The document discusses nuclear stability and binding energy. It provides three key points: 1) Nuclear stability is determined by the ratio of neutrons to protons in the nucleus, with a ratio around 1.5:1 being most stable. Only about 250 of over 1500 known isotopes are stable. 2) Nuclear binding energy is the energy required to separate nucleons in the nucleus. It is measured by the mass defect, which is the difference between the actual nuclear mass and the predicted mass of its constituents. 3) Binding energy per nucleon indicates the stability of a nucleus, with higher values corresponding to greater stability. For uranium-238, the binding energy per nucleon is calculated as 7.57

1. 1
• “Why do protons stay
together when
positive charges
repel each other?”
• The main reason is
because of a force
called Strong Force.
• Opposes the
electrostatic force.

2. Chemical Reactions
New substances are made through the
formation of new nanoscopic “units” by
making and/or breaking chemical bonds
(Dalton)
All the “action” is outside of the nuclei
Nuclei remain unchanged!
Chemical Bonding involves moving electrons,
not nuclei
*

3. Nuclear Reactions
It’s all about changing the nucleus!
Independent of any “standard”
chemical reactions
*

4. NUCLEAR STABILITY &
BINDING ENERGY
SHIELA MARIE B. SIBAYAN©

5. Two kinds of STABILITY
• One refers to whether a nuclide will undergo
spontaneous nuclear decay.
• Does the nuclide decay (unstable, radioactive) or not
(stable)?
• The “valley of stability”
Kinetic
Stability
Thermo-
dynamic
Stability
*
• One refers to how stable one nuclide is
compared to another, in terms of “overall
configuration of nucleons”
–Applies to all nuclides, radioactive or not
–Assessed by Binding energy per nucleon
Ex. 206Pb is a stable
nuclide. 238U is radioactive
Ex. 56Fe is more stable than 206Pb or 2H

6. 6
Nuclear Stability
•As a general rule, a
nucleus will need a
neutron/proton ratio
of 3:2 (or 1.5:1) in
order to stay together.
•This rule is more
precise for larger
nuclei.

7. 7
Nuclear Stability
• Of all known isotopes
of natural elements
(about 1500), only 250
of them are stable.
• All of these stable
isotopes have an
atomic number in
between 1 and 83.

8. Stability Curve
Atomic number Z
Neutron
number
N
Stable
nuclei
Z = N
20 40 60 80 100
40
100
140
20
60
80
120
Nuclear particles are held together
by a nuclear strong force.
A stable nucleus remains forever, but
as the ratio of N/Z gets larger, the
atoms decay.
Elements with Z > 82 are all
unstable.

9. Atomic Mass Unit, u
One atomic mass unit (1 u) is equal to one-twelfth of the mass of
the most abundant form of the carbon atom--carbon-12.
Atomic mass unit: 1 u = 1.6606 x 10-27 kg
Common atomic masses:
Proton: 1.007276 u
Neutron: 1.008665 u
Electron: 0.00055 u Hydrogen: 1.007825 u

10. 2 8
; 3 x 10 m/s
E mc c
 
Mass and Energy
The energy of a mass of 1 u can be found:
E = (1 u)c2 = (1.66 x 10-27 kg)(3 x 108 m/s)2
E = 1.49 x 10-10 J Or E = 931.5 MeV
When converting
amu to energy:
2 MeV
u
931.5
c 

11. Mass Defect
•The nucleus
• is composed of protons and neutrons
• the actual mass is less than the mass of the
separate particles.
•The "missing" mass is in the form of energy
holding the nucleus together.

12. Mass Defect
• Mass defect (M.D) is another way of saying nuclear
B.E. It is simply the nuclear B.E. expressed not as
MeV but in mass units (MeV/c2)
   
 
 
M
M
Z
.
.
X
Nm
Zm
X
Zm
Nm
m
D
M
A
Z
n
H
N
A
Z
e
n
p







   
 
 
  2
2
2
2
atom
mass
-
ts
constituen
mass
M
M
Z
.
c
c
X
Nm
Zm
c
X
c
Zm
Nm
m
E
B
A
Z
n
H
N
A
Z
e
n
p








= Mass constituents of atom – mass of atom

13. Uranium-238
238U
92
A proton is 1.00728 amu
A neutron is 1.00867 amu
atomic number
(protons)
nucleons
(protons & neutrons)
The nuclear mass
of uranium-238 is
238.0003 amu

14. Uranium-238
(92)(1.00728) = 92.6698
(146)(1.00867)= 147.2658
92 protons
146 neutrons
predicted mass = 239.9356
actual mass = 238.0003
mass defect = 1.9353 amu

15. Binding Energy of 238U
predicted mass
239.9356
actual mass
238.0003
1.9353 amu
DE = Dmc2 = 931.5 MeV/amu
What is the binding energy per nucleon of 238U?

16. Binding Energy of 238U
Binding energy
per nucleon =
(1.9353 amu)(931.5 MeV/amu)
238 nucleons
= 7.57 MeV

17. Binding Energy
•The mass defect indicates the total energy
involved in holding the nucleus together.
•To determine the stability of the nucleus,
the binding energy per nuclear particle is a
better measure.

18. The binding energy of an atom is the energy released as all the constituent particles (n, p and e)
come together FROM INFINITY under both the STRONG force and the EM force.
The binding energy is something that is LOST from the atomic system. Thus it is not something that
the system possesses.
BINDING ENERGY

19. SINGLE NEUTRON SEPARATION ENERGY
The same method can be used to easily compute the “Single
Neutron Separation Energy” – which is the energy required
to “pull” a neutron out of the nucleus.
   
   
  2
1
1
2
2
1
1
2
M
M
M
M
c
X
m
X
S
c
m
c
X
c
X
S
N
A
Z
n
N
A
Z
n
n
N
A
Z
N
A
Z
n











20. SINGLE PROTON SEPARATION ENERGY
The same clever strategy applies to finding the “Single Proton Separation
Energy” Sp. But note here there is a difference – we must be careful in
counting electron mass.
    2
2
2
1
1
2
M
M c
m
c
m
c
Y
c
X
S e
p
N
A
Z
N
A
Z
p 


 

   
 
   
  2
1
1
2
1
1
M
M
M
M
c
X
m
Y
c
X
m
m
Y
S
N
A
Z
H
N
A
Z
N
A
Z
e
p
N
A
Z
p












p
S [Mass of Final Products – Mass of Initial atom] c2

21. Nuclear Binding Energy
• Energy must be added to a
nucleus to separate it into its
individual nucleons (protons and
neutrons).
• The energy that must be added to
separate the nucleons is called
the binding energy EB.
• The binding energy is the energy
by which the nucleons are bound
together.

23. How much is electronic binding energy?
There are two types of binding energy in the atom – Strong Nuclear B.E.
and the Electromagnetic B.E. of the electrons to the nucleus.
     
 
Nuclear EM
5 7/3
Nuclear 2.08 10
A A A
Z Z Z
A
Z
B X B X B X
B X Z

 
   
   
7/3
238 5
92 U 2.08 10 92
0.795MeV
EM
B 
  
