UNIT 26 : NUCLEUS
(2 HOURS)
is defined as the
central core of an
atom that is
positively charged
and contains
protons and
neutrons.
13.1 Properties of nucleus
13.2 Binding energy and mass defect.
1
26.1 Properties of nucleus (1/2 Hour)
At the end of this topic, students should be
able to:
• State the properties of proton and neutron
• Define
– Proton number
– Nucleon number
– Isotopes
• Use
to represent a nuclide
2
26.1 Properties of nucleus
• A nucleus of an atom is made up of protons and
neutrons that is also known as nucleons.
~10-15 m
A nucleus
3
13.1 Properties of nucleus
Properties of proton and neutron.
particle
mass (kg)
Proton,p 1.672 x 10-27
Neutron,n 1.675 x 10-27
charge (C )
+1.60 x 10-19
(0) neutral
4
Proton number
• defined as the number of protons in the nucleus.
• also called as atomic number, Z.
Nucleon number
• defined as the total number of neutrons and
protons in the nucleus.
• also called as atomic mass number, A.
Isotopes
• defined as the atoms of the
same element whose nuclei
contain the same number of
protons (Z) but different
number of neutrons (N).
hidrogen
deuterium
tritium
5
• The atomic nucleus can be represented as
A
Z
X
where X = symbol for the element
Z = atomic number (number of protons)
A = atomic mass number
= total number of protons and neutrons
Example :
56
26
Fe
Iron-56
26 protons
56 – 26 = 30 neutrons
A-Z=N
6
Example 26.1
Complete the table below:
Element
nuclide
1
1
9
4
14
7
16
8
23
11
59
27
31
16
133
55
238
92
H
Be
N
O
Na
Co
S
Cs
U
Number of
protons
8
Number of
neutrons
8
Number of
electrons
8
7
26.2 Binding energy and mass
defect (1 1/2 Hours)
At the end of this topic, students should be
able to:
• Define and determine mass defect
• Define and determine binding energy,
• Identify the average value of binding
energy per nucleon of stable nuclei from
the graph of binding energy per nucleon
against nucleon number.
8
26.2 Binding energy and mass defect
Binding energy,E
• defined as the energy required to
separate a nucleus into its individual
protons and neutrons without providing
them with kinetic energy.
• An alternate interpretation of the binding
energy is the energy released (emitted)
when the nucleus is formed from its
individual nucleons.
9
26.2 Binding energy and mass defect
p n
n p
+
p
n
n
p
28.30 MeV
To separate a nucleus energy is required
p
n
n
p
p n
n p
+
28.30 MeV
To form a nucleus energy is released
10
26.2 Binding energy and mass defect
Mass defect Δm
• defined as the difference between the sum of
the masses of individual nucleons that form
an atomic nucleus and the mass of the
nucleus.
Δm  Zmp  Nmn  M A
mp : mass of a proton
M A  mass of a nucleus
mn : mass of a neutron
Z  number of protons
N  number of neutrons
11
26.2 Binding energy and mass defect
• The relationship between the binding energy
and mass defect is given by
in joule
E  m c
2
binding energy
speed of light
mass defect
• In nuclear physics, mass is measured in unified
atomic mass unit (u).
931.5 MeV
1u 
c2
E  m c2
E
m  2
c
12
26.2 Binding energy and mass defect
931.5 MeV
1 eV  1.6 x 10-19 J
1u 
c2
931.5 x106 1.6 x 10 -19

8 2
3x10




 1.656 x 10 -27 kg
931.5MeV
- 27
1u 

1.66

10
kg
2
c

 Zm

931.5MeV
 u
EB  Zm p  Nmn   M A c 2
EB
p
 Nmn   M A
13
26.2 Binding energy and mass defect
• The mean (average) binding energy of a nucleus is
callled binding energy per nucleon.
Binding energy ( EB )
Binding energy per nucleon 
Nucleon number( A)
E  m c
2
mc2
Binding energy per nucleon 
A
14
Example 26.2
a) Calculate the binding energy of the deuterium.
Given 12 H mass  2.013553 u
H  11p mass  1.007276 u
1
1
n mass  1.008665 u
1
0
Δm  Zm p  Nmn   M A
 11.007276  11.008665  2.013553
 0.002388 u
 0.002388(1.66 x 10-27 )
 3.96 x 10-30 kg
15
E  m c
2

30
E  3.96x10
3x10 
8 2
E  3.57x1013 J
E  2.23 MeV
or


931.5 MeV
EB  Zm p  Nmn   M A
u
EB  11.007276  11.008665  2.013553931.5 MeV
EB  2.22 MeV
16
20
b) The binding energy of the neon 10
Ne is
160.647 MeV. Find its atomic mass.
Given
1
1
p mass  1.007825 u
n mass  1.008665 u
1
0
19.992 u
17
Example 26.3
Calculate the average binding energy per
56
nucleon of the iron-56 26 Fe .

Given
56
26

Fe mass  55.93494 u
H  11p mass  1.00782 u
1
1
n mass  1.00867 u
1
0
Δm  Zm p  Nmn   M A
 261.00782  301.00867  55.93494
 0.52848 u
 0.52848(1.66 x 10
 8.77 x 10-28 kg
- 27
)
18
mc2
Binding energy per nucleon 
A

8.77 x 10 3 x 10 

- 28
8 2
56
 1.41 x10 -12 J/nucleon
or
E = 8.81 MeV/nucleon
19
Exercise
Determine the total binding energy and the
binding energy per nucleon for the nitrogen -14
14
nucleus 7 N .
Given 147 N mass  14.003074 u
 
H  11p mass  1.007825 u
1
1
n mass  1.008665 u
1
0
104.6 MeV,7.47 MeV/nucleon
20
Binding energy per nucleon (MeV/nucleon)
Greatest stability
Binding energy per nucleon as
a function of mass number,A
21
Mass number A
• The binding energy per nucleon is a measure of
stability of the nucleus.
• The greater the binding energy per nucleon, the
more stable the nucleus is.
From the graph:
• For light nuclei, the value of EB/A rises rapidly
from 1 MeV/nucleon to 8 MeV/nucleon with
increasing mass number A.
• For the nuclei with A between 50 and 80, the
value of EB/A ranges between 8.0 and 8.9
Mev/nucleon. The nuclei in these range are
very stable.
62
Ni has the largest binding
• The nuclide 28
energy per nucleon (8.7945 MeV/nucleon). 22
• For nuclei with A > 62, the values of EB/A
decreases slowly, indicating that the nucleons
are on average, less tightly bound.
• For heavy nuclei with A between 200 to 240,
the binding energy is between 7.5 and 8.0
MeV/nucleon.These nuclei are unstable and
radioactive.
Hidrogen with one proton has no
binding energy per nucleon.
23