9. Energy From The Nucleus

Question 1

State the law of the conservation of energy (with equation).

Answer 1

Total energy in an isolated system remains constant . Energy can neither be created or destroyed, only changed from one form to another.
E=mc^2

Question 2

What is u?

Answer 2

It is the atomic mass unit and is equal to 1.661x10^-27kg

Question 3

When a spring with a spring constant of 25Nm^-1 is stretched 0.1m, the energy stored is 0.125J. By how much does the spring’s mass increase.

Answer 3

1.4x10^-18kg

Question 4

When the temperature of an object is increased by using an electric heater, there is an energy input. If a 20W heater used for 5 minutes has 6000J supplied to it, what is the mass increase?

Answer 4

6.7x10^-14kg

Question 5

When is the only instance when alpha decay can be spontaneous? Why?

Answer 5

When the total mass of the alpha particle and the daughter nucleus is less than the mass of the parent nucleus.

The reason for this is that lower energy means that the products are more energetically stable than the parent making the decay energetically favourable.

Some of the mass must be converted into energy in order for the particles to recoil.

Question 6

When a uranium 235 nucleus emits an alpha particle, what is the average kinetic energy of the alpha particle?

Answer 6

5MeV

Question 7

How do you convert from Joules to electron volts?

Answer 7

J –> eV

Divide by 1.6x10^-19

Question 8

Describe the N:Z ratio as the atomic number increases (atoms become heavier).
Z=protons
N=neutrons

Answer 8

Below 20Z light stable nuclei contain equal numbers of N and Z however above 20Z the stable nuceli contain more neutrons than protons and this difference becomes greater for higher Zs.

Question 9

Why does beta minus decay occur?

Answer 9

The nucleus has too many neutrons and beta decay converts a neutron into a proton.

Question 10

Why does beta plus decay occur?

Answer 10

The nucleus has too many protons so beta plus decay occurs to increase the number of neutrons.

Question 11

Why does alpha decay occur?

Answer 11

Because the nucleus has too many protons and neutrons so by losing some it makes it more stable.

Question 12

How may a more massive particle be created from two smaller particles with less mass collectively than the new particle?

Answer 12

Particles are given kinetic energy in an accelerator and the particle(s) that result from the collision will have a mass equal to the sum of the mass of the colliding particles plus their kinetic energy.

Question 13

What is neutron flux? (Mentioned briefly but not explained in textbook)

Answer 13

The neutron flux is a quantity used in nuclear reactor physics corresponding to the total length travelled by all neutrons per unit time and volume, or nearly equivalently number of neutrons travelling through a unit area in unit time.

Question 14

What is coulomb repulsion?

Answer 14

The repulsive force between two positive, or two negative charges; as described by Coulomb’s law.

Question 15

When producing new nuclei, why are neutrons often used rather than protons, deuterons or alpha particles?

Answer 15

Protons, deuterons and alpha particles must be accelerated to much higher velocities than neutrons in order to overcome the coulomb repulsion due to the like positive charges of the particles.

Question 16

How can radioactive iodine 124 be created?

Answer 16

By bombarding antimony 121 with alpha particles in a cyclotron.

Question 17

How is radioactive carbon formed and how is it used for carbon dating?

Answer 17

When neutrons in cosmic rays enter the atmosphere, they interact with nitrogen nuclei in the upper atmosphere to form CARBON-14 AND A PROTON. Plants absorb the C14 through photosynthesis and incorporate it into their structures. Animals eat the plants and then incorporate it into theirs too.

It is used for carbon dating by comparing the activity of the radioactive carbon 14 in a set mass of the substance with a set mass of a new substance.

Question 18

Why do the carbon and proton produced when cosmic rays interact with nitrogen in the upper atmosphere have more kinetic energy than the original particles?

Answer 18

There is a mass decrease so the mass that is lost is converted into the kinetic energy of the new particles.

Question 19

What is the assumption we make in order for carbon dating to be accurate?

Answer 19

That the proportion of radioactive carbon in our atmosphere has always been the same.

Question 20

How would you work out the age of a material through carbon dating? (calculation)

Answer 20

A=Ao e^- COME BACK TO

Question 21

What is binding energy?

Answer 21

• The energy needed to separate one particle from another.
• AKA the energy required to disperse all of the particles of a system (the nucleus, in nuclear binding energy)
• Equal to the mass defect (nuclear binding energy)

Question 22

State 4 different types of binding energy.

Answer 22

CHEMICAL binding energy (energy required to break bonds between atoms in a molecule).

• Binding energy due to ATTRACTION OF CHARGES (eg ionisation energy is the binding energy of an electron… )
• NUCLEAR binding energy (energy to remove a nucleon from a nucleus)

Question 23

What is mass defect?

Answer 23

The difference in mass between the masses of individual protons and neutrons and the mass of the resulting nucleus.

Question 24

What is the binding energy per nucelon?

Answer 24

The average binding energy, calculated from the mass defect divided by the number of nucleons.

Question 25

How do the binding energies of different nuclei vary as the atomic number increases from 1 to 235? (describe binding energy graph)

Answer 25

Increase (in binding energy per nucleon) rapidly from hydrogen to helium with a peak at helium and then dropping and rising again to a higher peak at iron 56 and decreasing steadily from iron to uranium 235.

Question 26

Why is there a peak on the binding energy per nucleon graph at helium and iron?

Answer 26

Iron 56 is the most stable element so therefore it has the greatest binding energy per nucelon.

(??) Helium is also very stable due to its symmetry structure causing it to have a relatively high binding energy.

Question 27

Which elements will release energy via fusion and which will release energy via fission?

Answer 27

Lighter elements below Fe will release energy through FUSION and elements above Fe will release energy through FISSION.

Question 28

For a nucleus to undergo spontaneous decay, what must happen to the binding energy?

Answer 28

There must be an increase in the total binding energy when the decay occurs (as the binding energy increases, the nucleus becomes more stable which is the aim of nuclear decay).

Question 29

What does an increase in the total binding energy after decay mean for the daughter particles?

Answer 29

It means that energy was released in the form of kinetic energy of the daughter particles and the recoiling nucleus.

Question 30

What is nuclear fission? What are the two types of nuclear fission?

Answer 30

The splitting up of a nuclei into two smaller, nuclei.

• Spontaneous fission occurs when a nucleus decays by alpha emission without outside help.
• Neutron induced fission occurs when an extra neutron is introduced to the nucleus, making the nucleus unstable and causing it to decay.

Question 31

Who first demonstrated in 1942 that the power output from a nuclear reaction could be controlled? (sorry I had to include something about this paragraph…)

Answer 31

Fermi

Question 32

What are the nuclides most commonly used in nuclear reactors?

Answer 32

Uranium 235 and plutonium 239

Question 33

Describe the sequence of events that occur when a uranium 235 nucleus absorbs a slow moving neutron.

Answer 33

• The uranium 235 nucleus absorbs a slow moving neutron
• Forms a new intermediate nucleus, uranium 236 which is UNSTABLE
• This splits up into smaller fragments
• Two smaller nuceli are produced and two or three neutrons are produced too.

Question 34

Describe the graph for fission yield against nucleon number for uranium 235.

Answer 34

Udder shaped graph with two peaks.

Y axis is logarithmic, from 0.0001 to 10

Question 35

What does the change in binding energy in the decay for a uranium 235 nucleus mean

• in terms of energy
• in terms of mass

Answer 35

• Increase in binding energy means energy is given off during the reaction
• Change in binding energy means there is a decrease in mass.

Question 36

How do you calculate the energy released in a nuclear decay using masses?

Answer 36

Use the decay equation to see what the products and reactants are.
Calculate the mass number (using the mass of protons and neutrons separately) and multiply by the number in the nucleus of the particle.
Calculate the difference of total mass (may be in atomic mass units, u, or kilograms)
Calculate the energy equivalent to the change in mass using E=mc^2 (remember to convert u into kg before substituting into this equation).
Convert Joules into MeV if necessary.

Question 37

Go through the steps of calculating the energy that 1kg of uranium 235 produces when fissioned.
(We know that 1 decay releases 2.85x10^-11 J)

Answer 37

• We know that 235g of U235 contains 6.02x10^23 atoms.
• We can calculate, by dividing by 235 that there are 2.56x10^21 atoms in 1g of U235.
• By multiplying this by 1000, we know that there are 2.56x10^24 atoms in 1kg of U235.
• To find the total energy available from this 1kg, we multiply the energy released in one decay by the number of atoms in 1kg : 2.85x10^-11 x 2.56x10^24 to give 7.3x10^13 J

Question 38

Describe the series of reactions resulting in the formation of Plutonium 239.
DO NOT LOOK IN TEXT BOOK FOR INFORMATION ON THIS BECAUSE THE TEXT BOOK IS WRONG

Answer 38

• Neutron is captured by Uranium 238 –> Uranium 239 plus a gamma ray.
• Uranium 239 under goes beta minus decay to form NEPTUNIUM 239
• Neptunium 239 also undergoes beta minus decay which forms Plutonium 239

Question 39

What are the key features of a pressurised water reactor?

Answer 39

• Strong CONTAINING VESSEL- 20cm of steel surrounded by reinforced concrete.
• FUEL RODS
• MODERATOR (heavy water)- slows the neutrons down and takes energy away from the fuel rods (coolant)
• PRESSURISER- maintains a high pressure to ensure the water does not boil
• CONTROL RODS- to control power output
• HEAT EXCHANGER-transfers energy to the coolant in a secondary circuit causing the water to boil and produce steam to turn turbines to generate power.

Question 40

What is the critical mass?

Answer 40

The minimum mass of fuel which will produce a self sustaining chain reaction (however to start the chain reaction a source of neutrons is needed)

Question 41

Give an example of a source of neutrons to commence a nuclear chain reaction.

Answer 41

-Alpha particles colliding with a Beryllium nucleus produces neutrons.

Question 42

What happens if the mass of fuel is below the critical mass?

Answer 42

Too many neutrons escape and the reaction rate cannot keep going.

Question 43

What is the shape that produces the smallest critical mass and why?

Answer 43

A sphere because it has the smallest surface area to volume ratio so there is a decreased chance of neutrons escaping and therefore not continuing the chain reaction.

Question 44

Why is the moderator in a nuclear reactor so important?

Answer 44

It slows down the neutrons which is important because at high energies, the neutrons are more likely to be captured by Uranium 238 nuclei. Slowing them down means they are more likely to be captured by Uranium 235 and cause fission.

Question 45

What are slow moving neutrons called and why?

Answer 45

• Thermal neutrons
• Because their kinetic energy is such that they are in thermal equilibrium with the moderator
• NB on average they neither gain energy from the moderator nor give any energy to it.

Question 46

How does slowing down of neutrons occur in the moderator?

Answer 46

• Neutrons collide with the nucleus of the moderating material
• A neutron colliding head on with a proton in a hydrogen nucleus would transfer all its energy to the proton
• In other collisions neutrons are scattered in different directions (billiard ball-like collisions) where some of their energy is lost to the protons, subsequently reaching thermal equilibrium with the moderator

Question 47

What is the absorption cross section

Answer 47

It is πd^2 (where d is the diameter of the nucleus)

The neutron will be absorbed into the nucleus provided it is within πd^2 of the nucleus.

Question 48

What is the unit for absorption cross section and what is the value of one unit?

Answer 48

• The barn

- 1 barn= 10^-28 m^2

Question 49

With which variables does the cross section vary other than the diameter of the nucleus?

Answer 49

• Type of nucleus
• Speed of neutron (eg for U235, the absorption cross section is greater for slow neutrons and is smaller for fast neutrons)

Question 50

What are the control rods made of and why?

Answer 50

• Boron 10

- This material absorbs neutrons to form another stable isotope of boron- boron 11

Question 51

How is electricity produced in a nuclear fission reactor? Give cycle steps

Answer 51

• Heat generated boils water
• Steam turns turbines, generating electricity
• Steam condenses as it drives the turbines
• Further cooling takes place in the heat exchanger using water from the sea or a river
• Cold water returns to the reactor to be reheated. Warm water returns to the sea or river

Question 52

Describe the steps of the hydrogen fusion cycle that takes place in the sun.

Answer 52

1) In the plasma of the sun two protons fuse to form a deuteron and a positron and electron neutrino
2) Deuterium fuses with another proton to form Helium 3 and a gamma photon
3) Two Helium 3 nuclei fuse to form Helium 4 and two protons
4) The two protons go on to fuse in further reactions

NB. TWO STAGE 1 AND TWO STAGE 2 REACTIONS TAKE PLACE TO PRODUCE THE TWO HELIUM 3 NUCLEI THAT REACT IN STAGE 3.

Question 53

What happens to the positron produced in stage 1 of the hydrogen fusion cycle in the sun?

Answer 53

It annihilates with an electron in the sun’s plasma to produce more gamma radiation.

Question 54

'’How much energy?’’ See textbook for more information

Answer 54

Refer to textbook, page 190-191.

Question 55

Describe the carbon cycle.

Answer 55

• Carbon 12 fuses with proton to form a Nitrogen 13 molecule
• Nitrogen 13 decays to Carbon 13, emitting a positron and a neutrino
• This Carbon 13 fuses with a proton to form Nitrogen 14
• Nitrogen 14 then fuses with a proton to form Oxygen 15
• Oxygen 15 then decays to form Nitrogen 15 and a positron and an electron neutrino
• Nitrogen 15 then fuses with a proton to form Carbon 12 and a Helium 4 particle.

Question 56

How can deuterons produce energy? (Describe the stages).

Answer 56

1) Two deuterons fuse to form tritium (Hydrogen 3) and a proton
2) A second deuteron fuses with the tritium nucleus to produce Helium 5 and a beta particle and an electron anti-neutrino
3) Helium 5 decays to form Helium 4 and a neutron

Question 57

What is the formula for electrical potential energy? What is this formula used for?

Answer 57

Ep=Q1Q2/4π ε₀r

The equation for electrical potential energy gives the electrical potential energy that the nuclei have that is associated with the Coulomb forces that result from the configuration of point charges within a system (the force the nuclei have on each other due to their charge).

This electrical potential energy is equal to the kinetic energy that the particles must have in order to come close enough to fuse.

Question 58

In order for two nuclei to fuse, how close must they get?

Answer 58

They have to get close enough in order for the nuclear strong force to come into play (assuming they carry a positive charge).
Therefore, the separation must be equal to the sum of their radii.

Question 59

What is ‘cold fusion’?

Answer 59

The hypothesised type of nuclear reaction that occurs around room temperature.

Two scientist thought they had discovered this when they passed a current through heavy water and found that sometimes more energy was generated than was put in electrically.

However, there is no concrete evidence to suggest that what they observed was ‘cold fusion’.

Question 60

What is the equation for the mean kinetic energy of molecules of an ideal gas?

Answer 60

1/2mc(subscript rms)²=3/2kT
k= Boltzmann constant
T= Temperature in Kelvin

Question 61

In a theoretical nuclear fusion reactor, what factors does the conditions to produce a sustained fusion reaction depend on?

Answer 61

• CONFINEMENT TIME of the plasma (the time the plasma is maintained at a temperature above the critical ignition temperature). (Must be at this temperature for a minimum length of time to yield more energy from the fusion than has been invested to heat the plasma).
• DENSITY of the plasma (critical density of the ions must be maintained in order to make the probability of a collision high enough to achieve a net yield from the reaction).

Question 62

(Not mentioned explicitly but still very relevant/suggested) What is the coulomb barrier?

Answer 62

The energy barrier due to electrostatic interaction that two nuclei need to overcome in order to get close enough to undergo a nuclear reaction.

Question 63

How is the plasma contained in a nuclear fission reactor?

Answer 63

It is contained in the cavity in the torus (doughnut shaped)

Question 64

The high temperature plasma must not touch the walls of the torus because this would cool it and fusion would not be possible. How is the plasma made to not touch the walls?
What are the problems with this?

Answer 64

A large circular magnetic field is produced using large coils around the torus. The charged particles travel in spiral paths around the torus and are kept away from the walls.

The problem is that this path is unstable so it is likely that particles drift out of the region where they should be confined.

Question 65

How can the plasma be heated to a high enough temperature for fusion to be able to occur? Describe and explain.

Answer 65

• Passing a large electric current through the plasma (5x10^6 A)- temperature increases by IR^2 heating
• Inject energy in the form of electromagnetic waves (like a microwave). Particles in the torus move in spiral paths with a frequency corresponding to radio frequencies so by injecting energy from a radio frequency transmitter, the charged particles that resonate with the radio frequency transmitted gain energy.

Question 66

What is a lithium blanket in a fusion reactor and what does it do?

Answer 66

It is a layer surrounding the vessel in a fusion power plant that absorbs energy from the fusion neutrons produced in the plasma. The neutrons undergo a fission reaction with the Lithium 6 to produce Tritium and Helium 4.

The tritium can be removed from the lithium blanket and injected into the plasma as fuel.

This produces electricity because the energy of the helium nuclei and the energy released in the lithium neutron reaction raises the temperature of the lithium blanket and plasma and can be used to boil water to turn turbines etc…

Question 67

What are the advantages and disadvantages of fusion reactors commercially, although at the moment this is still theoretical

Answer 67

Advantages

• No nuclear waste
• Deuterium from water is plentiful
• Lithium is available and our supplies will last for about 1000 years

Disadvantages

• Issue of containing the plasma so it doesn’t touch the walls of the torus
• Maintaining the plasma in the reactor at a very high temperature (design problems etc…)

Question 68

What are the steps of carrying out a risk assessment? (soz lol i had to include something on this chapter)….(classic physics B)

Answer 68

• Identify the hazzards
• Who or what may be harmed and how does the harm occur?
• Evaluate the level of risk- how may it be eliminated or reduced to an acceptable level?
• Implement the decisions
• Continue review of risks as activity progresses

Question 69

What is a risk?

Answer 69

The probability of harm being caused by an activity.

Question 70

How is radiation dose monitored in a working environment? How does this method work?

Answer 70

A radiation badge (dosimeter) is used.

In one type, radiation falling on aluminium oxide puts them into an excited state and only relax when stimulated by radiation from a laser. As they relax, visible light is emitted and the intensity of the light is a measure of the dose.

Alternatively, radiation falling on a photographic film causes it to change colour and the dose can be found by measuring the depth of the dose.

Question 71

How can the dose of different types of radiation be measured using a dosimeter?

Answer 71

Absorbers of different materials and thicknesses can be placed in front of different parts of the film so that the dose of each type of radiation is known. (accounts for the different ionising abilities of different types of radiation which affects the damage they can do.

Question 72

How many days/ months/ time is an xray of
-an arm
-the abdomen
equivalent to in terms of days/ months/ time worth of background radiation

Therefore which one poses a greater risk?

Answer 72

• X ray of an arm is worth 1.5 days of background radiation
• X ray of an abdomen is worth 4 months of background radiation

Therefore the risk of carrying out an X ray of the abdomen is much greater.

Question 73

(3 marks)
The kinetic energy for 2 Helium nuclei to come close enough to fuse to form a Beryllium-8 nucleus is given by Ep=Q1Q2/4π ε₀r. Explain why this will not enable the nuclei to fuse and form the beryllium nucleus.

Answer 73

• Mass of Be > than 2 He nuclei
• When the 2 He nuclei touch, the Ke is 0, the only mass that is available is that of the alpha particles
• Extra Ke provides increase in mass of Be-8 compared to the 2 He-2 nuclei

Question 74

(2 marks)

Suggest why it is not possible to use all the uranium-235 in the reactor fuel rods.

Answer 74

• Probability of neutron colliding with uranium nucleus too low
• Too few neutrons produced to maintain chain reaction
• More absorption of neutrons in non-fission capture