Atoms and Nuclei Atoms Notes

ATOMS AND NUCLEI NUCLEI n=8 n=7 n=6 E = –0.54 eV n=5 Pfund Series E = –0.85 eV n=4 Brackett Series E = –1.51 eV n=3 Paschen Series E = –3.4 eV n=2 n=1 1. 2. 3. 4. 5. Balmer Series E = –13.6 eV Lyman Series Limitations of Bohr's Theory : This theory is applicable only to simplest atom like hydrogen, with Z = 1. The theory fails in case atoms of other elements for which Z > 1 The theory does not explain why orbits of electrons are taken as circular, while elliptical orbits are also possible. Bohr's theory does not explain the fine structure of spectral lines even in hydrogen atom. Bohr's theory does not say anything about the relative intensities of spectral lines. Bohr's theory does not take into account the wave properties of electrons. Excitation : It is the process of absorption of energy by an electron of an atom when it jumps from lower energy state to higher energy state. Excitation energy : It is defined as the energy required by an electron to jump from the ground satte to any on of the excited states, First excitation energy of hydrogen is = E2 – E1 = – 3.4 – (–13.6) = 10.2 eV Excitation potential : It is defined as the potential difference through which an electron in an atom must be accelerated so that it may go from the ground state to the excited state. First excitation potential of hydrogen = – 3.4 – (–13.6) = 10.2 V Second excitation potential of hydrogen = – 1.51 – (–13.6) = 12.09 V Ionisation : The process of knocking out an electron from the atom is called ionization. Ionisation energy : It is defined as the energy required to knock an electron completely out of the atom i.e. energy required to take an electron from its ground state to the outermost orbit (n = ). Ionisation energy of hydrogen = E – E1 = 0 – (–13.6) = 13.6 eV Ionisation potential : The potential difference through which an electron of the atom is accelerated so that it is knocked out of the atom. The ionization potential of hydrogen atom = 0 – (–13.6) = 13.6 V ATOMS AND NUCLEI Atomic Nucleus : Rutherford established that atomic nucleus is the central core of every atom, in which the entire positive charge & almost entire mass of the atom are concentrated. The atomic nucleus is regarded as a tiny sphere of diameter ranging from 1015 m to 10–14 m. Most of the space around the nucleus in an atom is empty space. Thus, a nucleus of an atom consists of positively charged particles called protons and neutral particles called neutrons. Atomic Number : The number of protons present inside the nucleus of an atom is called atomic number. It is equal to the number of electrons present in that atom. It is represented by Z. Mass Number : Mass number of an element is the total number of protons & neutrons present inside the nucleus of the element. It is represented by A. Number of protons = Number of electrons = 2 Number of nucleons = A Number of neutrons = A – Z An element is represented as zXA, where Z is the atomic number, A is the mass number & X is the chemical symbol of that element, Example nNa23 Nuclear Size : It is experimentally found that volume of a nucleus is proprotional to its mass number A. 4 R 3  A 3 where R is the radius of the nucleus.  R = R0A1/3 where R0 is called as empirical constant. R  A 1/ 3 Nuclear Density : Nuclear Density is the ratio of mass of nucleus to its volume. If m is the average mass of a nucleon then mass of nucleus = mA Volum of nucleus = 4 4 4 R 3  (R 0 A 1/ 3 )3  R 30 A 3 3 3 mA Nuclear density   4 R 30 A 3 3m  It is of the order of 1017 kg/m3 4R 30 Atomic Mass Unit (amu or u) : One atomic mass unit is defined as 1/12 th of the mass of an atom of 6C12 isotope. 1 amu = 166 × 10–27 kg Energy Equivalent of Atomic Mass Unit : According to Einstein's mass energy equivalent : E = mc2 m = 1 amu = 1.66 × 10–27 kg E = 1.66 × 10–27 × (3 × 108)2  E = 1.49 × 1010 E= 1.49  10 10 MeV 1.6  10 10 E = 931.25 MeV Hence 1 amu = 931 MeV Isotopes : Isotpes of an element are the atoms of the element which have the same atomic number but mass number. For e.g. 1 H1, 1H2 , 1H3 are the isotopes of hydrogen. 2 He3 , 2He 4 , 2He6 are the isotopes of helium. 6 C10 , 6 C11, 6 C12 , 6 C14 are the isotopes of carbon. ATOMS AND NUCLEI Isobars : Isobars are the atom of different elements which have the same mass number, but different atomic number. The total number of nucleons is same. For e.g. 11Na22 and 10Ne22 are isobars. Isotones : 1 H3 & 2He 4 are isotones 8 O16 & 6 C14 are isotones. Isomers : These are the nuclei with same atomic number and same mass number but existing in different energy states. Nuclear Forces : Nuclear forces are the strong attractive forces which hold together the nucleons (protons & neutrons) in the nucleus. Important characteristic of these force are : 1. Nuclear forces act between a pair of neutrons, a pair of protons & also between a neutron & a proton with the same strength. This shows that these forces are independent of charge. 2. Nuclear forces are the strongest forces in nature. 3. Nuclear forces are the very short-range forces. 4. Each nucleon interacts with its immediate neighbors only. 5. Nuclear forces are non-central forces. The force between two nucleons does not act along the line joining their centres. 6. Nuclear forces are exchange forces. These forces are due to exchange of  mesons between the nucleons. Various of PE of a pair of nucleons with distance : Nuclear binding force dominates over the Coulomb repulsive force between protons inside the nucleus. So nuclear force is stronger than the Coulomb force or gravitational force between two charges. PE r0 r (fm) (a) The PE is minimum at a distance r0 = 0.8 fm. For a distance greater than r0, the PE is negative which signifies that the nuclear force is attractive. It rapidly decreases with distance and becomes negligible small at a distance of about 4 fm. (b) For a distance less than r0, the nuclear force is strongly repulsive, so the PE is positive. Mass Defect : The different between the sun of the masses of the nucleons in a nucleus & the rest mass of the nucleus is known as mass defect. It is denoted by m. The nucleus of an atom X A, contains Z protons & z (A – Z) neutrons. Mass of the nucleons in the nucleus = Zmp + (A – Z)mn where mp is the mass of a proton and mn is the mass of a neutron. If m is mass of the nucleus of ZXA then mass defect is given by : m  [ Zm p  ( A  Z)mn ]  m When a nucleus is formed from its nucleons, some of their mass is converted into energy which binds the nucleons together inside the nucleus. This energy is called binding energy and is equivalent to mass defect. Mass defect is measured in a.m.u if atomic masses are in a.m.u and if atomic masses are in kg, then mass defect is measured in kg. ATOMS AND NUCLEI Binding energy : Binding energy of a nucleus is the energy required to break up a nucleus into its constituent protons and neutrons and to separate the nucleons at infinite distance apart from the nucleus, so that they may not interact with each other. If m is the mass defect of the nucleus. then according to Einstien's mass energy relation : Bonding energy = mc 2  [ ZmP  ( A  Z)mn  m] c 2 If m is in a.m.u. then Binding energy = |ZmP + (A – Z)mn – m| × 931.5 MeV Binding energy per nucleon : The binding energy per nucleon is the average energy required to extract one nucleon from the nucleus. It gives the measure of the stability of that nucleus. Greater the binding energy per nucleon, more stable is the nucleus. B.E. per nucleon = 2 B.E [Zmp  ( A  Z)mn  m]c  A A Bonding energy/nucleon (MeV) Binding energy curve : The variation of average B.E. per nucleon with mass number A is shown as : 10 O16 8 C12 He4 6 Fe56 S32 Mo100 I127 w184 U238 O18 N14 Li6 4 H3 2 H2 0 50 100 150 200 250 Mass number (Å) (i) Average B.E./nucleon for light nucei like 1H4, 1H2, 1H3 is small (ii) For mass numbers ranging from 2 to 20, there are sharply defined maxima peaks corresponding to 2He4, 6C12, 8O16. The peaks indicate that these nuclei are relatively more table the nuclei in their neighborhood like 3Li6, 5B10, 7N14 (iii) After mass number 20, binding energy per nucleon increases & for mass numbers between 40 & 120, the curve become more or less flat. For 26Fe56, the B.E./nucleon is maximum & it is equal to 8.75 MeV. The average value of B.E. / nucleon is this region is about 8.5 MeV (iv) As the mass number increases, the B.E./nucleon decreases gradually to abut 7.6 MeV for U238. The decrease is due to Coulomb repulsion between the protons. The heavy nuclei are 92 therefore, relatively less stable. (v) The B.E./nucleon has low value for both very light & very heavy nuclei. If order to attain higher value of B.E. / nucleon, the lighter nuclei may unit together (nuclear fusion) or a heavy nucleus may split into higher nuclei (nuclear fission). ATOMS AND NUCLEI Radioactivity : The spontaneous transformation of an element into another with the emission of some particles or radiations (-particles,  - particles, -rays) is called natural radioactivity. The substances capable of emitting radiations are called radioactivity was discovered by Becquerel, who noted that Uranium element gave out some invisible rays or radiations that can penetrate through several thick black papers and affect a photographic plate on the other side. Pierre Curie and Marie Curie then confirmed the same phenomenon. They named these rays as Becqurerel rays. Rutherford and this associates investigated the nature of Becquerel rays. These are of three types :  - rays,  - rays &  - rays. A sample of radiactive element (Radius) is placed in small cavity drilled in a lead block. The radiations coming out of the cavity are subjected to an electric field provided by two plates as shown in the figure.  – – – – – – – – – – – –  E    Magnetic field + + + + + + + + + + + +   Radioactive Substance Lead Block The -rays are defected through smaller angles towards the negative plate. The  - rays are deflected through larger angles towards the positive plate. The -rays or photons remains undeflected. So it was concluded that -rays consist a stream of positively charged particles, where as  - rays consists a stream of negatively charged particles. Since  - rays were undeflected they could be waves or uncharged particles. Same results were obtained when these radians were subjected to magnetic field applied are to plane of paper. Properties of -rays : 1. An  - particle is equivalent to a helium nucleus (2He4) consisting of two protons and two neutrons. 2. It has a positive charge equal to +2e. where e = 1.6 × 10–19C 3. Mass of  - particle is of the order of 4. Because of large mass, pentrating power of  -particles is very small,  - particles can be easily stopped by an AI sheet, 0.02 mm thick. 5. Because of large mass, penetrating power of -particles is very small. -particles can be easily stopped by an Al sheet, 0.02 mm thick. 6. Because of large mass and large velocity,  - particles have large ionizing power. 7. -particles produce fluorescene in certain substances like sinc sulphide. 8. They affect photographic plate. 9. They are deflected by electric & magnetic fields. 10. While passing through thin metal foils, they get scatted. 11. They cause burns on human body. 1 th of the velocity of light. 10 ATOMS AND NUCLEI Properties of -rays : 1. A  -particles is a fast moving electron (–1e0) 2. A -particle carries the charge of an electron i.e. 1.6 ×10–19 C of negative charge. 3. The rest mass of -particle is 9.1 × 10–31 kg. same as that of electron. 4. The velocity of -particle range from 33% to 99% of velocity of light. So -particles are fast moving electrons. 5. Because of small mass, the penetrating power of -particles is very large. They can easily pass through a few millimeter of Ai sheet. Their penetrating power is 100 times that of particles. 6. The -particles ionize the gas through which they pass, but their ionizing power is 1/100th that of -particles. 7. They can also produce fluorescence in certain substances like Zinc Sulphide. 8. They affect photographic plate. 9. They are deflected by electric & magnetic fields. Properties of -rays : 1. They are electromagnetic waves which have wavelength less than of X-rays. 2. -rays are not deflected by electric & magnetic field showing that they do not have any charge. 3. -rays travel with the speed of light. The rest mass of a -photon is zero. 4. -rays have very large penetrating power. Their penetration power is 100 greater than that of -particles. They can pass through several cm. of iron & lead sheet. 5. They have small ionising power. Their ionizing power is about 1/100 times the ionizing power of -particles. 6. They can produce fluorescence in certain substances. 7. They can knock out electrons from the surface on which they fall. 8. They affect a photographic plate more than -particles. 9. They can produce nuclear reactions. Radioactive transformation : 1. Radioactivity is a spontaneous phenomenon i.e. it does not depend upon external factors like temperature pressure etc. 2. When a radioactive atom disintegrates, either an -particle or a -particle is emitted. Both are never emitted simultaneously. Also at a time, a radioactive atom can never emit more than one -particle or -particle. 3. The emission of -particle by a radioactive atom results in a new atom whose atomic number is 2 units less & mass number is 4 units less than the original atom z 4.   decay X A   z  2 Y A  4 The emission of -particle by a radioactive atom results in a new atom, whose atomic number is one unit more but mass number is same that of original atom. z   decay X A   z 1Y A Radioactive decay law : This law states that the number of nuclei disintegrated per second of a radioactive sample at any instant is directly proportional to the number of undecayed nueli present in the sample at that insant. ATOMS AND NUCLEI Mathematical form of decay law : Let N0 be the total no. of nuclei present originally in a sample at t = 0. Let N be the total no. of nuclei left in the sample at time t and dN be the total no. of dN nuclei that disintegrate in time dt. Rate of disintegration R = – Here(–) ve sign indicates dt that no. of nuclei left undecayed decrease with time. According to radioactive decay law : dN dN  N  R  N ...(1) dt dt where  is called as disintegration constant or decay constant. Eq. (1) can be written as : dN  dt N N Integrating both sides :  N0 1 dN    dt N 0  loge N – loge N0 = – t loge N0 N N  t   e  t N0 N0 number of atoms left (N) N  N e e  t t 0 Graph of radioactive decay shows that the number of active nuclei in the sample decreases exponentially with time. Decay or Disintegration Constant : We have N  Ne e  t N0 l 1  0.368 N0 we get, N  N0 e   e Thus disintegration constant of a radioactive element is the reciprocal of time at the end of Substituting t =  1 which, the number of active nuclei left undecayed in a radioactive substance reduces to   e times or 36.8% of its initial value. Its SI unit is s–1. Half Life of Radioactive Element : Half life of radioactive element is defined as the time during which half the number of radioactive nuceli present initially in the sample of the element decay. It is represented by T1/2. When t = T1/2, N = N0/2 Substituting in N = N0e–t, we get N0  N0 e  T1/ 2 2  1  e  T1/ 2  2  e T1/ 2 2 Taking log of both sides :  T1/ 2 log e e  log e 2  2.303 log10 2  T1/ 2  1  loge 2  2.303  0.3010 T1/ 2  of N0. 0.693 Thus half life is inversely proportional to decay constant and independent  N0 When t = T1/2, N = 2 After 3 half lives, N  After 2 half lives, N  1  N0   1    N0   2 4  2 n 1  N0   1    N0   2 2  2 2 3  1  1 After n half lives, N  N0    N0   2 2 ........................................... T1 / 2 where t = n × T1/2 is the total time of n half-lives. ATOMS AND NUCLEI Average life or Mean life of Radio effective Element : The average time for which the nuceli of radioactive sample exist is called mean life or average life of that sample. Average life of radioactive element can be determined by calculating the total life time of all the nuclei & dividing it by the total number of nuclei present initially in the sample. Total life of dN nuclei = t dN N0 Total life time of all the N0 nuclei =  t dN 0 N0 Average life Tav   t dN 0 N0  1 N0 N0  t dN 0 We know dN   Ndt  (N0 e  t ) dt Therefore, Tav  1 N0 0  – N e  t 0 dt  t  when N = 0, t =  & when N = N0, t = 0   Tav   te  t dt 0 Integrating by parts, we get Tav  1  Thus average life is the reciprocal of decay constant. As  = Therefore, Tav  0.693 T1/ 2 T1/ 2  1.44 T1/ 2 0.693 Decay rate or activity of a radioactive sample : The activity of a radioactive sample is defined as the number of radioactive disintegration taking place per second in the sample. If a radioactive sample contains N radionucleir at any time t, then activity R is given by R sage of time dN Here (–) sign indicates that activity of the sample decreases with the pasdt We know N  N0 e  t so, R   R  N  dN d   (N0 e  t )  N0 e  t dt dt 0.693 N More is the half life, less is the activity of the substance. T1/ 2 Units of Activity : 1. Becquered (Bq) : The activity of a radioactive substance is said to be 1bequerel if it has 1 disintegration per second. 1 Becquerel = 1 disintegration/second. 2. Curie (Ci) : The activity of a radioactive substance is said to be 1 Curie if it has 3.7 × 1010 disintegrations per second. 1 Curie = 3.7 × 1010 disintegration/second = 3.7 × 1010 Bq 3. Rutherford (rd) : The activity of a radioactive substance is said to be 1 Rutheford if it has 106 disintegrations per second. 1 Rutherford = 106 disintegration/second. ATOMS AND NUCLEI Alpha Decay : Alpha decay is a process in which an unstable nucleus transforms into a new nucleus by emitting an  - particle. When a nucelus emits an  - particle its mass number decreases by 4 & atomic number decreases by 2. z X A  z  2 Y A  4  2 He 4  Q where Q is the energy released in the decay. Q is calculated by Einstein mass energy relation E = mc2 Q  (m x  m y  mHe ) c 2 e.g. : 92 U238 90 Th234  2 He4  Q Beta Decay : It is the penomenon of spontaneous emission of an electron (e–) or a position (e4) from a radioactive nucleus. Beta minus decay : In – decay, the mass number remains unchanged but its atomic number  increases by one. An electron and a new particle antineutrino (  ) are emitted from the nucleus. z e.g. : X A  z 1 Y A  1 e 0  v or z X A  z 1 Y A   –  v 15 P 32 16 S 32  e –  v Beta plus decay : In + decay, the mass number remains unchanged but its atomic number decreases by one A position and a new particle neutrino () are emitted from the nucleus. z e.g. X A  Z 1 Y A  1 e0   or Na 22 10 Ne 11 22 z X A  Z 1 Y A       e' Note : A nucleus does not contain any electron, positron neutrino and antineutrino, yet it can eject these particles. In beta-minus decay, a neutron transforms into a proton inside the nucleus via the reaction. n  p  e   In beta-plus decay, a proton transforms into a neutron inside the nucleus via the reaction. p  n  e   It shows that a beta decay process involves the conversion of a neutron into a proton or vice-versa. These nucleons have nearly equal mass. That is why the mass number A undergoing beta decay does not change. The graph between energy of -particles & their number is as shown : (i) Most of the -particles emitted carry small energies (ii) Only very few -particles carry maximum energy called end point energy. (iii) The energy spectrum of emitted  - particles is continuous i.e. - particles can carry all possible energies from zero to maximum. Number of   particles end point energy   particle energy ATOMS AND NUCLEI Gamma Decay : It is phenomenon of emission of gamma ray photon from a radioactive nucleus. It occurs when an excited nucleus makes a transition to a state of lower energy. Z X A  Z X A   After an -or -dacay, the nucleus is usually in an excited state & it attains ground state by emitting one or more -rays photons. e.g. : The -decay of excited Co60 transforms it into an 27 Ni60 nucleus. This reaches the ground sate by emission of -rays of energies 1.17 28 MeV & 1.33 MeV. The energy level diagram is as shown. 27 CO60 28 Ni60**  1 e0 28 Ni60  28 Ni60*  E  (1.17MeV) 28 Ni60   28 Ni60*  E  (1.33MeV) Nuclear Reaction : it represents the transformation of stable nucleus of one element into stable nucleus of another element. Rutherford bombarded nitrogen with -particle given by 7 N14  2 He 4 8 O17 1 H1 In any nuclear reaction the quantities conserved are : Momentum, Nucleon, Charge and Energy. Nuclear Fission : The phenomenon of splitting of a heavy nucleus into two or more lighter nuclei. e.g. : 92 U235  0 n1 56 Ba141  36 Kr 92  3 0 n1  Q Mass defect in this reaction is 0.2153 amu. Energy released per fission of 92 U235  0.2153  931 MeV  200.4 Chain Reaction : In the above reaction three neutrons produced may bring about the fission of three more 92 U235 nuceli & produce 9 neutrons, which in turn bring fission of nine U235 92 nuclei & so on. Thus a continuous reaction called chain reaction would start & a huge amount of energy is released in a short time. It is of two types : (i) Uncontrolled chain reaction : If the fissionable material has a mass greater than the critical mass, then the reaction will accelerate at such a rapid rate that the whole material will explode within a microsecond, liberating a hage amount of energy. Such a chain reaction is called uncontrolled chain reaction. It forms the underlying principle of atom bombs. Kr2 U Kr U n U Ba U Ba U U Ba U (ii) Controlled chain reaction : If the chain reaction is controlled and maintained at steady state by absorbing a suitable number of neutrons at each stage, then the reaction is called as controlled chain reaction. Here the energy released does not get out of control. A nuclear reactor works on this principle. ATOMS AND NUCLEI Multiplication Factor : It is defined as the ratio of rate of production of neutrons to the rate of loss of neutrons. k rate of production of neutrons rate of loss of neutrons (i) If k = 1, the chain reaction will be steady. The size of the fissionable mateial is said to be the critical size and its mass, the critical mass. (ii) If k > 1, the neutron population increases exponentially with time and the chain reaction accelerates resulting in an explosion. The size of the material in this case is said to besupercritical. (iii) If k < 1, the neutron population decreases exponentially with time and the chain reaction gradually dies out. The size of the material in this case is said to be subcritical. Nuclear Reactor : The controlled nuclear Fission chain reactions for peaceful purposes can be carried out in nuclear reactors. It works on the principle of controlled chain reaction and provides energy at a constant rate. Construction : Its essential parts are : 1. Nuclear fuel : Uranium isotope (U235), Thorium isotope (Th232), etc are the most commonly used fuels in the reactor. 2. Moderator : Moderator is used to slow down the fast moving neutrons. Most commonly used moderator are graphite, heavy water etc. When heavy water is used as moderator, then nonenriched U can be used as fuel because heavy water has more neutrons to produce fission. 3. Control Rods : They are used to control the chain reaction and to maintain a stable rate of reaction. It controls the number of neutrons available for the fission. Cadmium rods are inserted into the core of the reaction because they can absorb the neutrons. The neutrons available for fission are controlled by moving the cadmium rods in or out of the core of the reactor. 4. Coolant : It is a cooling material that removes the heat generated due to fission in the reactor, Commonly used coolants are water, liquid sodium etc. 5. Protective Shields : A protective shields in the form of aconcrete thick wall surrounds the core of the reactor to save the person working around the reactor from the hazardous radiations. Cd Rods Conerete wall coolant out Moderator H To electric generator Condenser Uranium rod Heat exanger coolant in coolant ATOMS AND NUCLEI Working : A few 92U235 nuclei undergo fission liberating fast neutrons. These fast neutrons are slowed down by surrounding moderator. The cadmium rods are used to control the chain reaction. The fission produces heat in the nuclear core. The coolant transfers this heat from the core to the heat exchanger, where steam is formed. This steadm produced at very highpressure runs a turbine and the electricity is obtained at the generator. The dead steam from the turbine condenses into water and is returned to the heat exchange. The process repeats and combinuous supply of electrical energy is obtained. In addion to the production of electricity, nuclear reactor is used to produce radioactive isotopes. Nuclear Fusion : The phenomenon of fusing two or more lighter nuclei to form a single heavy nucleus. The mass of product nuclear is slightly less than the sun of the mass of the higher nuclei fusing together. This difference in masses results in the release of tremendous amount of energy. e.g. H1 1 H1 1 H2  e     0.42 MeV (i) 1 (ii) 1 (iii) 1 H2 1 H2  2 H3  n  3.27 MeV H2 1 H2 1 H3 1 H1  4.03 MeV In (i) two protons combine to form a deutron & a positorn with release of 0.42 MeV In (ii) two deutrons combine to form a light isotope of He & a neutron with release of 3.27 MeV In (iii) two deutrons combine to form triton & a proton with release of 4.03 MeV The essential conditions for carrying out nuclear fusion are : (i) High temperature is necessary for the light nuclei to have sufficient kinetic energy so that they can ovecome nutual Coulombic repulsions and come closer than the range of nuclear force. This process is called thermonuclear fusion. (ii) High density or pressure increases the rate of fusion. Energy source of start : Protons are most abundant in the body of sun and stars. At extremely high temperatures protons fuse together to form helium nuclei, liberating a huge amount of energy. This fusion takes place via two different cycles : (i) Proton-proton cycle (P-P cycle) (ii) Carbon - Nitrogen cycle (C-N cycle) (i) P-P cycle H1 1 H1 1 H2  e   0.42 MeV 1 e   e       1.02 ev H2 1 H1  2 He3    5.49 MeV 1 2 He 3  2 He3  2 He 4 1 H1  12.86 MeV ATOMS AND NUCLEI For the fourth reaction to occur, the first three reactions must occur twice. Thus the net reaction will be : 41H1  2e   2He 4  2  6  26.7 MeV Thus four protons combine to form one helium nucelus with the liberation of 26.7 MeV of energy. (ii) C-N cycle : 6 C12 1 H1 7 H13    1.93 MeV 7 H13  6 C13  e     1.20 MeV 6 C13 1 H2 7 H14    7.6 MeV 7 C14 1 H1 8 H15    7.39 MeV 8 O15  7 N15  e   v  1.71MeV 7 O15 1 N1 6 C12  2 He 4  4.99 MeV The overall reaction is : H1  6 C12  2 He 4  6 C12  2e   2  3   24.8 MeV 1 Thus four protons combine to form a helium nucleus, gamma rays and neutrons to liberate about 25 MeV of energy. Both P - P and C - NB cycles participate almost equally in the generation of energy in the sun. Starts hotter than the sun get their energy from the C - N cycle, while those cooler than sun get their energy from P - P cycle. continuously and can be used for generation of electrical power. The energy produced by fusion is clean and is not polluted by any radioactive waste. Moreover, the fuel is available in plenty in sea water. But it is very difficult to set up a sustained and controllable source of energy because fusion requires a very high temperature to 106 – 107 K. This temperature is attained by causing explosing through a fission process. Moreover, no solid container can withstand such a high temperature.