Particle & Nuclear Physics

Nuclear Physics
 Atomic structure
 Representation of nuclides
 Isotopes and type
 Stability curve
 Radioactive disintegration
 Uranium disintegration series
 Properties of radioactive emission
 Mass defect and Nuclear binding energy
 Stability of nuclei
 Nuclear reactions (Nuclear Fusion & Nuclear Fission)
 Half life, and decay curve and activity
 Mathematical descriptions of radioactive decay
Nuclear Physics
Isotopes: Isotope are different forms of the same element
which have the same number of protons but different
numbers of neutrons in their nuclei.
Stability Curve
Radioactive decay: It is the spontaneous disintegration
of the nucleus (Radioactive nucleus) of an atom which
results in the emission of particles and/or electromagnetic
radiation.
Properties of Radioactive Emission
Fundamental Particles
Those particle which can not be spilt up into anything
simpler are called fundamental particle. By definition an
electron is a fundamental particle, but a proton is not.
 Nineteenth century (Atom was consider to be FP)
 Towards the end of 19 century it is discovered that atom
has a nucleus containing proton surrounded by electron.
 In 1932 Chadwick discovered neutron and then proton,
neutron and electron are considered to be FP
 Existence of strong force in order to maintain atomic
structure
 Strong force acts on protons and neutrons but not on
electrons
Hadrons and Leptons
 Special theory of relativity and Quantum theory suggested that all
FP have a corresponding antimatter particle, this is supported
after the discovery of antimatter in cosmic radiation.
 The matter and antimatter particles have the same mass but
opposite charge.
 anti-protons, anti-electron and anti-neutrons are required to

support the theory.
 Through out the 20th century many other particles were

discovered in cosmic radiation giving support for the idea that
electron, proton and neutron were not only FP.
Hadrons and Leptons
 We have learned about the subatomic particles known as protons neutrons
and electrons. However there are many more subatomic particles than this
that can be divided into two groups.
 Hadrons − Hadrons are particles that interact using the strong nuclear force.
(protons and neutrons and their respective antiparticles) Hadrons come in
two further groups, (Baryons and Mesons. Not needed for A Level)
 Leptons are particles that interact using the weak nuclear force and are not
affected by strong force. Leptons are fundamental particles and so can not
be split into any smaller particles (electron, positron, neutrino etc and their
respective antiparticles)
 Many different particles discovered in CR have been reproduced in high-

energy collision using accelerators and found two conclusions
1. The total electrical charge remains constant
2. The total number of nucleons normally remain constant
The Quark Model of Hadrons
In this model, the hadrons are made up of three smaller particles
called quarks. There are: up (u), down (d) and strange(s) quarks.
The type of quark, called flavours of quark. All quarks flavours have
charge and strangeness as shown.
There are three antiquarks anti up, anti down and anti strange they
have opposite value of charge and strangeness.
Protons and Neutrons
Protons and Neutrons consist of three quarks
as shown
Protons and Neutrons
The structure of protons, neutrons, anti-protons

and anti-neutrons can now be described:
up quark (u), down quark (d)
Proton uud ( +2/3 +2/3 -1/3 =
+1 )
Neutron u d d ( +2/3 -1/3 -1/3 = 0 )
anti-proton ( -2/3 -2/3 +1/3 = -1 )
anti-neutron ( -2/3 +1/3 +1/3 = 0 )
Leptons
Leptons are particles that interact using the weak nuclear force
and are not affected by strong force. Leptons are fundamental
particles and so can not be split into any smaller particles
(electron, positron, neutrino etc and their respective
antiparticles). The lepton number is +1 for the particle and -1 for
the antiparticle. The total lepton number before a reaction is
equal to the total lepton number after the reaction.
Leptons
The quark flavour is not conserved as a down quark
has changed to an up quark(1) and an up quark has
changed to a down quark (2) . The reaction can not
be due to strong force. The β-decay must be due to
another force. This force is called the weak force or
weak interaction
Mass Defect & Nuclear Binding Energy
Atomic Mass Unit: one atomic mass unit (1U) is defined as
being equal to one-twelfth of the mass of a carbon-12 atom.
1U= 1.66*10-27kg
Mass of proton(mp)= 1.007276 U

Mass of neutron (mn)= 1.008665 U
Mass of electron (me)= 0.000549 U
Mass Defect: The mass defect of a nucleus is the difference

between the total mass of the separate nucleons and the
combined mass of the nucleus.
Mass defect = Expected mass of nucleus – actual mass of nucleus

Calculations:
1) Calculate the mass defect of for Helium-4 nucleus.

The measured mass (actual mass) is 4.001508 U
2) Calculate the mass defect of for Carbon-14 nucleus.

The measured mass is 14.003240 U
Mass of proton(mp)= 1.007276 U

Mass of neutron (mn)= 1.008665 U
Mass of electron (me)= 0.00549 U
Mass- energy equivalence and Binding energy
E = mc2
Where E is energy m is mass defect & c is speed of light.
Calculate the energy equivalent to 1 U. (931 MeV)
electron volt (eV) is a unit of energy equal to the work done on an

electron in accelerating it through a potential difference of one volt.
Binding Energy: Binding energy is the energy equivalent to the

mass defect of a nucleus. It is the energy required to separate to
infinity all the nucleons of a nucleus.
Binding energy per nucleon: Binding energy per nucleon is defined

as the total energy needed to completely separate all the nucleons
in a nucleus divided by the number of nucleons in the nucleus.
Calculations
1)Calculate the binding energy and binding energy per nucleon in MeV of carbon-12
and carbon-14 nucleus. Given that actual mass of carbon-12 atom and carbon-14
atom are 12.000000 U and 14.003240 respectively.
2) Find the B.E. and BE per nucleon of the nucleus of gold (Au-197).Mass of an atom
of gold is 196.967 U.
3) Calculate the amount of energy released during the α-

decay of Uranium- 238. Given that
Mass of Uranium – 238 nucleus = 238.05082 U
Mass of Thorium(Th)-234 nucleus = 234.04364
Mass of Helium (He) nucleus (α particle) = 4.001508 U
4) Calculate the amount of energy released during the decay of 50 g radium-226 by

α particle emission. Also calculate the ratio of velocity of helium to the velocity
of radon.
Mass of Radium(Ra)-226 nucleus = 226.025400 U
Mass of Radon (Rn)- 222 nucleus = 222.017600 U
Nuclear Reaction
For a reaction to occur spontaneously, there must be a mass defect so that

the product of the reaction have some KE and mass-energy is conserved.
However in the given reaction mass of products is greater, for this reaction
to take place the helium nucleus must have some KE of at least 1.2 MeV
when it bombards the nitrogen nucleus.
Binding Energy Per Nucleon curve
Nuclear Fusion
Nuclear reaction in which two or more lighter nuclei fuse together, to
form a heavier nucleus is called Nuclear Fusion. Although nuclear fusion
reactions are the source of solar energy presently we could not duplicate
this reaction in a controlled manner on Earth. Because this reactions to
occur nuclei involved have to be brought very close to each other. For
this conditions of extremely high temperature and pressure, similar to
those found at the center of the Sun are required. Reactions requiring
those conditions are called thermonuclear reactions.
Nuclear Fission (Induced)
Nuclear fission is the splitting of a heavy nucleus into

two lighter nuclei of approximately the same mass.
Spontaneous and Random nature of Radioactive decay
Radioactive decay is a spontaneous process because it is not
affected by any external factors, such as temperature or pressure.
Radioactive decay is a random process in that it can not be

predicted which nucleus will decay next. There is a constant
probability that a nucleus will decay in any fixed period of time
Spontaneous and Random nature of Radioactive decay
Half-Life
The half-life(T1/2) of a radioactive nuclei is the time taken
for the number of undecayed nuclei to be reduced to half
its original number.
Law of Radioactive Disintegration
The rate of disintegration of radioactive substance at any time is directly
proportional to the number of radioactive nuclei present at that instant. If N is
the radioactive nuclei present at any instant then at this instant the rate of
disintegration is (-dN/dt)
ie dN/dt α N
ie dN/dt = -λN => dN/N = -λdt =>
……………………
…………………….
N = No e – λt
This equation shows that radioactive nuclei decrease exponentially
with time.
Similarly T1/2 = 0.693/ λ

Mathematical description of Radioactive decay
Activity: The activity of a radioactive source is the

number of nuclear decays occurring per unit time in
the source. Activity is measured in becquerel (Bq),
where 1 Bq is 1 decay per second (1 Bq = 1s-1).
Activity (A) = λN
Decay Constant: For radioactive decay, the decay

constant λ is the probability per unit time of the
decay of a nucleus.
Decay constant (λ) = 0.693/ T1/2
Calculation
1. A sample of radioactive substance initially contains 1000 undecayed
nuclei of an isotope, whose decay constant λ = 0.1 min-1. Calculate the
value of undecayed nuclei (N) at interval of 1 min for 10 min, then draw
a graph to show how the sample will decay over a period of 10 min and
use it to find the half-life of sample. Compare this half-life with that you
get by calculation. (N = No e – λt)
Time/ 0 1 2 3 4 5 6 7 8 9 10
min
N 1000 905 819 741 670 607 549 497 449 407 368
2. A laboratory has 1.4 micro gram of pure 13N which has a half-life of 10
min.
a) How many nuclei are present initially? (6.90x1016)
b) What is the activity initially and after 1 hour? (8.0x1013 and 1.25x1012)
c) After approximately how long will activity drop to 1s-1.(7.66 hr)

Particle & Nuclear Physics

Uploaded by

Copyright:

Available Formats

Particle & Nuclear Physics

Uploaded by

Document Information

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Particle & Nuclear Physics

Uploaded by

Copyright:

Available Formats

Nuclear Physics

 anti-protons, anti-electron and anti-neutrons are required to

 Through out the 20th century many other particles were

 Many different particles discovered in CR have been reproduced in high-

The structure of protons, neutrons, anti-protons

Mass of proton(mp)= 1.007276 U

Mass Defect: The mass defect of a nucleus is the difference

Mass defect = Expected mass of nucleus – actual mass of nucleus

1) Calculate the mass defect of for Helium-4 nucleus.

2) Calculate the mass defect of for Carbon-14 nucleus.

Mass of proton(mp)= 1.007276 U

Calculate the energy equivalent to 1 U. (931 MeV)

electron volt (eV) is a unit of energy equal to the work done on an

Binding Energy: Binding energy is the energy equivalent to the

Binding energy per nucleon: Binding energy per nucleon is defined

3) Calculate the amount of energy released during the α-

4) Calculate the amount of energy released during the decay of 50 g radium-226 by

For a reaction to occur spontaneously, there must be a mass defect so that

Nuclear fission is the splitting of a heavy nucleus into

Radioactive decay is a random process in that it can not be

Similarly T1/2 = 0.693/ λ

Activity: The activity of a radioactive source is the

Decay Constant: For radioactive decay, the decay

You might also like