The document discusses properties of the nucleus, including:
- The nucleus contains positively charged protons and uncharged neutrons.
- Isotopes of an element have the same number of protons but different numbers of neutrons.
- A mass spectrometer can be used to separate isotopes based on their different masses, producing a characteristic pattern on a photographic plate.
Although ATP production is very important for mitochondria, little is known about the actual rate of production and the value of “unit of currency” for mitochondrial energy transactions. “Unit of currency” for all transactions in general is named “quantum” in Physics, and no value of ATP quantum is accurately given in bibliography, other than rough estimates. This work focuses to calculating produced energy unit in mitochondrial metabolism (Quantum for ATP, or QATP for sort) and the rate of ATP production (power of “mitochondrial factory”)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Although ATP production is very important for mitochondria, little is known about the actual rate of production and the value of “unit of currency” for mitochondrial energy transactions. “Unit of currency” for all transactions in general is named “quantum” in Physics, and no value of ATP quantum is accurately given in bibliography, other than rough estimates. This work focuses to calculating produced energy unit in mitochondrial metabolism (Quantum for ATP, or QATP for sort) and the rate of ATP production (power of “mitochondrial factory”)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
NEET Previous Year Question Paper | NEET 2016 Phase 2StudMonkNEET
Download NEET 2016 Phase 2 previous year question paper pdf for you to practise. It will help you to crack NEET 2017.
For More Information: https://goo.gl/3WWTZJ
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
NEET Previous Year Question Paper | NEET 2016 Phase 2StudMonkNEET
Download NEET 2016 Phase 2 previous year question paper pdf for you to practise. It will help you to crack NEET 2017.
For More Information: https://goo.gl/3WWTZJ
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
The Propagation and Power Deposition of Electron Cyclotron Waves in Non-Circu...IJERA Editor
By solving the plasma equilibrium equation, ray equations, and quasi-linear Fokker-Planck equation, the ray
trajectories and power deposition of EC wave has been numerically simulated in non-circular HL-2A tokamak
plasma. The results show that shaping effect and temperature profile has little influence on ECRH, while plasma
density affect propagation and power deposition obviously. when the ordinary mode of EC waves are launched
from the mid-plane and low-field-side, ray trajectories are bended as the parallel refractive index increases and
even recurve to the low-field side when the parallel refractive index reaches to a certain value. Single absorption
decreases with increasing both poloidal and toroidal injection angle, and can be 100% when poloidal injection
angle is 180o and toroidal injection angle is less than 10o.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdfPaige Cruz
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Generative AI Deep Dive: Advancing from Proof of Concept to ProductionAggregage
Join Maher Hanafi, VP of Engineering at Betterworks, in this new session where he'll share a practical framework to transform Gen AI prototypes into impactful products! He'll delve into the complexities of data collection and management, model selection and optimization, and ensuring security, scalability, and responsible use.
Le nuove frontiere dell'AI nell'RPA con UiPath Autopilot™UiPathCommunity
In questo evento online gratuito, organizzato dalla Community Italiana di UiPath, potrai esplorare le nuove funzionalità di Autopilot, il tool che integra l'Intelligenza Artificiale nei processi di sviluppo e utilizzo delle Automazioni.
📕 Vedremo insieme alcuni esempi dell'utilizzo di Autopilot in diversi tool della Suite UiPath:
Autopilot per Studio Web
Autopilot per Studio
Autopilot per Apps
Clipboard AI
GenAI applicata alla Document Understanding
👨🏫👨💻 Speakers:
Stefano Negro, UiPath MVPx3, RPA Tech Lead @ BSP Consultant
Flavio Martinelli, UiPath MVP 2023, Technical Account Manager @UiPath
Andrei Tasca, RPA Solutions Team Lead @NTT Data
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How world-class product teams are winning in the AI era by CEO and Founder, P...
Phy 310 chapter 7
1. Dr Ahmad Taufek Abdul Rahman
School of Physics & Material Studies, Faculty of Applied Sciences, Universiti Teknologi MARA Malaysia, Campus of Negeri Sembilan
CHAPTER 7: Nucleus
(3 Hours)
is defined as the
central core of an
atom that is
positively
charged and
contains protons
and neutrons.
1
2. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Learning Outcome:
7.1 Properties of nucleus (1 hour)
At the end of this chapter, students should be able to:
State the properties of proton and neutron.
Define
proton number
nucleon number
isotopes
Use
A
to represent a nucleus.
ZX
Explain the working principle and the use of mass
spectrometer to identify isotopes.
2
3. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
7.1 Properties of nucleus
7.1.1 Nuclear structure
A nucleus of an atom is made up of protons and neutrons that
known as nucleons (is defined as the particles found inside
the nucleus) as shown in Figure 7.1.
Proton
Neutron
Electron
Figure 7.1
3
4. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Proton and neutron are characterised by the following properties
in Table 7.1.
Proton (p)
Charge (C)
Mass (kg)
Neutron (n)
+e
0
(uncharged )
(1.60 10
19
)
1.672 10 27
1.675 10
27
Table 7.1
For a neutral atom,
The number of protons inside the nucleus
= the number of electrons orbiting the nucleus
This is because the magnitude of an electron charge
equals to the magnitude of a proton charge but opposite
in sign.
4
5. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Nuclei are characterised by the number and type of nucleons
they contain as shown in Table 7.2.
Number
Symbol
Definition
Atomic number
Z
The number of protons in a nucleus
Neutron number
N
The number of neutrons in a nucleus
Mass (nucleon)
number
A
The number of nucleons in a nucleus
Table 7.2
Relationship :
(7.1)
Any nucleus of elements in the periodic table called a nuclide is
characterised by its atomic number Z and its mass number A.
The nuclide of an element can be represented as in the Figure
7.2.
5
6. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Mass number
Element X
Atomic number
Figure 7.2
The number of protons Z is not necessary equal to the number
of neutrons N.
e.g. : 24 Mg
12
;
32
16
Z 12
N A Z 12
S ; 195 Pt
78
6
7. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Since a nucleus can be modeled as tightly packed sphere
where each sphere is a nucleon, thus the average radius of
the nucleus is given by
R R0 A
1
3
(7.2)
R : average radius of nucleus
15
R0 : constant 1.2 10 m OR 1.2 fm
A : mass (nucleon) number
where
femtometre (fermi)
1 fm 11015 m
7
8. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Example 1 :
Based on the periodic table of element, Write down the symbol of
nuclide for following cases:
a. Z =20 ; A =40
b. Z =17 ; A =35
c. 50 nucleons ; 24 electrons
d. 106 nucleons ; 48 protons
e. 214 nucleons ; 131 protons
Solution :
a. Given Z =20 ; A =40
A
Z
X
40
20
Ca
c. Given A=50 and Z=number of protons = number of electrons =24
A
Z
X
50
24
Cr
8
9. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Example 2 :
What is meant by the following symbols?
1
0
1
1
0
1
n; p ; e
State the mass number and sign of the charge for each entity
above.
Solution :
1
0
n
Neutron ; A=1
Charge : neutral (uncharged)
1
1
p
Proton ; A=1
Charge : positively charged
0
1
e
Electron ; A=0
Charge : negatively charged
9
10. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Example 3 :
Complete the Table 7.3.
Element Number of Number of
nuclide
protons
neutrons
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
16
15
Table 7.3
Total charge
in nucleus
Number of
electrons
16e
16
10
11. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
7.1.2 Isotope
is defined as the nuclides/elements/atoms that have the
same atomic number Z but different in mass number A.
From the definition of isotope, thus the number of protons or
electrons are equal but different in the number of neutrons
N for two isotopes from the same element.
For example :
Hydrogen isotopes:
1
1
H : Z=1, A=1, N=0
2
: Z=1, A=2, N=1
1H
proton(1 p)
1
deuterium( 2 D)
1
tritium (31T)
: Z=1, A=3, N=2
H
not equal
Oxygen isotopes: equal
3
1
16
8
17
8
18
8
O : Z=8, A=16, N=8
O : Z=8, A=17, N=9
O : Z=8, A=18, N=10
equal
not equal
11
12. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
29.1.3 Bainbridge mass spectrometer
Mass spectrometer is a device that detect the presence of
isotopes and determines the mass of the isotope from known
mass of the common or stable isotope.
Figure 7.3 shows a schematic diagram of a Bainbridge mass
spectrometer.
Ion source
S1
Plate P1
E
-
Evacuated
chamber
Figure 7.3
- + S2
-
Ions beam
Separation
between isotopes
Plate P2
+
+
+ +
Photographic plate
+ B
d
+ 1
S3
m2
m1
r
1
r2
B
2
12
-
13. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Working principle
Ions from an ion source such as a discharge tube are narrowed
to a fine beam by the slits S1 and S2.
The ions beam then passes through a velocity selector (plates
P1 and P2) which uses a uniform magnetic field B1 and a uniform
electric field E that are perpendicular to each other.
The beam with selected velocity v passes through the velocity
selector without deflection and emerge from the slit S3. Hence,
the force on an ion due to the magnetic field B1 and the electric
field E are equal in magnitude but opposite in direction (Figure
7.4).
Plate P1
Plate P2
Figure 7.4
FE
v
B
F
Using Fleming’s
left hand rule.
13
14. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Thus the selected velocity is
FB FE
qvB1 sin 90 qE
E
v
B1
The ions beam emerging from the slit S3 enter an evacuated
chamber of uniform magnetic field B2 which is perpendicular to
the selected velocity v. The force due to the magnetic field B2
causes an ion to move in a semicircle path of radius r given by
FB Fc
mv 2
qvB2 sin 90
r
mv
r
B2 q
and
E
v
B1
14
15. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
mE
r
B1 B2 q
(7.3)
Since the magnetic fields B1 and B2 and the electric field E are
constants and every ion entering the spectrometer contains the
same amount of charge q, therefore
E
constant
r km and k
B1B2 q
rm
If ions of masses m1 and m2 strike the photographic plate with
radii r1 and r2 respectively as shown in Figure 7.3 then the ratio
of their masses is given by
m1 r1
m2 r2
(7.4)
15
16. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Example 4 :
A beam of singly charged ions of isotopes Ne-20 and Ne-22 travels
straight through the velocity selector of a Bainbridge mass
spectrometer. The mutually perpendicular electric and magnetic
fields in the velocity selector are 0.4 MV m1 and 0.7 T respectively.
These ions then enter a chamber of uniform magnetic flux density
1.0 T. Calculate
a. the selected velocity of the ions,
b. the separation between two isotopes on the photographic plate.
(Given the mass of Ne-20 = 3.32 1026 kg; mass of Ne-22 =
3.65 1026 kg and charge of the beam is 1.60 1019 C)
Solution : E 0.4 10 6 V m 1 ; B1 0.7 T; B2 1.0 T
a. The selected velocity of the ions is
E
v
B1
0.4 10 6
v
0.7
v 5.71 10 5 m s 1
16
17. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Solution : E 0.4 10 6 V m 1 ; B 0.7 T; B 1.0 T
1
2
b. The radius of the circular path made by isotope Ne-20 is
m1 E
r1
B1 B2 q
3.32 10 0.4 10
r
0.7 1.01.60 10
26
6
19
1
0.119 m
and the radius of the circular path made by isotope Ne-22 is
3.65 10 0.4 10
0.7 1.01.60 10
26
r2
6
19
0.130 m
Therefore the separation between the isotope of Ne is given by
d d 2 d1
Figure 7.3
d 2r2 2r1
2r2 r1
20.130 0.119
d 2.2 10 2 m
17
18. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Learning Outcome:
7.2 Binding energy and mass defect (2 hours)
At the end of this chapter, students should be able to:
Define mass defect and binding energy.
Use formulae
E mc 2
Identify the average value of binding energy per
nucleon of stable nuclei from the graph of binding
energy per nucleon against nucleon number.
18
19. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
7.2 Binding energy and mass defect
7.2.1 Einstein mass-energy relation
From the theory of relativity leads to the idea that mass is a
form of energy.
Mass and energy can be related by the following relation:
E mc 2
where
(7.5)
E : amount of energy
m : rest mass
c : speed of light in vacuum (3.00 108 m s 1 )
e.g. The energy for 1 kg of substance is
E mc 2
(1)(3.00 108 ) 2
E 9.00 1016 J
19
20. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Unit conversion of mass and energy
The electron-volt (eV)
is a unit of energy.
is defined as the kinetic energy gained by an electron in
being accelerated by a potential difference (voltage) of 1
volt.
19
1 eV 1.60 10 J
1 MeV 106 eV 1.60 1013 J
The atomic mass unit (u)
is a unit of mass.
1
is defined as exactly
the mass of a neutral carbon-12
12
atom.
mass of 12C
6
1u
12
1 u 1.66 1027 kg
20
21. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
1 atomic mass unit (u) can be converted into the unit of
energy by using the mass-energy relation (eq. 7.5).
E mc 2
(1.66 10 27 )(3.00 108 ) 2
E 1.49 10 10 J
in joule,
1 u 1.49 1010 J
in eV/c2 or MeV/c2,
1.49 10 10
E
931.5 10 6 eV/c 2
1.60 10 19
1 u 931.5 106 eV/ c 2
OR
1 u 931.5 MeV/ c 2
21
22. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
7.2.2 Mass defect
The mass of a nucleus (MA) is always less than the total mass
of its constituent nucleons (Zmp+Nmn) i.e.
M A Zmp Nmn
where
mp : mass of a proton
mn : mass of a neutron
Thus the difference in this mass is given by
m Zm p Nmn M A
(7.6)
where m is called mass defect and is defined as the mass
difference between the total mass of the constituent
nucleons and the mass of a nucleus.
The reduction in mass arises because the act of combining
the nucleons to form the nucleus causes some of their mass
to be released as energy.
Any attempt to separate the nucleons would involve them
being given this same amount of energy. This energy is called
22
the binding energy of the nucleus.
23. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
7.2.3 Binding energy
The binding energy of a nucleus is defined as the energy
required to separate completely all the nucleons in the
nucleus.
The binding energy of the nucleus is equal to the energy
equivalent of the mass defect. Hence
Binding energy
in joule
EB mc 2
Mass defect in kg
(7.7)
Speed of light in
vacuum
7.2.4 Nucleus stability
Since the nucleus is viewed as a closed packed of nucleons,
thus its stability depends only on the forces exist inside it.
The forces involve inside the nucleus are
repulsive electrostatic (Coulomb) forces between
protons and
attractive forces that bind all nucleons together in the
23
nucleus.
24. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
These attractive force is called nuclear force and is responsible
for nucleus stability.
The general properties of the nuclear force are summarized
as follow :
The nuclear force is attractive and is the strongest force
in nature.
It is a short range force . It means that a nucleon is
attracted only to its nearest neighbours in the nucleus.
It does not depend on charge; neutrons as well as protons
are bound and the nuclear force is same for both.
e.g. proton-proton (p-p)
The magnitude of nuclear
neutron-neutron (n-n)
forces are same.
proton-neutron (p-n)
The nuclear force depends on the binding energy per
nucleon.
24
25. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Note that a nucleus is stable if the nuclear force greater than
the Coulomb force and vice versa.
The binding energy per nucleon of a nucleus is a measure of
the nucleus stability where
Binding energy ( EB )
Binding energy per nucleon
Nucleon number( A)
mc 2
Binding energy per nucleon
A
(7.8)
Figure 7.5 shows a graph of the binding energy per nucleon as
a function of mass (nucleon) number A.
25
26. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Binding energy per
nucleon (MeV/nucleon)
Greatest stability
Figure 7.5
Mass number A
26
27. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
From Figure 7.5,
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. The maximum value of the
curve occurs in the vicinity of nickel, which has the most
stable nucleus.
For A > 62, the values of EB/A decreases slowly, indicating
that the nucleons are on average less tightly bound.
The value of EB/A rises rapidly from 1 MeV/nucleon to 8
MeV/nucleon with increasing mass number A for light nuclei.
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.
Figure 7.6 shows a graph of neutron number N against atomic
number Z for a number of stable nuclei.
27
28. Neutron number, N
DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Line of
stability
N=Z
Figure 7.6
Atomic number Z
28
29. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
From Figure 7.6,
The stable nuclei are represented by the blue dots, which lie
in a narrow range called the line of stability.
The dashed line corresponds to the condition N=Z.
The light stable nuclei contain an equal number of
protons and neutrons (N=Z) but in heavy stable nuclei
the number of neutrons always greater than the number
of protons (above Z =20) hence the line of stability
deviates upward from the line of N=Z.
This means as the number of protons increase, the
strength of repulsive coulomb force increases which
tends to break the nucleus apart.
As a result, more neutrons are needed to keep the
nucleus stable because neutrons experience only the
attractive nuclear force.
29
30. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Example 5 :
Calculate the binding energy of an aluminum nucleus
27
13 Al
in MeV.
(Given mass of neutron, mn=1.00867 u ; mass of proton,
mp=1.00782 u ; speed of light in vacuum, c=3.00108 m s1 and
atomic mass of aluminum, MAl=26.98154 u)
Solution :
27
13 Al
Z 13 and N 27 13
N 14
The mass defect of the aluminum nucleus is
m Zmp Nmn M Al
13 1.00782 14 1.00867 26.98154
m 0.2415 u
30
31. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Solution :
The binding energy of the aluminum nucleus can be calculated by
using two method.
2
1st method:
1 u 1.66 1027 kg
E m c
B
in kg
m 0.2415 1.66 1027
28
4.0089 10 kg
28
EB 4.0089 10 3.00 10
EB 3.608 1011 J
8 2
Thus the binding energy in MeV is
11
3.608 10
EB
1.60 10 13
EB 226 MeV
1 MeV 1.60 1013 J
31
32. DR.ATAR @ UiTM.NS
Solution :
2nd method:
PHY310 NUCLEUS
EB mc 2
1 u 931.5 MeV/c 2
in u
931.5 MeV/ c 2 2
c
m
1u
931.5 MeV/ c 2 2
c
0.2415 u
1u
EB 225 MeV
32
33. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Example 6 :
Calculate the binding energy per nucleon of a boron nucleus
in J/nucleon.
B
10
5
(Given mass of neutron, mn=1.00867 u ; mass of proton,
mp=1.00782 u ; speed of light in vacuum, c=3.00108 m s1 and
atomic mass of boron, MB=10.01294 u)
Solution :
10
5
B
Z 5
and
N 10 5
N 5
The mass defect of the boron nucleus is
m Zmp Nmn M B
5 1.00782 5 1.00867 10.01294
m 0.06951 u
33
34. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Solution :
The binding energy of the boron nucleus is given by
EB mc 2
0.06951 1.66 10
27
3.00 10
8 2
EB 1.04 1011 J
Hence the binding energy per nucleon is
EB 1.04 1011
A
10
EB
1.04 10 12 J/nucleon
A
34
35. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Example 7 :
Why is the uranium-238 nucleus 238 U less stable than carbon-12
92
12
nucleus
? Give an explanation by referring to the repulsive
6C
coulomb force and the binding energy per nucleon.
(Given mass of neutron, mn=1.00867 u ; mass of proton,
mp=1.00782 u ; speed of light in vacuum, c=3.00108 m s1; atomic
mass of carbon-12, MC=12.00000 u and atomic mass of uranium238, MU=238.05079 u )
Solution :
From the aspect of repulsive coulomb force :
Uranium-238 nucleus has 92 protons but the carbon-12
nucleus has only 6 protons.
Therefore the coulomb force inside uranium-238 nucleus
is 92 or 15.3 times the coulomb force inside carbon-12
6
nucleus.
35
36. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Solution :
From the aspect of binding energy per nucleon:
12
Z 6 and N 6
Carbon-12 : C
6
The mass defect :
m Zmp Nmn M C
6 1.00782 6 1.00867 12.00000
m 0.09894 u
The binding energy per nucleon:
mc
EB
A
A C
931.5 MeV/ c 2 2
c
0.09894 u
1u
12
EB
7.68 MeV/nucleo n
36
A C
2
37. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
238
Uranium-238 :
92 U
The mass defect :
Z 92 and N 146
m 92 1.00782 146 1.00867 238.05079
m 1.93447 u
The binding energy per nucleon:
931.5 MeV/ c 2 2
c
1.93447 u
1u
EB
238
A U
EB
7.57 MeV/nucleo n
A U
Since the binding energy of uranium-238 nucleus less than the
binding energy of carbon-12 and the coulomb force inside uranium238 nucleus greater than the coulomb force inside carbon-12
nucleus therefore uranium-238 nucleus less stable than carbon-12
nucleus.
37
38. DR.ATAR @ UiTM.NS
PHY310 NUCLEUS
Exercise 7.1 :
Given c =3.00108 m s1, mn=1.00867 u, mp=1.00782 u
1.
Calculate the binding energy in joule of a deuterium nucleus.
The mass of a deuterium nucleus is 3.34428 1027 kg.
ANS. : 2.781013 J
20
2. The mass of neon-20 nucleus 10 Ne is 19.99244 u. Calculate
the binding energy per nucleon of neon-20 nucleus in MeV
per nucleon.
ANS. : 8.03 MeV/nucleon
3. Determine the energy required to remove one neutron from an
oxygen-16 16 O . The atomic mass for oxygen-16 is
8
15.994915 u
(Physics, 3rd edition, James S. Walker, Q39, p.1108)
ANS. : 15.7 MeV
38