95
Disadvantages of the electron scattering method
- Electrons must be accelerated to very high speeds to maximise the resolution - This is because significant diffraction takes place when the electron wavelength is similar in size to the nucleus. Higher speeds are needed to shorten the de Broglie wavelength since λ = h / mv - Electrons can be scattered by both protons and neutrons. If there is an excessive amount of scattering, then the first minimum of the electron diffraction can be difficult to determine
96
How can we calculate the radius of a nucleus using electron scattering?
- We can plot the graph of intensity against angle obtained through electron diffraction - The pattern formed by this diffraction has a predictable minimum which forms at an angle θ to the original direction - To determine an accurate value for nuclear radius R, a multiplication factor of 1.22 is required - sinθ = 1.22λ / 2R - θ = angle of the first minimum
97
How is nuclear radius measured?
- Nuclear radii are measured by the order of 10^-15m of 1fm
98
What is the graph of nuclear radius against nucleon number?
- The graph starts with a steep gradient at the origin, and the gradient gradually decreases to almost zero - This shows that as more nucleons are added to the nucleus, the nucleus gets bigger however, the number of nucleons A is NOT proportional to the size R
99
What is the nuclear radius equation?
- R = R₀A^(1/3) - R = nuclear radius - R₀ = constant of proportionality = 1.05fm - A = nucleon / mass number
100
Derive the equation for the volume of a nucleus
- Assuming that the nucleus is spherical, its volume is equal to: V = 4/3 πR³ - We know R is the nuclear radius: R = R₀A^(1/3) - Combining the equations gives: V = 4/3 πR₀³A - Therefore, the nuclear volume V is proportional to the mass of the nucleus A (as π and R₀ are constant)
101
Derive the equation for the density of a nucleus
- We know that the volume of a nucleus is: V = 4/3 πR₀³A - We also know that ρ = m / V - Further, we know that the mass of a nucleus is equal to: m = Au where A is the mass number and u is 1 atomic mass unit - Combining the 3, we find that the density of a nucleus is equal to: ρ = 3u / (4πR₀³)
102
What does the equation for the density of a nucleus show us?
- Since the mass number A cancels out, the remaining quantities in the equation are all constant - Therefore, this shows the density of the nucleus is constant and independent of the radius - This shows that nucleons are spread evenly throughout the nucleus, regardless of their size
103
What does the density of a nucleus tell us?
- Nuclear density is significantly larger than atomic density - This shows that the majority of the atom's mass is contained in the nucleus - The nucleus is very small compared to the atom - Atoms must be predominantly empty space
104
What is mass-energy equivalence?
- Matter can be considered a form of energy - Therefore, mass can be converted into energy - Energy can be converted into mass
105
What is the equation for mass-energy equivalence?
- E = mc² - E = energy (J) - m = mass (kg) - c = speed of light (m/s)
106
What are some examples of mass-energy equivalence?
- The fusion of hydrogen into helium in the centre of the sun - The fission of uranium in nuclear power plants - Nuclear weapons - High-energy particle collisions in particle accelerators
107
What is mass defect?
- The difference between a nucleus's mass and the sum of the masses of its protons and neutrons - The total mass of a nucleus is less than the sum of the masses of its constituent nucleons. This difference is known as mass defect
108
What does the mass defect tell us about energy?
- Due to the equivalence of mass and energy, the mass defect implies that energy is released in the process - Since nuclei are made up of neutrons and protons, there are forces of repulsion between the positive protons - Therefore, it takes energy (binding energy) to hold the nucleons together as a nucleus
109
What is binding energy?
- The amount of energy required to separate a nucleus into its constituent protons and neutrons
110
What type of reaction is the formation of a nucleus and how do we know?
- Since we know that there is a mass defect, and that mass and energy are proportional, we also know that the total energy of a nucleus is less than the sum of the energies of its nucleons - Therefore, the formation of a nucleus is an exothermic reaction: it releases energy
111
How can we calculate how much energy is released by the formation of a nucleus?
- E = Δmc² - Δm = mass defect (kg)
112
How is binding energy measured and what does this tell us?
- Binding energies are measured in MeV - This is much larger than the few eV associated with the binding energies of electrons - This means that nuclear reactions release much more energy than chemical reactions
113
What is the unified atomic mass unit approximately equal to?
- It is roughly equal to the mass of one proton or neutron - 1u = 1.66 x 10^-27 kg
114
What is the unified atomic mass unit in terms of energy?
- Since mass and energy are interchangeable, the atomic mass unit can be expressed in MeV - 1u = 931.5 MeV
115
What is nuclear fusion?
- The joining together of two small nuclei to produce a larger nucleus
116
What type of nuclei can undergo fusion?
- Low mass nuclei such as hydrogen and helium
117
What happens when two hydrogen nuclei fuse together?
- A deuterium nucleus is produced - A positron and electron neutrino are also produced as one of the protons converts into a neutron through beta-plus decay
118
What fusion occurs in the centres of stars?
- Four hydrogen nuclei fuse to produce a helium nucleus, plus the release of energy - This provides fuel for the star to continue burning
119
What fusion are we trying to achieve on Earth?
- Research is focused on achieving the deuterium-tritium reaction - This involves fusing a deuterium nucleus and a tritium nucleus to form a helium nucleus and a neutron
120
What is required for nuclear fusion and where is it found?
- It takes a great deal of energy to overcome the electrostatic force of repulsion between protons in two nuclei - Therefore, fusion can only be achieved in an extremely hot and dense environment, such as the core of a star
121
Why is a lot of energy required for nuclear fusion?
- Both nuclei must have high kinetic energy. This is because the nuclei must be able to get close enough to fuse; however, two forces acting within the nuclei make this difficult: - Electrostatic repulsion as the nuclei are positively charged, meaning they will repel each other - Strong nuclear force: the force binds nucleons together but only acts at very short distances. Therefore, nuclei must get very close together for the strong nuclear force to take effect
122
What is nuclear fission?
- The splitting of a large atomic nucleus into smaller nuclei
123
What type of nuclei undergo nuclear fission?
- High mass nuclei (such as uranium) can undergo fission and release energy
124
What is induced fission?
- Fission might be induced by firing neutrons at a nucleus - When a neutron strikes a nucleus, it splits into two or more daughter nuclei - During fission, neutrons are ejected from the nucleus, which in turn can collide with other nuclei, triggering a cascading 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
125
Where is nuclear fission used?
- Fission is the process which produces energy in nuclear power stations, where it is well controlled
126
What happens if nuclear fission is not controlled?
- The chain reaction can cascade to produce the effects of a nuclear bomb
127
How can the energy from fission / fusion be calculated?
- The binding energy is equal to the amount of energy released in forming a nucleus. It can be calculated by: - E = Δmc² - E = binding energy released (J) - Δm = mass defect (kg)
128
Why is energy released in nuclear fusion and fission?
- The daughter nuclei produced as a result of both fission and fusion have a higher binding energy per nucleon than the parent nuclei - Therefore, energy is released as a result of the mass difference between the parents and the daughter nuclei
129
What is binding energy per nucleon?
- The binding energy of a nucleus divided by the number of nucleons in the nucleus
130
What does binding energy per nucleon tell us?
- It is used to compare nuclear stability - A higher binding energy per nucleon indicates a higher stability - This is because more energy is required to separate the nucleons contained within the nucleus
131
How can we compare the stability of elements?
- By plotting a graph of binding energy per nucleon against nucleon number (atomic mass number)
132
What is the graph of binding energy per nucleon against nucleon number at low values of A?
- When A (nucleon number) is low (A < 56): - Nuclei have lower binding energies per nucleon than at large values of A, but they tend to be stable when N=Z - This means light nuclei have weaker electrostatic forces and will undergo fusion - The gradient is much steeper compared to the gradient at large values of A. This means that fusion reactions release a greater binding energy than fission reactions
133
What is the graph of binding energy per nucleon against nucleon number at high values of A?
- When A (nucleon number) is high (A > 56): - Nuclei have generally higher binding energies per nucleon, but this gradually decreases with A - This means the heaviest elements are the most unstable and will undergo fission - The gradient is less steep compared to the gradient at low values of A - This means that fission reactions release less binding energy than fusion reactions
134
What is the most stable element and why?
- Iron (A = 56) has the highest binding energy per nucleon, which makes it the most stable element
135
Similarities between nuclear fusion and fission
- In both fission and fusion, the total mass of the products is slightly less than the mass of the reactants - The mass defect is equivalent to the binding energy that is released - Both fusion and fission release energy
136
Differences between nuclear fusion and fission
- In fusion, two smaller nuclei fuse to form a larger one. In fission, one larger nucleus splits to form two smaller nuclei - Fusion occurs between light nuclei (A<56), and fission occurs between heavy nuclei (A>56) - Fusion releases much more energy per kg than fission - Fusion requires a greater initial input of energy than fission
137
When does induced fission occur?
- When a stable nucleus splits into small nuclei due to the absorption of a slow-moving neutron
138
How is fission induced in Uranium-235?
- When a nucleus of Uranium-235 absorbs a neutron, it becomes Uranium-236 - A Uranium-236 nucleus is highly unstable and will decay into two smaller nuclei almost immediately - This is why it is not usually shown in nuclear decay
139
What are the properties of thermal neutrons?
- They have low kinetic energy - They are slow moving
140
Why must we use a thermal neutron during induced fission?
- Only slow-moving neutrons can be absorbed by Uranium-235 - If a fast-moving neutron is incident on a Uranium-235 nucleus, it will rebound from it
141
What is a thermal neutron?
- A neutron which is in thermal equilibrium with its surroundings
142
How are thermal neutrons produced?
- In nuclear reactors, neutrons are slowed until they are in thermal equilibrium with the moderator - This corresponds to a core reactor temperature of about 300K
143
What is the kinetic energy of a thermal neutron?
- Thermal neutrons have kinetic energies associated with 3/2KT
144
What are chain reactions in nuclear fission?
- The products of fission are two daughter nuclei and two or three neutrons - The neutrons released during fission go on to cause more fission reactions, leading to a chain reaction where each fission goes on to cause at least one more fission
145
What is critical mass?
- The minimum mass of fuel required to maintain a steady chain reaction - Rate of neutron loss = rate of neutron creation by fission
146
How are nuclear reactions self-sustaining?
- This is achieved by using a precise amount of uranium fuel, known as the critical mass
147
What is the point of critical mass?
- Using exactly the critical mass of fuel will mean that a single fission reaction will follow the last - This will allow the nuclear reaction to be self-sustaining and controlled
148
What is the subcritical mass?
- Using less than the critical mass - This would lead the reaction to eventually stop
149
What is the supercritical mass?
- Using more than the critical mass - This would lead to a runaway reaction and eventually an explosion
150
What must be controlled in a nuclear reactor and when?
- When the reactor is producing energy at the required rate, two factors must be controlled: - The number of free neutrons in the reactor - The energy of the free neutrons
151
What are the main components of a nuclear reactor?
- A moderator - Control rods - Coolant
152
What is the purpose of a moderator in a nuclear reactor?
- To slow down neutrons
153
What are moderators made from in nuclear reactors?
- Must be made from light nuclei, which are not fissionable and will not absorb neutrons, but will absorb a large amount of energy from them - Usually made from graphite or water
154
What is a moderator in a nuclear reactor?
- A material that surrounds the fuel rods and control rods inside the reactor core - They are used to slow down neutrons without absorbing them
155
How do moderators inside nuclear reactors work?
- The fast-moving neutrons produced by the fission reactions slow down by colliding with the molecules of the moderator, causing them to lose some momentum - The neutrons are slowed down so that they are in thermal equilibrium with the moderator - This ensures the neutrons can react efficiently with the uranium fuel
156
What is the purpose of control rods in a nuclear reactor?
- To absorb neutrons
157
What are control rods made from in nuclear reactors?
- Control rods are made of a material that absorbs neutrons without becoming dangerously unstable or decaying themselves - Usually made of boron or cadmium
158
How do control rods inside nuclear reactors work?
- The number of neutrons absorbed is controlled by varying the depth of the control rods in the reactor core - Lowering the rods further decreases the rate of fission, as more neutrons are absorbed - Raising the rods increases the rate of fission, as fewer neutrons are absorbed
159
Why do we use control rods in a nuclear reactor?
- Control rods are adjusted automatically so that exactly one fission neutron produced by each fission event goes on to cause another fission - In the event the nuclear reactor needs to be shut down, the control rods can be lowered all the way, so no reaction can take place
160
What is the purpose of coolant in nuclear reactors?
- To transfer thermal energy efficiently between the water systems of a nuclear power plant
161
What water systems require regulating in a nuclear reactor?
- The coolant (usually water) used in the reactor vessel - The water and steam that drive the turbine - The condenser that cools the steam
162
What is the heat exchanger in a nuclear reactor?
- The heat exchanger mediates the thermal energy exchanges between the water systems of a nuclear reactor
163
How does the coolant in a nuclear reactor work?
- The coolant is a substance, such as water, that is pumped into the reactor at a cold temperature to extract the heat released by the fission reactions - In the heat exchanger, the coolant transfers the heat to water that is pumped in externally to produce steam - This steam then goes on to power electricity-generating turbines
164
Why is water used as a coolant in a nuclear reactor?
- Water has a high specific heat capacity - This means it can transfer large amounts of thermal energy
165
What materials are used as a coolant?
- Water - Sometimes molten salt or inert gas
166
What are the first few collisions between neutrons and a moderator like?
- The first few collisions transfer sufficient energy to excite nuclei in the moderator without being absorbed - Then they subsequently de-excite, this energy is released as gamma radiation
167
What are the elastic collisions between neutrons and a moderator like?
- After the first few collisions, the following collisions are elastic - In these collisions, momentum is transferred to the moderator atoms - With each elastic collision, the neutron slows down until the average kinetic energy of the neutrons corresponds to that of the moderator nuclei
168
What happens after many collisions between neutrons and a moderator?
- Eventually (after about 50 collisions), the neutrons reach speeds associated with thermal random motion - At these speeds, neutrons can cause fission rather than rebound off the uranium nuclei
169
What is shielding in a nuclear reactor?
- Alpha and beta radiation can be stopped by a few cm of material; however, gamma radiation is much more penetrating - Therefore, lead or concrete is needed to ensure there are no radiation leakages
170
Why are radioactive substances dangerous?
- Some substances have a very long half-life - This means that they will be emitting harmful radiation well above background radiation for a very long time
171
What are some methods of storing nuclear waste and why?
- Common methods are water tanks and storage underground - This is to prevent damage to people and the environment now and for many years into the future - Sealing them underground means that they are less likely to be dislodged or released due to natural disasters
172
What is enriched uranium?
- The fuel used in nuclear reactors - This is U-238 enriched with U-235 as U-235 is the isotope that undergoes fission - The U-238 isotope absorbs fission neutrons, which helps to control the rate of fission reactions
173
What measures are in place to reduce a worker's exposure to radiation?
- The fuel rods are handled remotely (by machines) - The nuclear reactor is surrounded by a thick lead or concrete shielding, so radiation doesn't escape - In an emergency, the control rods are fully lowered into the reactor core to stop fission reactions by absorbing all of the free neutrons in the core
174
What are the main types of nuclear waste?
- Low-level - Intermediate-level - High-level
175
What is low-level nuclear waste?
- This is waste such as clothing, gloves and tools which may be slightly contaminated
176
How is low-level nuclear waste handled?
- This type of waste will be radioactive for a few years, so it must be encased in concrete and stored a few metres underground until it can be disposed of with regular waste
177
What is intermediate-level nuclear waste?
- This is everything between the daily used items and the fuel rods themselves - Usually, this is the waste produced when a nuclear power station is decommissioned and taken apart
178
How is intermediate-level nuclear waste handled?
- This waste will have a longer half-life than low-level waste, so it must be encased in cement in steel drums and stored securely underground
179
What is high-level nuclear waste?
- This waste comprises the unusable fission products from the fission of Uranium-235 or from spent fuel rods - This is by far the most dangerous type of waste as it will remain radioactive for thousands of years
180
Why is high-level nuclear waste so dangerous?
- It will remain radioactive for thousands of years - The spent fuel rods are extremely hot and require additional care when being handled and stored
181
How is high-level nuclear waste handled?
- The waste is initially placed in cooling ponds near the reactor for a number of years - Isotopes of plutonium and uranium are harvested to be used again - Waste is mixed with molten glass and made solid (this is known as vitrification) - Then it is encased in containers made from steel, lead or concrete - This type of waste must be stored very deep underground
182
What is different about the history of nuclear energy compared to other fields in physics?
- It is much more recent and controversial
183
What impact does nuclear energy have on the world?
- A significant proportion of the world's electricity is generated by nuclear fission reactors - The threat of nuclear weapons highlights the importance of international cooperation and peace
184
What has nuclear energy caused in society?
- People in society tend to have mixed feelings about nuclear power, with some viewing it positively, while others are fearful - With increased education on nuclear energy, people in society can use this knowledge to inform their own decisions and opinions
185
What are the benefits of nuclear power?
- Power stations produce very little pollution (no carbon dioxide or sulphur dioxide) - Highly reliable source - Can adjust output to meet higher demand - Nuclear fuel has the highest energy density of any fuel - Nuclear reactors produce some useful by-products (such as molybdenum-99)
186
What are the risks of nuclear power?
- Nuclear fuels are non-renewable energy resources - The production of radioactive waste is very dangerous and expensive to deal with - Commissioning and decommissioning a nuclear power station is expensive and time-consuming - A nuclear meltdown could have catastrophic impacts on the environment and residants