Chapter 12: Nuclear Reaction

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1 Chapter 12: Nuclear Reaction A nuclear reaction occurs when a nucleus is unstable or is being bombarded by a nuclear particle. The product of a nuclear reaction is a new nuclide with an emission of a nuclear particle or radiation.

2 Overview Nuclear Reaction Conservation Laws Nuclear Reaction Energy, Q Nuclear Process Conservation of Charge (Z) Conservation of Nucleon Number (A) Nuclear Fission Chain Reaction Nuclear Fusion Nuclear Fusion in the Sun Nuclear Reactor

3 12.1 Nuclear Reaction State conservation of charge (Z) and nucleon number (A) in a nuclear reaction. Write and complete equation of nuclear reaction Calculate energy released in nuclear reaction Learning Objectives

4 Nuclear Reaction A nuclear reaction is defined as a physical process in which there is a change in identity of an atomic nucleus. Nuclear reaction do not obey the normal classical laws of conservation of energy and of mass. In Nuclear Physics: i. Mass and energy are equivalent. ii. Total of mass + energy is conserved

5 Nuclear Reaction If mass of A Missing mass at RHS turned to energy Absorb Energy If mass of A B B C Missing mass at LHS means this interaction needs energy supply for it to happen D mass of A BC D A B mass of Release Energy C C D D

6 Conservation Laws Several conservation laws should be obeyed by every nuclear reaction but primarily conservation of atomic number and of mass number. Conservation of charge (atomic number Z) number Z atomic reaction before atomicnumber after reaction Z Conservation of mass number A (nucleon) mass number A beforereaction mass number A after reaction

7 Reaction Energy Reaction energy is the energy released (liberated) in a nuclear reaction in the form of kinetic energy of the particle emitted, the kinetic energy of the daughter nucleus and the energy of the gamma-ray photon that may accompany the reaction. The reaction energy Q is the energy equivalent to the mass defect m of the reaction, thus 2 Q m c

8 Reaction Energy Mass defect Δm Q 2 Δmc mass of nucleus beforereaction Δm or Q > 0 (positive value) exothermic (exoergic) reaction energy is released reaction occur mass of nucleus products after reaction Δm or Q < 0 (negative value) endothermic (endoergic) reaction energy is required/ absorbed in the form of kinetic energy of the bombardment particle Without external energy, the reaction does not occur K > Q Reaction occur K < Q Reaction does not occur

9 Radioactive Decay Radioactive decay is defined as the phenomenon in which an unstable nucleus disintegrates to acquire a more stable nucleus without absorbs an external energy. The disintegration is spontaneous and most commonly 4 involves the emission of an alpha particle ( OR 2 He), a 0 beta particle ( OR ) and gamma-ray ( ). It also 1e releases an energy Q known as disintegration energy. Po Pb He Q Ni X e Q Example Ti Ti γ

10 Example 1 Radium nucleus decays by alpha emission to radon nucleus can be represented by equation below : Calculate Ra 86 Rn2He Q 226 a. the energy Q released in this decay. b. the wavelength of the gamma-ray produced. (Given mass of Ra-226, m Ra = u; mass of Rn- 222, m Rn = u and mass of particle, m = u)

11 Example 1 Solution

12 Example 1 Solution

13 Bombardment with Energetic Particle Bombardment with energetic particles is defined as an induced nuclear reaction that does not occur spontaneously; it is caused by a collision between a nucleus and energetic particles such as proton, neutron, alpha particle or photon. Consider a bombardment reaction in which a target nucleus X is bombarded by a particle x, resulting in a daughter nucleus Y, an emitted particle y and reaction energy Q: X x Y y Q

14 Bombardment with Energetic Particle Sometimes this reaction is written in the more compact form: Daughter Target (parent) X x, yy nucleus nucleus Bombarding particle Emitted particle 14 7 N 4 2 He Li1H B 1 0 n Li O 1 1 H He Q 4 2 He Q Q OR OR 7 3 OR Li N 17, p O 4 p, He B 2 7 n, Li 3 8 Example

15 Example 2 When lithium 7 Li is bombarded by a proton, two alpha 4 He particles are produced. Calculate the reaction energy. Given 1 1 H mass u 7 3 Li mass 4 2 He mass u u

16 Example 2 Solution

17 Nuclear Fission Nuclear fission is defined as a nuclear reaction in which a heavy nucleus splits into two lighter nuclei. Energy is released by the process because the average binding energy per nucleon of the fission products is greater than that of the parent. The energy released is in the form of increased kinetic energy of the product particles (neutrons) and any radiation emitted (gamma ray). It can be divided into two types: Spontaneous fission & induced fission

Nuclear Fission (Example) 235 U is bombarded by a slow neutron: 92 1 236 * 85 148 92U0n 92U 35Br 57La 3 235 1 0 n Q Excited state

18 Nuclear Fission (Example) 235 U is bombarded by a slow neutron: * U0n 92U 35Br 57La n Q Excited state (unstable) * U0n 92U 36Kr 56Ba * U0n 92U 38Sr 54Xe n Q n Q Other possible reactions

19 Graph of Binding Energy per Nucleon Against Nucleon Number

20 Graph of Binding Energy per Nucleon Against Nucleon Number Explanation: An estimate of the energy released in a fission reaction can be obtained by considering the graph in Figure above. From the Figure above, the binding energy per nucleon for uranium is about 7.6 MeV/nucleon, but for fission fragment (Z~100), the average binding Energy per nucleon is about 8.5 MeV/nucleon. Since the fission fragments are tightly bound, they have less mass.

21 Graph of Binding Energy per Nucleon Against Nucleon Number The difference in mass (or energy) between the original uranium nucleus and the fission fragments is about = 0.9 MeV per nucleon. Since there are 236 nucleons involved in each fission, the total energy released is 0.9 MeV 1nucleon 236nucleons 200MeV

22 Example 3 Calculate the energy released when 10 kg of uranium-235 undergoes fission according to U0n35Br 57La n Q Given: 92U mass n mass Br mass 235.1u 1.01 u 84.9 u 57 La mass u 148

23 Example 3 Solution U0n35Br 57La n Q The mass defect of the fission reaction is Δm m m m m 3m 0.20 u U n Ba Kr n The energy released is Q m MeV Q MeV For 1 nuclei

24 Example 3 Solution kg of uranium-235 contains atoms Molar mass in gram (g) is same as atomic mass in amu (u) For 1 mol 10 kg of urainum-235 contains 10 kg atoms atoms kg Therefore energy released by 10 kg of urainum MeV

25 Chain Reaction Chain reaction is defined as a nuclear reaction that is selfsustaining as a result of the products of one fission reaction initiating a subsequent fission reaction.

26 Chain Reaction

27 Chain Reaction From figure, one neutron initially causes one fission of a uranium-235 nucleus, the two or three neutrons released can go on to cause additional fissions, so the process multiples. Conditions to achieve chain reaction in a nuclear reactor: Slow neutrons are better at causing fission. The fissile material must more than a critical size. (The critical size/mass is defined as the minimum mass of fissile/fission material required to produce a sustained chain reaction.)

28 Nuclear Reactor

29 Nuclear Reactor A nuclear reactor consists of fuel rods (fission material, eg U-235), movable control rods and a moderator (water). Nuclear reactors use a combination of U-235 and U-238 (3-5% 235 U). The U-235 will undergo the fission reaction, while the U-238 (more stable) merely absorbs neutrons (slow neutrons). In a nuclear reactor, the chain reaction is controlled so that only one of the secondary neutrons from the fission of a U-235 nucleus is allowed to continue the fission reaction. In this manner, energy is released at a constant rate.

30 Nuclear Reactor Then the emitting neutrons with high energy are slowed down by collisions with nuclei in the surrounding material, called moderator, so that they can cause further fissions and produce more energy. In order to release energy at a steady rate, the rate of the reaction is controlled by inserting or withdrawing control rods made of elements (often cadmium) whose nuclei absorb neutrons without undergoing any additional reaction. Water circulating in the core of the reactor acts as coolant. The heated water flows to a heat exchanger where steam is produced. The steam then rotates a turbine that generates electricity.

32 Nuclear Fusion Nuclear fusion is defined as a type of nuclear reaction in which two light nuclei fuse to form a heavier nucleus with the release of large amounts of energy. The energy released in this reaction is called thermonuclear energy. 2 1 H 3 1 H 4 2 He 1 0 n Q

33 Graph of Binding Energy per Nucleon Against Nucleon Number

34 Graph of Binding Energy per Nucleon Against Nucleon Number From figure above, the binding energy per nucleon for the lighter nuclei ( 2 H) is small compared to the heavier nuclei. The energy released per nucleon in the fusion process is given by the difference between two values of binding energy per nucleon. And it is found that the energy released per nucleon by this process is greater than the energy released per nucleon by fission process.

35 Example 4 A fusion reaction is represented by the equation below: 2 1 H 2 1 H 3 1 H 1 1 H Q Calculate: a. The energy in MeV released from this fusion reaction. b. The energy released from fusion of 1.0 kg deuterium. (Given mass of proton = u, mass of tritium = u and mass of deuterium = )

36 Example 4 Solution

37 Example 4 Solution

38 Nuclear Fusion in the Sun The sun is a small star which generates energy on its own by means of nuclear fusion in its interior. The fuel of fusion reaction comes from the protons available in the sun. The protons undergo a set of fusion reactions, producing isotopes of hydrogen and also isotopes of helium. However, the helium nuclei themselves undergo nuclear reactions which produce protons again. This means that the protons go through a cycle which is then repeated. Because of this proton-proton cycle, nuclear fusion in the sun can be self-sustaining.

39 Nuclear Fusion in the Sun The set of fusion reactions in the proton-proton cycle are given The amount of energy released per cycle is about 25 MeV. Nuclear fusion occurs in the interior of the sun because the temperature of the sun is very high (approximately 1.5 x 10 7 K).

40 Nuclear Fusion in the Sun

41 Comparison between Fission and Fusion Table below shows the differences between fission and fusion reaction. Fission Heavy to light nucleus Neutron to bombard Produce more than 1 nucleus Easy to handle & control Fusion Light to heavy nucleus High temperature Produce 1 nucleus Difficult to handle & control The similarity between the fission and fusion reactions is: Both reactions produce energy. Mass is reduced after reaction. New product is produced.

42 Comparison between Fission and Fusion

Nuclear Physics and Nuclear Reactions

Slide 1 / 33 Nuclear Physics and Nuclear Reactions The Nucleus Slide 2 / 33 Proton: The charge on a proton is +1.6x10-19 C. The mass of a proton is 1.6726x10-27 kg. Neutron: The neutron is neutral. The