Chapter 26 - Nuclear Physics

Question 1

what is Einstein’s mass-energy equation

Answer 1

E = mc^2

Question 2

what are the main two ideas behind his mass-energy equation and give an example of each

Answer 2

1) Mass is a form of energy
- mass can be destroyed, releasing huge amounts of energy
- e.g. annihilation of an electron-positron pair into gamma photons

2) Energy has mass
- a change in energy of a system can lead to a change in mass of a system
- e.g. a tennis ball stationary weighs less than a moving one with K.E.

Question 3

what can we say about the mass of the decay products of an alpha decay compared to the parent nuclei and what has happened to the lost mass

Answer 3

mass of the daughter nucleus and emitted particle < mass of the parent nucleus

• this is because energy is released when the particle is emitted
• this released energy has a mass equal to the difference in mass between the parent nucleus and the daughter nucleus/emitted particle

Question 4

what occurs in annihilation

Answer 4

• when a particle and an antiparticle meet they completely destroy each other and all of their mass is converted to energy
• this energy is in the form of two very high energy photons

Question 5

what are some minimum energies/energy changes for an electron-positron annihilation

Answer 5

change in mass = 2(Me)
change in energy = 2(Me)(c^2)
energy of a single photon = (Me)(c^2)

Question 6

what occurs in pair production

Answer 6

• a high energy photon can disappear and form a particle and its respective antiparticle

Question 7

why does a full nucleus weigh a different amount to the same number of protons/neutrons but separated

Answer 7

• when you separate nucleons, work must be done to overcome the strong nuclear force
• therefore the individual nucleons have a greater energy than the nucleus as a whole
• therefore they have a greater mass according to E = mc^2

Question 8

define mass defect

Answer 8

“the mass defect of a nucleus is the difference in mass between the compete nucleus and the sum of the masses of the separate nucleons”

Question 9

define binding energy

Answer 9

“the binding energy of a nucleus is defined as the MINIMUM energy required to completely separate a nucleus into its constituent nucleons”

Question 10

how can we calculate binding energy from mass defect

Answer 10

binding energy = mass defect x c^2

Question 11

is binding energy the same for all nuclei

Answer 11

no

Question 12

how can we tell the stability of a nucleus

Answer 12

• calculate its binding energy per nucleon

Question 13

how to calculate binding energy per nucleon

Answer 13

binding energy per nucleon = total binding energy / number of nucleons

Question 14

what are the 4 main points we should remember about binding energy per nucleon and nucleon number

Answer 14

• for nuclei where A < 56, B.E. per nucleon increases with A
• for nuclei where A > 56, B.E. per nucleon decreases with A
• 56,26 Fe is the most stable nucleus
• 4,2 He, 12,6 C, and 16,8 O are have abnormally high B.E. per nucleon

Question 15

how can we explain energy changes of spontaneous radioactive decay (alpha) in terms of binding energy

Answer 15

• binding energy of a parent nucleus < binding energy of daughter nucleus + alpha particle
• therefore energy is released as the kinetic energy of the alpha particle

Question 16

how can we explain energy release of nuclear fusion in terms of binding energy

Answer 16

• two small (low mass/low A number) nuclei bond to form a bigger (higher mass/higher A number) nucleus
• given B.E. per nucleon increases with A for small nuclei, the total binding energy of the resultant nucleus is greater than the total binding energy of the individual nuclei
• therefore energy is released

Question 17

how can we explain energy release of nuclear fission in terms of binding energy

Answer 17

• a big (high mass/high A number) nucleus splits into 2 smaller (lower mass/lower A number) nuclei
• given B.E. per nucleon increases when A decreases for a large nucleus, the total binding energy of the resultant nuclei is greater than the total binding energy of the parent nucleus
• so energy is released

Question 18

how do we know where fission will occur in terms of nucleon number

Answer 18

• where A is large, fission will occur because binding energy per nucleon will increase when A decreases (nucleus splits)
• this means the products will be more energetically stable

Question 19

how do we know where fusion will occur in terms of nucleon number

Answer 19

• where A is small, fusion will occur because binding energy per nucleon will increase when A increases (nuclei fuse)
• this means the product will be more energetically stable

Question 20

what does fission involve and what is induced fission

Answer 20

• fission involves the splitting of a large nucleus into smaller daughter nuclei
• some isotopes split by themselves but many are induced by absorbing a neutron

Question 21

what is the isotope generally used in fission reactors and what is used to induce its fission, which isotopes split spontaneously

Answer 21

Uranium - 235
U - 235

• we use ‘slow’ or thermal neutrons to induce fission as they will be absorbed by the nucleus making it unstable and causing it to undergo spontaneous fission
  U-238 and U-235 rarely split spontaneously but U-236 does hence making U-235 absorb a neutron

Question 22

what is the equation for nuclear fission, briefly explain what happens and how we can check it is correct

Answer 22

1,0 n + 235,92 U —> 236,92 U
—> 141,56 Ba + 92,36 Kr + 3(1,0 n)

• U-235 absorbs a slow neutron
• this makes it U-236
• this isotope is very unstable and breaks down into 3 fast neutrons and two daughter nuclei, Ba and Kr (or La and Br)

Question 23

why is energy released in nuclear fission and how can we calculate this

Answer 23

• the mass of U-235 is higher than the mass of the daughter nuclei
• because the total binding energy of the daughter nuclei is higher than the total binding energy in U-235
• this missing mass/mass defect is released as energy in the form of kinetic energy
• we can use E=mc^2 to calculate it

Question 24

what is the importance of chain reactions in nuclear fission and how can these be controlled

Answer 24

• the fission of U-235 produces 3 fast moving neutrons
• if these neutrons could be slowed then the reaction could be made into a chain reaction
• but the number of neutrons and therefore rate of reaction would grow exponentially if not controlled
• so control rods and moderators are used to help control this and prevent an uncontrolled reaction
• it is made so that on average, 1 of the 3 fast moving neutrons survives as a slow neutron

Question 25

what are the same general components that all fission reactors have

Answer 25

all have:

• fuel rods
• control rods
• coolant
• moderator

Question 26

explain what fuel rods are

Answer 26

generally enriched uranium rods evenly spaced in the reactor core, contain mostly U-238 but about 2-3% U-235

Question 27

explain what the moderator is and what it does

Answer 27

• the moderator must slow down fast moving electrons but NOT ABSORB them
• fast neutrons are not slowed sufficiently by their collisions with Uranium because their collisions are generally elastic
• they are slowed when they collide with water/heavy water or carbon because the collisions are inelastic
• so these make good moderators

Question 28

explain what control rods are and how they can be used to control the reaction

Answer 28

• they absorb excess neutrons, they are usually made of boron or cadmium
• they can be lifted or dropped to control the rate of reaction
• if lifted, the reaction rate increases as more neutrons are available
• if dropped, the reaction rate decreases as fewer neutrons are available

Question 29

explain what the coolant is and what the two types are

Answer 29

primary coolant - carries heat from the reactor core, usually gas or liquid, becomes radioactive

secondary coolant - water, heated to produce steam to turn the turbines, does not become radioactive

Question 30

describe some advantages of nuclear power

Answer 30

• Uranium is non-renewable but there is plenty of it so can almost be classed as such
• no greenhouse gases are produced, only water vapour
• millions of times more energy is released from nuclear power than an equal mass of fossil fuels would produce

Question 31

describe the issues associated with nuclear waste

Answer 31

• U-238 can absorb medium energy neutrons to form Pu -239, this is highly toxic, radioactive and has a very long half life, it also forms radioactive daughter nuclei
• spent fuel rods are high level waste, they are generally stored underground but there are limited facilities for this
• low level waste is also produced but this is generally stored on site

Question 32

define what nuclear fusion is and give an example of where it occurs

Answer 32

“nuclear fusion is a process in which small nuclei bond together/fuse to form larger nuclei”

it occurs in the sun

Question 33

how does fusion occur/what conditions

Answer 33

• for nuclei to fuse together they must get very close, about 10^-15m
• at this distance the strong nuclear force acts and attracts them
• high temperatures are required for fusion to occur, this is because the nuclei need a very high kinetic energy in order to do work against and overcome the strong electrostatic repulsion between them
• high pressures/densities can also help

Question 34

what is the most basic example of nuclear fusion and what is a link we can draw to radiation

Answer 34

two protons fuse together to form deuterium
(1,1)p + (1,1)p —-> (2,1)H + (0,1)e + v

it effectively forms (2,2)He then decays via Beta +

Question 35

what fusion can occur to a deuterium nucleus and a proton

Answer 35

(2,1)H + (1,1)p —-> (3,2)He

a deuterium nucleus fuses with a proton to form a helium nucleus

Question 36

what fusion can occur between helium nuclei and how does this link to the most simple fusion reaction

Answer 36

(3,2)He + (3,2)He —-> (4,2)He + 2(1,1)p

these two protons formed can again fuse to form deuterium and keep a chain going

Question 37

why is energy released in nuclear fusion

Answer 37

• when small nuclei fuse, the binding energy per nucleon increases, this causes the overall binding energy to increase so energy is released because the products have a greater binding energy than the reactants

Question 38

why can we not produce efficient fusion on earth yet

Answer 38

• it requires very high temperatures and pressures for long durations

Question 39

what form is energy released in during nuclear fission or fusion

Answer 39

kinetic (and therefore thermal)

Question 40

what temperature does fusion (of hydrogen) generally occur at and why can fusion sometimes occur at lower temperatures

Answer 40

generally around 10^9K
sometimes occurs lower at 10^7K because MEAN Ek is directly prop to temperature but at a lower temp some molecules will still have a high enough Ek to fuse as they have higher than average Ek

Question 41

Describe the process of nuclear fission

Answer 41

• a neutron is absorbed by a massive (uranium) nucleus

- the nucleus splits and undergoes fission to form two smaller daughter nuclei AND one or more neutrons

Question 42

Compare the energy release of nuclear fusion of hydrogen with alpha particle decay

Answer 42

• energy is released in both
• more energy is released in fusion of hydrogen because the mass defect is greater/ there is a greater difference in binding energy

Question 43

explain the importance of gravity in making fusion reactions possible inside the sun

Answer 43

• gravity pulls together plasma/protons etc.
• so increases density
• so frequency of collisions between nuclei is greater
• GPE to thermal transfer of energy gives the high temperatures required