Stable Nuclei | Nuclear and Particle Physics for GATE - GATE Physics PDF Download

 Page 1


 
   
 
  
 
    
 
 
1(e). Stable Nuclei 
Not all combination of neutrons and protons 
form stable nuclei. In general, light nuclei 
? ? 20 ? A contain equal numbers of neutrons 
and protons, while in heavier nuclei the 
proportion of neutrons becomes 
progressively greater. This is evident in 
figure as shown below, which is plot of N 
versus Z for stable nuclides. 
The tendency for N to equal Z follows from 
the existence of nuclear energy levels. 
Nucleons, which have spin ½, obey 
exclusion principle. As a result, each energy level can contain two neutrons of opposite 
spins and two protons of opposite spins. Energy levels in nuclei are filled in sequence, 
just as energy levels in atoms are, to achieve configurations of minimum energy and 
therefore maximum stability. Thus the boron isotope 
12
5
B has more energy than the 
carbon isotope
12
6
C because one of its neutrons is in a higher energy level, and 
12
5
B is 
accordingly unstable. If created in a nuclear reaction, a 
12
5
B nucleus changes by beta 
decay into a stable 
12
6
C nucleus in a fraction of second. 
 
 
 
 
 
 
 
Figure: Neutron-proton diagram for 
stable nuclides. 
Neutron number (N)  
Proton number (Z) 
Stable nuclei 
N=Z line 
C
13
6
Proton Neutron
Figure: Simplified energy level diagrams of some boron and carbon isotopes. 
Stable Unstable
Stable
Stable
B
10
5
B
11
5
? ? B
12
5
Energy
12
6
C
Page 2


 
   
 
  
 
    
 
 
1(e). Stable Nuclei 
Not all combination of neutrons and protons 
form stable nuclei. In general, light nuclei 
? ? 20 ? A contain equal numbers of neutrons 
and protons, while in heavier nuclei the 
proportion of neutrons becomes 
progressively greater. This is evident in 
figure as shown below, which is plot of N 
versus Z for stable nuclides. 
The tendency for N to equal Z follows from 
the existence of nuclear energy levels. 
Nucleons, which have spin ½, obey 
exclusion principle. As a result, each energy level can contain two neutrons of opposite 
spins and two protons of opposite spins. Energy levels in nuclei are filled in sequence, 
just as energy levels in atoms are, to achieve configurations of minimum energy and 
therefore maximum stability. Thus the boron isotope 
12
5
B has more energy than the 
carbon isotope
12
6
C because one of its neutrons is in a higher energy level, and 
12
5
B is 
accordingly unstable. If created in a nuclear reaction, a 
12
5
B nucleus changes by beta 
decay into a stable 
12
6
C nucleus in a fraction of second. 
 
 
 
 
 
 
 
Figure: Neutron-proton diagram for 
stable nuclides. 
Neutron number (N)  
Proton number (Z) 
Stable nuclei 
N=Z line 
C
13
6
Proton Neutron
Figure: Simplified energy level diagrams of some boron and carbon isotopes. 
Stable Unstable
Stable
Stable
B
10
5
B
11
5
? ? B
12
5
Energy
12
6
C
 
   
 
  
 
    
 
 
The preceding argument is only part of the story. Protons are positively charged and repel 
one another electrically. This repulsion becomes so great in nuclei with more than 10 
protons or so that an excess of neutrons, which produce only attractive forces is required 
for stability. Thus the curve departs more and more from N Z ? line as Z increases. 
                                             Sixty percent of stable nuclides have both even Z and even N; 
these are called “even-even” nuclides. Nearly all the others have either even Z and odd N 
(“even-odd” nuclides) or odd Z and even N (“odd-even” nuclides) with the numbers of 
both kinds being about equal. Only five stable odd-odd nuclides are known:
 
2 6 10 14 180
1 3 5 7 73
H, Li, B, N and Ta . Nuclear abundances follow a similar pattern of favoring 
even numbers for Z and N.   
 These observations are consistent with the presence of nuclear energy levels that can 
each contain two particles of opposite spin. Nuclei with filled levels have less tendency to 
pick up other nucleons than those with partially filled levels and hence were less likely to 
participate in the nuclear reactions involved in the formation of elements. 
Nuclear forces are limited in range, and as a result nucleons interact strongly only with 
their nearest neighbors. This effect is referred to as the saturation of nuclear forces. 
Because the coulomb repulsion of protons is appreciable throughout the entire nucleus, 
there is a limit to the ability of neutrons to prevent the disruption of large nucleus. This 
limit is represented by the bismuth isotope
209
83
Bi , which is the heaviest stable nuclide. 
All nuclei with 83 Z ? and 209 A ? spontaneously transform themselves lighter ones 
through the emission of one or more alpha particles, which are
4
2
He nuclei: 
Alpha decay                            
A A 4 4
Z Z 2 2
X Y He
?
?
? ? 
Since an alpha particle consists of two protons and two neutrons, an alpha decay reduces 
the Z and N of the original nucleus by two each. If the resulting daughter nucleus has 
either too small or too large a neutron/proton ratio for stability, it may beta-decay to a 
more appropriate configuration. 
 
Page 3


 
   
 
  
 
    
 
 
1(e). Stable Nuclei 
Not all combination of neutrons and protons 
form stable nuclei. In general, light nuclei 
? ? 20 ? A contain equal numbers of neutrons 
and protons, while in heavier nuclei the 
proportion of neutrons becomes 
progressively greater. This is evident in 
figure as shown below, which is plot of N 
versus Z for stable nuclides. 
The tendency for N to equal Z follows from 
the existence of nuclear energy levels. 
Nucleons, which have spin ½, obey 
exclusion principle. As a result, each energy level can contain two neutrons of opposite 
spins and two protons of opposite spins. Energy levels in nuclei are filled in sequence, 
just as energy levels in atoms are, to achieve configurations of minimum energy and 
therefore maximum stability. Thus the boron isotope 
12
5
B has more energy than the 
carbon isotope
12
6
C because one of its neutrons is in a higher energy level, and 
12
5
B is 
accordingly unstable. If created in a nuclear reaction, a 
12
5
B nucleus changes by beta 
decay into a stable 
12
6
C nucleus in a fraction of second. 
 
 
 
 
 
 
 
Figure: Neutron-proton diagram for 
stable nuclides. 
Neutron number (N)  
Proton number (Z) 
Stable nuclei 
N=Z line 
C
13
6
Proton Neutron
Figure: Simplified energy level diagrams of some boron and carbon isotopes. 
Stable Unstable
Stable
Stable
B
10
5
B
11
5
? ? B
12
5
Energy
12
6
C
 
   
 
  
 
    
 
 
The preceding argument is only part of the story. Protons are positively charged and repel 
one another electrically. This repulsion becomes so great in nuclei with more than 10 
protons or so that an excess of neutrons, which produce only attractive forces is required 
for stability. Thus the curve departs more and more from N Z ? line as Z increases. 
                                             Sixty percent of stable nuclides have both even Z and even N; 
these are called “even-even” nuclides. Nearly all the others have either even Z and odd N 
(“even-odd” nuclides) or odd Z and even N (“odd-even” nuclides) with the numbers of 
both kinds being about equal. Only five stable odd-odd nuclides are known:
 
2 6 10 14 180
1 3 5 7 73
H, Li, B, N and Ta . Nuclear abundances follow a similar pattern of favoring 
even numbers for Z and N.   
 These observations are consistent with the presence of nuclear energy levels that can 
each contain two particles of opposite spin. Nuclei with filled levels have less tendency to 
pick up other nucleons than those with partially filled levels and hence were less likely to 
participate in the nuclear reactions involved in the formation of elements. 
Nuclear forces are limited in range, and as a result nucleons interact strongly only with 
their nearest neighbors. This effect is referred to as the saturation of nuclear forces. 
Because the coulomb repulsion of protons is appreciable throughout the entire nucleus, 
there is a limit to the ability of neutrons to prevent the disruption of large nucleus. This 
limit is represented by the bismuth isotope
209
83
Bi , which is the heaviest stable nuclide. 
All nuclei with 83 Z ? and 209 A ? spontaneously transform themselves lighter ones 
through the emission of one or more alpha particles, which are
4
2
He nuclei: 
Alpha decay                            
A A 4 4
Z Z 2 2
X Y He
?
?
? ? 
Since an alpha particle consists of two protons and two neutrons, an alpha decay reduces 
the Z and N of the original nucleus by two each. If the resulting daughter nucleus has 
either too small or too large a neutron/proton ratio for stability, it may beta-decay to a 
more appropriate configuration. 
 
 
   
 
  
 
    
 
 
In negative beta decay, a neutron is transformed into a proton and an electron is emitted: 
Negative beta decay                            
0
n p e
? ?
? ? 
In positive beta decay, a proton becomes a neutron and a positron is emitted: 
Positron emission                             
0
p n e
? ?
? ? 
Thus negative beta decay decreases the proportion of neutrons and positive beta decay 
increases it. A process that competes with positron emission is the capture by a nucleus of 
an electron from its innermost shell. The electron is absorbed by a nuclear proton which 
is thereby transformed into neutron: 
Electron Capture                            
0
p e n
? ?
? ?  
Figure below shows how alpha and beta decays enable stability to be achieved.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Proton number (Z) 
Figure: Alpha and beta decays permit an unstable nucleus to reach a stable configuration. 
Neutron number (N) 
Alpha decay 
N increases by 1 
Z decreases by 1 
Positive beta decay or 
electron capture  
Z decreases by 2 
N decreases by 2 
Stability curve 
Negative beta decay 
N decreases by 1 
Z  increases by 1