B.Sc.SemVI Unit i

As per the syllabus of Gondwana University Gadchiroli

1. Unit-I

2. Mass –energy equivalence relation According to special theory of relativity , it is necessary to treat mass as another form of energy. Einstein gave the famous energy mass equivalence relation E= m Where ,c is velocity of light= 3x m/s  

3. Atomic mass unit ( a.m.u .) One atomic unit i.e. a.m.u . is defined as 1/12 mass of carbon atom The carbon has 6 protons and 6 neutrons It has the mass 1.992647x kg. According to the definition of a.m.u . 1a.m.u.= = = 1.6605x kg  

4. To convert mass into energy , we multiply it by Where C= m/s = velocity of light E = mx = 1.6605x x = 1.4924x Joules = = 0.9315x Mev = 931.5 Mev  

5. Binding Energy The binding energy of a nucleus is defined as the amount of energy required to break up the nucleus into it’s constituents protons and neutrons. binding energy is the energy required to separate the nucleons from nucleus. Thus , binding energy of nucleus is the energy equivalent to the mass defect. The binding energy of the nucleus is given by B.E. = Mx = {[ Z (A-Z) } x  

6. Average Binding Energy The average binding energy is defined as the binding energy per nucleon. Average B.E. = = = {[ Z (A-Z) } x  

7. Binding Energy curve A graph between B.E. per nucleons and mass number A for large number of nuclei is called B.E. curve. It is as shown in fig.

8. From Binding Energy curve , it is clear that 1)The B.E. for all stable nuclei is positive. 2) The B.E. per nucleon for very light nuclei such as is very small. 3) The B.E. curve rises steeply at first and then more gradually upto 8.8 Mev for most stable isotope of iron . 4) The B.E.curve drops slowly to about 7.6 Mev for Uranium. 5) The B.E. curve has sharps five peacks for He,Be,C ,O and Ne. 6)The B.E. per nucleons is maximum in the range of A= 50 to A= 60  

9. 7)The B.E. per nucleons is almost constant in the range of A= 30 to A= 170 8)The B.E. per nucleons has lower value for the light nuclei A<30 and heavy nuclei A>170.

10. Significance of B.E. Curve The B.E. per nucleons is a measure of nucleus stability .Greater the value of The B.E. per nucleons , nucleus will be more stable. From B.E. per nucleon curve , it is observed that B.E. per nucleon value is less for light and heavy nuclei. B.E . per nucleon curve is most significant because we concluded following two important points.

11. If a heavy nuclei for A=240 is caused to break down into two intermediate nuclei then the resulting nuclei will be more stable than initial two heavy nuclei . This process is called nuclear fission. If two light nuclei fuse together , then the resulting nuclei is more stable than initial two light nuclei. This process is known as nuclear fusion.

12. Peaks in B.E. Curve There are five peaks in B.E. curve for the mass number 4,8,12,16 and 20. The nuclei corresponding to these peaks have even number of protons and even number neutrons. These nuclei are more stable than their immediate neighbors and have higher value of binding energy , give rise to peaks.

13. Packing fraction The mass number of nucleus is not whole number but it may very close to whole number The deviation of mass number from its nearest whole number is called Packing fraction. Packing Fraction f =  

14. F = But , M-A = = mass defect. Hence Packing fraction, f = = Hence ,the packing fraction is equal to mass defect per nucleon of the nucleus.  

15. Packing Fraction curve It is the graph between packing fraction(f) and mass number (A)

16. From packing fraction curve ,it I found that For the light nuclei , the packing fraction (f) is maximum and positive this indicates that these nuclei are unstable. The packing fraction is zero for oxygen As the mass number (A) is increases beyond 16,the packing fraction (f) becomes negative .This continue upto A= 180 and then again become positive for heavy nuclei A= 180 and these heavy nuclei are unstable.

17. The value of packing fraction for iron is minimum so it is more stable. The nuclei in middle range are stable

18. Spin Angular Momentum Protons and neutrons inside the nucleus called as nucleons have spin about their axis . This spin motion is quantized Inside the nucleus each nucleon has spin angular momentum and it’s magnitude is given by = Where , =  

19. Here ‘s’ is called spin angular momentum quantum number. This momentum has two components along z-axis = + and = - This represents the direction of spin.  

20. Orbital angular momentum The orbital motion of nucleons is also quantized . Inside the nucleus each nucleon has orbital angular momentum and it’s magnitude is given by = Where , =  

21. Where , is orbital angular momentum quantum number and it has only integral values 0,1,2,3,…….. The component of has along z –direction is quantized is given by, = ,( -1),( -2),……. +1,0,-1,……- ( -1),..-  

22. Total angular momentum The total angular momentum of nucleon ( ) is the vector sum of orbital angular momentum ( ) and spin angular momentum ( ) . ( ) = ( ) + ( ) The magnitude orbital angular momentum is given by = Where , =  

23. The spin angular momentum has two components along z-axis = + and = - Hence total angular momentum has only two values , j = + and j = If = 0 then j = + because j is always positive  

24. Parity Parity describes a nuclear state. According to quantum mechanics , the behavior of nuclear particle can be describe in terms of wave function ( ). The wave function ( ) depends upon the coordinates x,y and z of particle. The nuclear parity is based on the symmetry properties of wave function.  

25. If coordinate of particle is ( x,y,z ) and if they are changed to (-x,-y,-z), which is mirror image of the particle, then the behavior of wave function under the inversion of coordinates through the origin decides the parity of the nuclear system. If the wave function satisfies the following eq. ( x,y,z ) = (-x,-y,-z) i.e. no change in the sign of then it is called even parity or + parity.  

26. On other hand if ( x,y,z ) = (-x,-y,-z) i.e. the change in the sign of then it is odd parity or – ve parity. in general ( x,y,z ) = (-x,-y,-z) where P is a quantum number and property defined by it is called parity of the system. P= +1 means even parity and P= -1 means odd parity