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 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 reactions Atomic bomb

Ch. 8 Fission and fusion FissionFusion A X -> A2 X 2 + A1 X 1 + Q f – fission – splitting of heavy nucleus into two parts with release of enormous of energy Q f M(A,Z)–[M(A 1,Z 1 )+M(A 2,Z 2 )] = A 1 B(A 1,Z 1 )+A 2 B(A 2,Z 2 )-AB(A,Z)=Q f B(A,Z)=a V A – a S A 2/3 -a C Z(Z-1)A -1/3 – a A (Z-A/2) 2 /A – a P A -1/2 Endothermic process (absorption of energy ) Exothermic processes (release of energy )

2Nuclear 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 235 U 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 235 U n high excitation and strong oscillation formation of a neck (electrical repulsion pushes the lobes apart) n n Heavy nuclei (e.g., 238 U) undergo fission when it acquires enough excitation energy (typically a few MeV or so). A few nuclei, notably 235 U, are sufficiently excited by the mere absorption of a neutron (even this is just a thermal neutron). 235 U absorbs the neutron to become 236 U, 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 stable

Fission Barrier Ground states spontaneous fission half-lives for 235 U: (9.8  2.8) x y 238 Pu: (4.70  0.08) x y 256 Fm: 2.86 h 238 U: (8.2  0.1) x y 254 Cf: 60.7 y Sg: 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. U UBUB rr0r0 range of the nuclear force barrier ~1/r electric potential energy total energy of fragments

Ch.8 Nuclear Physics Applications 8.1 Fission – splitting of the heavy nuclei into 2 parts Fission is energetically favourable - it reduces Coulomb energy E.g. - lots of energy libirated Actually: Diffuse barrier, gradual shape evolution of nucleus Activation energy E act < V C (a)-Q a =R(1+ε) V=4/3πR 3 V= 4/3πab 2 b=R/(1+ε) 1/2 Binding energy depends on deformations: Surface energy: E S =a S A 2/3 (1+2/5 ε 2 +…) Coulomb energy: E C =a C Z 2 A -1/3 (1-1/5 ε 2 +…) ΔB=B(ε)-B(0)= 1/5ε 2 (2a S A 2/3 –a C Z 2 A -1/3 ) =0 for Z 2 /A~47 if ΔB 0 if ΔB>0 – energy gain by increasing ε : rapid fission Fission is tunneling of the fragments through potential barrier

8.1 Fission (cont’s): some features Cold nuclei (δE- n-induced ): Asymmetric fission (A 1 ≠ A 2 ) due to shell effects Hot nuclei : Symmetric fission (A 1 ≈ A 2 ≈A mother /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 E x >S n νeνe e-e- νeνe e-e- Neutrons may trigger new fissions -> chain reaction! Used in reactors and atomic bombs Neutron induced fission cross section: σ n->F (E n )=σ n (E n ) P(E x ) with E x ~E n +S n ( n+1 X) σ n (E n ) ~1/v n neutron capture cross section P(E x ) ~1 – fission probability for E x > E act 235 U: E act ~kT~0.025eV 238 U: E act ~1.2MeV+S n ( 239 U) (odd) – needs fast neutrons

Chain Reactions A fission chain reaction produces intermediate mass fragments which are highly radioactive and produce further energy by their radioactive decay. Some of them produce neutrons, called delayed neutrons, which contribute to the fission chain reaction. Because 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 235 U 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). If the reaction will sustain itself, it is said to be "critical", and the mass of 235 U required to produced the critical condition is said to be a "critical mass". A critical chain reaction can be achieved at low concentrations of 235 U if the neutrons from fission are moderated in water to lower their speed, since the probability for fission with slow neutrons is greater.

8.1 Induced Fission and chain reactions

=Σ n=1 ∞ np(1-p) n-1 =p∂/ ∂q Σ n=1 ∞ q n = =p ∂/∂q 1/(1-q)=p/(1-q) 2 =1/p, where q=1-p

Nuclear Reactors For 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 235 U 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, 238 U can absorb neutrons to form 239 U. Naturally occurring uranium contains 99.3% 238 U and only 0.7% of fissionable 235 U - enrichment is required to increase the percentage of 235 U. 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 Reactions A fission chain reaction produces intermediate mass fragments which are highly radioactive and produce further energy by their radioactive decay. Some of them produce neutrons, called delayed neutrons, which contribute to the fission chain reaction. Because 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 235 U 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). If the reaction will sustain itself, it is said to be "critical", and the mass of 235 U required to produced the critical condition is said to be a "critical mass". A critical chain reaction can be achieved at low concentrations of 235 U if the neutrons from fission are moderated in water to lower their speed, since the probability for fission with slow neutrons is greater.

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 235 U) (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). 1 st gen.2 nd gen.3 d 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 235 U nuclei:  ~10 -7 s is the mean life-time of neutrons in 235 U A – the number of generations  22 33 time # of neutrons the number of fission reactions should be equal to the total # of U atoms in 1kg - this means that the last generation will have the number 80 The total time of the explosion: The energy release:

A-bomb race – the heavy water saga

Hiroshima and Nagasaki

How does an A bomb work?

Nagasaki before and after bombing

Chernobyl the lava under the Chernobyl-4 Lumps of graphite moderator ejectedgraphitemoderator The nuclear reactor after the disaster. Reactor 4 Leonid Telyatnikov ( ) 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.Nuclear fissionsteamradioisotope thermoelectric generatorfusion Chernobyl Chern obyl-2 RBMK shut down in ,000 Chern obyl-3 RBMK shut down in ,000 Chern obyl-4 RBMK destro yed in the 1986 accide nt 1986 accide nt 9251,000 Chern obyl-5 RBMK constr uction cancell ed in ,000 Chern obyl-6 RBMK constr uction cancell ed in ,000 Chernobyl-1Chernobyl-1 RBMK-1000 shut down in