Ch.8.Nuclear Applications

• 8.1 Nuclear Fission - release of energy due to splitting of heavy elements into two parts

(atomic bomb and nuclear reactors)• 8.2 Nuclear Fusion - fusion of light nuclei into heavier with

release of energy (creation of heavy elements inside the stars – burning of hydrogen in the core of Sun)

• 8.3 Nuclear weapons (fission and fusion devices)• 8.4 Biomedical applications : radiation therapy, Medical

imaging, tomography, magnetic resonance• 9.7 Nuclear medicine cancer therapy• 9.8 Power production and Nuclear Waste

Nuclear fission, chain reactionsAtomic bomb

Ch. 8 Fission and fusion

Fission Fusion

AX -> A2X2+ A1X1 + Qf – fission – splitting of heavy nucleus into two parts with release of enormous of energy Qf

M(A,Z)–[M(A1,Z1)+M(A2,Z2)] = A1B(A1,Z1)+A2B(A2,Z2)-AB(A,Z)=Qf

B(A,Z)=aVA – aSA2/3-aCZ(Z-1)A-1/3 – aA(Z-A/2)2/A – aPA-1/2

Endothermic process (absorption of energy)Exothermic processes (release of energy)

2 Nuclear fusion

Nuclear fusion occurs in the core of the Sun, giving out heat and light. The reaction takes place continuously for billions of years.

(Photo credit: US NASA)

Neutron-Induced Fission

1932: discovery of neutrons by James Chadwick

1932: experiments on neutron bombardment of uranium and observation of induced radioactivity in stable elements by Enrico Fermi (Nobel 1938)

1933: Leo Szilard proposed nuclear chain reaction

1938: discovery of neutron-stimulated nuclear fission of 235U by Otto Hahn (Nobel 1944), Fritz Strassmann, Lise Meitner, and Otto Frisch

1942: the first artificial chain reaction (Enrico Fermi)

1945: first nuclear explosion in Alamogordo (New Mexico, USA)

The neutrons do not feel the Coulomb repulsion, only the nuclear attraction. Therefore nuclear reactions can be induced by neutrons of arbitrarily low energies.

Neutron-Induced Fission of 235U

n

high excitation and strong oscillation

formation of a neck (electrical repulsion pushes the lobes

apart)

n

n

Heavy nuclei (e.g., 238U) undergo fission when it acquires enough excitation energy (typically a few MeV or so). A few nuclei, notably 235U, are sufficiently excited by the mere absorption of a neutron (even this is just a thermal neutron). 235U absorbs the neutron to become 236U, and this new nucleus is so unstable that it “explodes” into two fragments.

Because heavy nuclei have a greater n/p ratio than the lighter ones, the fragments contain an excess of neutrons. To reduce this excess, two or three neutrons are emitted instantly (instant neutrons), and subsequent beta decays and neutron emission (delayed neutrons) bring the n/p ratios in the fragments to stable values.

an average 2.5 neutrons per

fission

23592 U 236

92 U

9438Sr

14054 Xe

stable

Fission Barrier

Ground states spontaneous fission half-lives for235U: (9.8 2.8) x 1018 y 238Pu: (4.70 0.08) x 1010 y 256Fm: 2.86 h 238U: (8.2 0.1) x 1015 y 254Cf: 60.7 y 260

106Sg: 7.2 ms

Spontaneous fission occurs via a quantum mechanical tunneling through the fission barrier. Spontaneous fission is possible only for elements with A 230 and x 45.

Fission occurs if an excitation energy is greater than the potential barrier that separates the two configurations (fragments inside the same nucleus and completely separated fragments) or if there is an appreciable probability for tunneling through the potential barrier.

UUB

rr0range of the nuclear force

barrier

~1/r electric potential energytotal energy of

fragments

Ch.8 Nuclear Physics Applications8.1 Fission – splitting of the heavy nuclei into 2

parts

Fission is energetically favourable - it reduces Coulomb energyE.g. - lots of energy libirated238 114

92 462 , 214U Pd Q MeV

2m 1 / 2bG = [V(r) - Q] dra2h2Z Z c1 2V (a) =

C 4πε (R + R )0 1 2

λfi

Coulomb bssi

- limitted bon-2GP

y

with

- fragments t

a

o

e ,

uc

rrier

hing

Actually: Diffuse barrier, gradual shape evolution of nucleusActivation energy Eact < VC(a)-Q

a =R(1+ε)

V=4/3πR3 V= 4/3πab2

b=R/(1+ε)1/2

Binding energy depends on deformations:Surface energy: ES=aSA2/3 (1+2/5 ε2 +…)Coulomb energy: EC=aCZ2A-1/3(1-1/5 ε2 +…)ΔB=B(ε)-B(0)= 1/5ε2 (2aSA2/3 –aCZ2 A-1/3) =0 for Z2/A~47 if ΔB<0 – energy lost by increasing ε : Eact >0 if ΔB>0 – energy gain by increasing ε : rapid fission

Fission is tunneling of the fragments through potentialbarrier

8.1 Fission (cont’s): some features

Cold nuclei (δE- n-induced ): Asymmetric fission (A1≠ A2) due to shell effectsHot nuclei : Symmetric fission (A1≈ A2 ≈Amother/2) Neutron-rich fragments:

Prompt neutrons Delayed neutrons Closer to stability: Statistical emission after β-decay long-lived Multiplicity Steep mass parabola, β-activity distributionP(ν) β-daughters must have Ex>Sn

νe

e-

νe

e-

Neutrons may trigger new fissions -> chain reaction!Used in reactors and atomic bombs

Neutron induced fission cross section: σn->F (En)=σn (En) P(Ex) with Ex~En +Sn(n+1X) σn (En) ~1/vn neutron capture cross section P(Ex) ~1 – fission probability for Ex > Eact235U: Eact < Sn(236U) (even-even) – needs <En>~kT~0.025eV 238U: Eact ~1.2MeV+Sn(239U) (odd) – needs fast neutrons

Chain ReactionsBecause fission reaction produce neutrons, a self-sustained sequence of fissions is possible. The threshold for such a chain reaction: one neutron from each fission strikes another 235U nucleus and initiates another fission.

Neutron multiplication factor: f

Sub-critical regime (f < 1): if too few neutrons initiate fissions, the reaction will slow down and stop.

Critical regime (f = 1): precisely one neutron per fission causes another fission, energy is released at a constant rate (nuclear reactor).

Super-critical regime (f > 1): more than one neutron per fission causes another fission, the frequency of fission increases exponentially, and an explosion occurs (atomic bomb).

8.1 Induced Fission and chain reactions

8.1 Induced Fission and chain reactions

<n>=Σn=1∞np(1-p)n-1=p∂/ ∂q Σn=1

∞qn==p ∂/∂q 1/(1-q)=p/(1-q)2 =1/p, where q=1-p

Nuclear ReactorsFor a self-sustained chain reaction, the multiplication factor f should be =1. What are the factors that control f ?1. The probability of absorbtion of a neutron by 235U nuclei is large only for slow neutrons. The neutrons produced by fission have too much energy. A moderator should be used to slow them down. An effective moderator should contain nuclei whose mass is close to that of neutrons. Hydrogen would be a good moderator, but it absorbs neutrons to form deuterium. Deuterium does not absorb neutrons, it is used as a moderator in the form of heavy water. Another common moderator – graphite.2. Neutrons can produce reactions other than further fission. For example, 238U can absorb neutrons to form 239U. Naturally occurring uranium contains 99.3% 238U and only 0.7% of fissionable 235U - enrichment is required to increase the percentage of 235U. A reactor that uses highly enriched uranium can use ordinary water (instead of heavy water) as a moderator.

3. Neutrons can escape from the reaction zone (the mean free path the size of the zone). Thus the mass of the nuclear fuel must be sufficiently large for a self-sustained chain reaction to take place (critical mass). The value of the critical mass depends on the fuel and the moderator (typically, a few kg).

To maintain critical regime (f = 1), the reactors should have a negative feedback. They are equipped with movable control rods (usually made of cadmium or boron) whose function is to absorb neutrons (if the rods malfunction – Chernobyl !). The time constant of the feedback loop can be reasonably long due to an existence of delayed neutrons (~1% of the total amount of neutrons) emitted by neutron-rich fission fragments having lifetimes on the order of seconds (even thermal neutrons move with v ~ 2km/s, so without delayed neutrons, the feedback should operate on the time scale ~ 0.1m/2000m/s ~10-4 s !)

8.1 reactors (cont’s)

Chain ReactionsBecause fission reaction produce neutrons, a self-sustained sequence of fissions is possible. The threshold for such a chain reaction: one neutron from each fission strikes another 235U nucleus and initiates another fission.

Neutron multiplication factor: f

Sub-critical regime (f < 1): if too few neutrons initiate fissions, the reaction will slow down and stop.

Critical regime (f = 1): precisely one neutron per fission causes another fission, energy is released at a constant rate (nuclear reactor).

Super-critical regime (f > 1): more than one neutron per fission causes another fission, the frequency of fission increases exponentially, and an explosion occurs (atomic bomb).

How does an A bomb work?To realize a super-critical regime, we need a critical mass of the material that undergoes fission (~ 1kg for pure 235U) (the critical mass depends on the probability of capture of neutrons by the nuclei that undergo fission, i.e. on the mean free path of neutrons in the material).

1st gen. 2nd gen. 3d gen.

Assuming that each fission produces 2 neutrons, and both neutrons cause further fission reactions (an ideal chain reaction), let’s find the time T required to split all 235U nuclei:

~10-7 s is the mean life-time of neutrons in 235U A – the number of generations

2 32 22 23

time# of neutrons

2 3 12 2 2 .... 2 2A AN

T A

the number of fission reactions should be equal to the total # of U atoms in 1kg

24 81

27

12.6 10 2

235 1.66 10

kgN

kg

ln 2.6 24ln10 ln 2x

- this means that the last generation will have the number 80

The total time of the explosion:

780 1 10 8T s s

The energy release: 24 8 19 132.6 10 2 10 1.6 10 / 8 10E MeV J eV J

A-bomb race – the heavy water saga

A-bomb race – the heavy water saga

A-bomb race – the heavy water saga

Hiroshima and Nagasaki

How does an A bomb work?

Nagasaki before

and after bombing

Chernobyl 26.05.1986

the lava under the Chernobyl-4 Lumps of graphite moderator ejected

The nuclear reactor after the disaster. Reactor 4

Leonid Telyatnikov (1951-2004) decorated

• Nuclear power is the use of sustained Nuclear fission to generate heat and do useful work. Nuclear Electric Plants, Nuclear Ships and Submarines use controlled nuclear energy to heat water and produce steam, while in space, nuclear energy decays naturally in a radioisotope thermoelectric generator. Scientists are experimenting wit fusion

energy for future generation, but these experiments do not currently generate useful energy.

Chernobyl 26.05.1986

Chernobyl-2

RBMK-1000

shut down in 1991

925 1,000

Chernobyl-3

RBMK-1000

shut down in 2000

925 1,000

Chernobyl-4

RBMK-1000

destroyed in the 1986 accident

925 1,000

Chernobyl-5

RBMK-1000

construction cancelled in 1988

950 1,000

Chernobyl-6

RBMK-1000

construction cancelled in 1988

950 1,000

Chernobyl-1 RBMK-1000 shut down in 1996 740 800