Eram RizviSemester B - 2020

Introduction to Energy & Environmental Physics

SPA4250

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 2

Course adjustments Tuesday 17th lecture to continue in-person

• bring your essay plan / outline / questions • I will speak with each of you in-turn to discuss your essays

Please submit homework 6 (deadline Tuesday 17th March) by email to me • I only accept single document PDF format • Make sure your surname is in the document title and IEEP-hw6

This is the last submitted homework From this week please concentrate on essays and presentations

Similarly there are no more exercise classes as there are no more homeworks If you have questions about essays please contact me by email

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 3

SPA4250 Introduction to Energy & Environmental Physics Essay Project

The titles in blue have been randomly allocated to the class according to the table below. If you are not happy with the title that you have been allocated please choose another from the titles in black (or propose another one) then inform me either in class or by email. The titles are in the form of a question.

Allocation

1. Mo Nasif Can Algae Farms and Hydrogen Power Help to Reduce the UK's CO2 emissions by 2050?

2. Mateusz Molenda Is storing nuclear waste underground safe? 3. Suraj Pandya Harnessing the Sun - Roadmap For A Solar Future 4. e

d Jonathon Joyce Are electric cars environmentally friendly?

5. Jordan Aaron What effect is plastic having on our environment?" 6. Caleigh Lin How can a building be made to be sustainable?

7. Ross Herencia Summarise the conclusion of December 2019 COP25 summit in Madrid

8. Adam Khan How long does CO2 stay in the atmosphere after release?

9. Anna Almassy Carbon trading: how does it work and can it be considered a success?

10. Amr Abdelhady When will ITER start producing power?

11. Andrew Allinson-Bullman

Is recent freak weather the result of greenhouse gas emissions?

12. Zipora Atonga Is carbon sequestration the answer?

13. Peter Fisher Why does higher average global temperature mean more freak weather ?

14. Zuzanna Jonczyk What is the best prediction for average global temperature global increase by 2100?

15. Hershey Pasicolan When will peak oil occur? 16. Mia Pole How did Germany achieve the shift to 25% solar energy? 17. Edward Powell How does the UK intend to keep the lights on? 18. Urtzi Quintana Salgado Will taxing polluters pay for the switch to renewables? 19. Ferenc Sandor Is climate change El Niño’s fault? 20. Karmen Tatisheva How can we reduce the negative climate impact of air travel?

21. Lewis Welsh-Clark Can we store power when it is not in demand and release it when it is?

22. Kaung Kyaw Divestment from fossil fuel companies: Will this prevent further climate change?

Basics Write a 4 page essay (i.e. 4 sides of A4) on your topic question. Bibliography and diagrams are excluded from the page count. The opening part of the essay should be devoted to framing the question. Your report should include some of the underlying physics, with basic equations, and concrete typical numbers. Attempt to follow the methodology of MacKay discussed in class as part of Homework 4. Schedule You can start working on your essay project at any time but the main period devoted to this task is Weeks 6-10:

Length: 4 sides A4 References & diagrams excluded Arial 11 point font PDF format only Deadline 5pm 17th April

Essay Projects & Presentations

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 4

Presentation slot Time Allocation number

Monday 30 March 10:00 – 11:00 1 – 4

Monday 30 March 11:00 – 12:00 5 – 8

Tuesday 31 March 12:00 – 13:00 9 – 12

Monday 6 April 10:00 – 11:00 13 – 16

Monday 6 April 11:00 – 12:00 17 – 19

Tuesday 7 April 12:00 – 13:00 20 – 22

Scientific Rating (Including content and comprehension) /50

Presentation (including diagrams, spelling, references) /50

Marking scheme

Essays are to be written for an audience of your classmates, i.e. assume all information covered in this lecture course is already known. Do not repeat information from lectures

Presentations 10 minute online presentation to class on your essay topic All presentations to be sent to me by email by 12pm Sunday 29th March Only PDF format will be accepted Name your file: AllocNr_Surname_Title.pdf e.g. 07_Rizvi_Nuclear_Fusion.pdf

During presentation you will have a partner Partner will note all questions / discussion from class Use this to update your essay

From Tuesday 7th April to Friday 10th April you can vote for the best presentation

• how much did you learn • level of detail covering the topic • clarity of slides and presentation

Best presentation wins a prize £50 Amazon voucher

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 5

Nuclides

A Nuclide is a particular nucleus and is designated by the following notation:

Nuclides with identical Z but different N are called ISOTOPES. Nuclides with identical A are known as ISOBARS. Nuclides with identical N are known as ISOTONES. Long-lived (meta-stable) excited states of nuclei are known as ISOMERIC.

Z = Atomic Number (no. of Protons) A = Atomic Mass Number (no. of Nucleons) A = Z+N (Nucleons = Protons + Neutrons) N = Number of Neutrons (Sometimes Omitted)

14 nucleons 6 protons 8 neutrons

AZCN

The liquid drop model: earliest model of nucleus nucleus thought of as collection of bound objects 'objects' are in constant motion

Nuclear Binding Energy

Nuclear radius proportional to A1/3

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 6

Many other models exist describing nuclear phenomena Liquid Drop Model gives us the quantitative Semi-Empirical Mass Formula Quantifies properties of nuclei: binding energies mass stability decays Not a fundamental model - semi-empirical Only has qualitative treatment of nuclear force Quantitative power comes from fitting model parameters to data Nonetheless its makes some powerful quantitative predictions

A

Nuclear Binding Energy

u = atomic mass unit equal to 1/12 of C12 mass

C12 is 6 neutrons + 6 protons therefore u is the average nucleon mass

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 7

Liquid drop model arose from observation that B/A ~ constant across periodic table

Analogous to liquid drop: nucleons attracted by short range force, but do not collapse due to shorter range repulsive force

Surface of drop is well defined

Drop held together by surface tension ∝ Area

This plot has important implications

Explains abundance of Iron

Offers understanding of nucleosynthesis

Nuclear Binding Energy

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 8

Each nucleon contributes approx. same BE ⇒ B ∝ A (or B/A ~ const)

Each nucleon only feels neighbours not all nucleons otherwise get B ∝A(A-1) Nuclear density is ~ constant out to surface ⇒ surface nucleons contribute less B

Surface area ~ R2 and R ~ A1/3 therefore surface area ~ A2/3

Binding energy B = Edrop - Econstituents

A drop will form if energetically favourable i.e. Edrop < Econstituents

Postulate three terms for binding energy:

volume term ∝ volume - nucleons are attractive & “condense” into nuclei

surface term ∝ area - surface nucleons less tightly bound - fewer neighbours!

coulomb term ∝ Z2/radius - for uniform charge distribution within drop

A ∝ Volume

What sign will each term have?

Larger B means more tightly bound nucleus - more stable!

Nuclear Binding Energy

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 9

Qualitatively behaviour is as expected: l surface term: largest effect for small nuclei l volume term is constant by construction l Coulomb term: largest effect for high Z nuclei

This formula is incomplete: predicts greatest binding energy for Z=0 (for fixed A)

Sum of volume, surface and Coulomb terms show positive slope

We forgot to include QM nature of nucleons symmetry!

aV aS and aC are constants determined from the BE/A vs A curve on previous page

B(Z,A) = aV A� aSA2/3 � aC

Z(Z � 1)

A1/3

Nuclear Binding Energy

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 10

neutrons & protons are fermions ⇒ Paul Exclusion Principle

forbids identical fermions from same QM state will influence nucleons in potential wells ΔE is similar for neutron & proton ⇒ for fixed A, energy is minimised by having Z=N

N

Z

Stable nuclei prefer to have (i.e. Z=N) Strongly obeyed for low Z nuclei, weakly observed for high Z

Postulate Binding Energy term ~

Reduces BE when Z ≠ N quadratically Suppressed as A increases

Z = A /2

−(A − 2Z )2

A

Nuclear Binding Energy

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 11

Experiments show that 2p or 2n are always more strongly bound than 1p+1n

We add a pairing term the equation l For odd A nuclei (δ=0)

Z even, N odd Z odd, N even

l For A even

Z odd, N odd (−δ) Z even, N even (+δ) Pairing Term

Contribution to binding energy is

Approx. 3000 have been studied - only ~240 are stable 170 stable with even N and even Z 60 stable with even N and odd Z 4 stable with odd N and odd Z

�(Z,A) =aPA1/2

Spin effects produce the pairing term Nucleon pairs with net spin = 0 are more bound Such nucleons have very closely overlapping wave functions They tend to be closer together - thus more bound

Nuclear Binding Energy

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 12

Semi Empirical Mass Formula

The constants are obtained by fitting data (A>20) Light nuclei not used - additional structure due to shell closure (see later)

Given the binding energy we can calculate nuclear masses:

Nuclear masses are difficult to measure (need to remove all electrons!) Much easier to compare to measurements of atomic masses Take into account mass of electrons:

mp= proton mass mn= neutron mass

nuclear mass MN (A,Z) = Zmp + (A� Z)mn �B/c2

B(Z,A) = aV A� aSA2/3 � aC

Z(Z � 1)

A1/3� aA

(A� 2Z)2

A+ �(A,Z)

Nuclear Binding Energy

How do we measure binding energy? Measure nuclear mass and sum of nucleons to determine B

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 13

aV=15.56 MeV

aS=17.23 MeV

aC=0.697 MeV

aA=23.285 MeV

–12.0/A1/2 (oo nuclei)

δ = 0 (eo/oe nuclei)

+12.0/A1/2 (ee nuclei){

oo = odd-odd nuclei = N is odd and Z is odd ee = even-even nuclei = N is even and Z is even

Nuclear Binding Energy

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 14

Nuclear Binding Energy

Consider a nuclear reaction A + C → X + Y

238U has B/A ~ 7.6 MeV/nucleon If splits in two (A=119) → B/A = 8.5 MeV / nucleon Much more tightly bound nucleus

Releases (8.5-7.6)*238 = 214 MeV!

Compare with <10 MeV for alpha decay

Energy mostly kinetic energy Coulomb repulsion of fragments Appears as thermal energy

23892U

11946Sn

Energy release = Q value for reaction:

Spontaneous decay ONLY if Q>0 Can now predict which nuclei undergo alpha & beta decay!

Q = (X

i

Mi �X

f

Mf )c2

= Tf � Ti

sum of initial masses minus sum of final masses

Q =MA +MC �MX �MY

Q =BX +BY �BA �BCcan also be written in terms of binding energies B

Binding energy per nucleon B/A

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 15

How Does Spontaneous Fission Occur?

l 238U is also alpha emitter

l t1/2=109 y but partial t1/2 for fission is 1016 y

l Something inhibits fission... l Fission occurs due to balance of strong and Coulomb forces in nucleus l Lets loosely consider fission like an α-decay process l 238U can briefly exist as two fragments 119Sn l Coulomb potential for 2 fragments touching = 250 MeV l Very similar to 214 MeV released in process l Calculation is very crude! fission to two identical fragments may not be realistic additional neutron release can make large differences Coulomb repulsion effect for 2 hard edged sphere ...

Nevertheless refined calcs show that coulomb barrier is only just greater than energy release

a b

Q

V(r)~1/r

-V0

r

250 MeV214 MeV

Nuclear Fission

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 16

How Does Induced Fission Occur?

Ef is the activation energy: height of barrier above ground state

Liquid drop models provides intuitive picture of fission

Activation energy creates a deformation of the nucleus

Deformation becomes extreme

Results in nucleus splitting into 2

Nuclear Fission

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 17

Energy In Fission

Consider 235U + n → 236U* Excitation energy, Eex = [m(236U*)-m(236U)]c2

Assuming negligible neutron kinetic energy: m(236U*) = m(235U) + mn

Then, Eex = 6.5 MeV

Activation energy for 236U is 6.2 MeV Thus 235U can be fissioned with neutrons of negligible energy!

Similarly for 238U activation energy = 6.6 MeV, but Eex= 4.8 MeV

Thus for 238U neutrons must have ~MeV energy for fission to occur

(neglecting binding energy of this neutron!)

236U* is a compound nucleus: quasi-stable Last neutron is only very weakly bound

Nuclear Fission

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 18

Mass Distribution of Fission Fragments

Fission products are not unique A distribution of masses is produced Characteristic of low n energy induced fission One example:

235U + n → 93Rb + 141Cs + 2n Note: distribution is symmetric Note: equal A fragments are suppressed This is not yet understood

Nuclear Fission

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 19

Prompt Neutron Energy Spectrum From 235U Fission

On average: 2.5 neutrons per fission 2 MeV energy per neutron

Problem: Natural abundances of uranium are: 0.72% 235U and 99.28% 238U

Thus 235U produces more neutrons Each can induce fission again This is a chain reaction!

Nuclear Fission

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 20

Delayed Neutrons

Often delayed neutrons are also observed

These are emitted ~ seconds after fission

Come from beta decay of fragments which then emit a neutron

If fragment is in excited state & energy is larger than neutron separation energy neutron is emitted from nucleus

For 93Rb (fission fragment of 235U) energy diagram is:

In this case number of delayed neutrons is ~1 per 100 fissions

These are vital to control of nuclear reactions...

Nuclear Fission

Reading for week 9 MacKay: Chapter 24 Andrews & Jelley: chapter 8:

SPA4250 - IEEP - Week 9 - 2020Eram Rizvi 21

Backup