Nuclear chemistry B Sc III-SEM-VI

Shri Shivaji Science College Amravati
Shri Shivaji Science College AmravatiShri Shivaji Science College Amravati
Dr. Y. S. THAKARE
M.Sc. (CHE) Ph D, NET, SET
Assistant Professor in Chemistry,
Shri Shivaji Science College, Amravati
Email: yogitathakare_2007@rediffmail.com
UNIT- VI
PART-I
Nuclear Chemistry
1. INTRODUCTION
Chemical transformations involve the changes in valence electrons of the
participating atoms while their atomic nuclei remain unaffected. In the beginning
of 20th century other kinds of transformations, involving changes in the atomic
nuclei were observed by the scientists, these transformations are called as nuclear
reactions. The study of nuclear reactions led to the development of a new branch
of chemistry called nuclear chemistry. Nuclear chemistry is defined as “the branch
of chemistry which deals with the study of properties and structure of atomic
nuclei, nuclear force and nuclear reactions. Nuclear chemistry originates in the
discovery of natural radioactivity by Henry Becquerel in 1896. A good deal of
knowledge was accumulated during the next few decades and this led to the
discovery of artificial radioactivity. The release of a tremendous amount of energy
in a nuclear fission reaction and the associated technological developments
culminated in various peaceful applications of nuclear energy. As the fossil fuels
are rapidly dwindling and the burning of which releases CO2 (a green house gas),
nuclear energy turns out to be a good carbon free energy source. You were
introduced to this novel branch of chemistry in XII standard where you have
studied the fundamentals of nuclear chemistry. In this unit, you will learn nuclear
properties, nuclear models and various aspects of nuclear reactions.
2. COMPOSITION OF NUCLEUS
After the discovery of neutron in 1932, it became clear that the
nucleus contains protons and neutrons. For lighter elements the
number of protons is equal to number of neutrons but for
heavier elements, the number of neutrons is more than the
number of protons. A nucleus is characterized by the number of
protons(Z) and the total number of protons and neutrons (A).
Such a nucleus with known composition is called as nuclide and is
represented by a symbol
𝑍
𝐴
𝑋
Where, ‘X’ is the chemical symbol of that element, 'Z’ is atomic
number and ‘A’ is atomic mass number (A= Z+ N). Nuclides are
classified as stable and unstable (radioactive). The number of
stable nuclides is only 274 where as we have large number
(>2000) of radioactive nuclides. Characteristic properties of the
nuclei suggest that nucleus is not a structure less entity but must
have definite structure.
 Nuclear chemistry B Sc III-SEM-VI
Nuclide OR Nucliede : Nucleus with known composition
ISOTOPES :
 Nuclear chemistry B Sc III-SEM-VI
ISOBARS :
ISOTONES :
 Nuclear chemistry B Sc III-SEM-VI
3. THE NUCLEAR MODELS
Nuclear properties clearly indicate that nucleus is very complex. In
order to explain the observed nuclear properties, various theories
of structure of nucleus have been put forward. Such theories are
called as nuclear models which are the contributions of a large
number of dedicated scientists. Complex nature of the nucleus
nececiates the development of several nuclear models. We shall
discuss below the silent features of nuclear shell model and liquid
drop model.
3.1. THE NUCLEAR SHELL MODEL
Inspiration for developing shell model of nucleus was derived from a
very successful electronic shell model of atom. An electronic shell is
completely filled (closed shell) when it contains a certain definite
number of electrons. An atom with closed shell electronic
configuration is very stable and exhibits chemical inertness(zero
group elements). In the nuclear world, it was observed that nuclei
with 2,8,20,50,82and 126 protons (Z) or neutrons (N) or both exhibit
exceptional stability as compared to closed neighbours. Since no
theoretical explanation was available for the extra stability
associated with these numbers, these were called as magic
numbers. Today we have the explanation in terms of nuclear shell
model but still the name continues. In 1948, this model was
mathematically developed by Mayer, Jensen, Hexel and Suess by
applying quantum mechanics on the basis of certain assumptions
(postulates).
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
a) Postulates of Shell model
i) Each nucleon moves in its own orbit which is determined by
the nuclear potential
ii) Nucleons are distributed in a series of discrete energy levels
iii) As the capacity of each orbit is reached, a closed shell is
formed.
iv) A proton forms a pair with a proton. Similarly, a neutron forms
a pair with a neutron but a proton can not form a pair with neutron.
v) In case of odd N or odd Z (or both) nuclides, the nuclear
properties like spin, parity and magnetic moment are due to the
presence of unpaired nucleon.
vi) This model is mainly applicable in the ground state of the
nucleus.
Nuclear energy levels in a shell model.
3.2. LIQUID DROP MODEL
Liquid drop model is statistical in nature and was developed by N.
Bohr and J Wheeler ( 1936) and independently by Frenkel on the
basis of certain assumptions.
a) Postulates of Liquid Drop Model-
i) Nucleus is a homogeneous entity consisting of certain
number of protons and neutrons.
ii) Each nucleon interacts strongly with all its neighbours.
iii) Considers the collective motion of all the nucleons.
iv) The interaction force (nuclear force) is assumed to be a short
range one tending to saturation. Thus, nuclear force is similar to that
of intermolecular force of attraction in a liquid drop.
v) Nuclear force is independent of charge and spin of the
nucleons.
vi) Behavior of nucleus is comparable to that of a liquid drop.
Liquid Drop Nucleus
1) Consists of large number of molecules.
2) Homogeneous and incompressible
3) Density is independent of the size of the drop.
4) Intermolecular force of attraction is a short
range force with saturation nature.
5) Liquid drop is spherical due to surface tension.
6) Large liquid drop captures a small droplet to
form a compound drop.
7) Large drop when exited breaks into smaller
droplets.(fission)
8) Small droplets fuse together to form a larger
drop (fusion )
9) Excited liquid drop may de-excite by cooling or
by evaporation.
1) Consists of nucleons.
2) Homogeneous and incompressible.
3) Density is independent of mass
number.(nuclear size).
4) Nuclear force is attraction is a short range force
with saturation nature.
5) Nucleus also exhibits surface tension.
6) Large Nucleus captures a small projectile to
form a compound nucleus.
7) Heavy nucleus when excited breaks into two
smaller nuclei.(Nuclear fission)
8) Lighter nuclei fuse together to form a heavier
nucleus. (Nuclear fusion)
9) Excited compound nucleus may de-excite by γ-
ray emission or by the emission of particles(α, β, p,
n etc)
b) Comparison of the nucleus with that of a liquid drop-
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
c) Advantages of Liquid drop model
i) It provides basis for the equation of Weizsacker for
calculating the accurate binding energies of nuclei and
hence their atomic masses.
ii) Radioactive decay could be predicted, correctly.
iii) It could explain nuclear fission reaction.
iv) It explains the mechanism of low energy nuclear
reactions.
v) It predicts α- and β-emission properties.
vi) Capable of explaining nuclear properties in excited
state.
d) Limitations of Liquid drop Model
i) The Periodicity in nuclear properties at magic numbers of
protons and neutrons dose not find any satisfactory explanation in
this model i.e. fails to explain magic numbers.
ii) It fails to explain the stability of heavy nuclides.
iii) This model is not consistent with the p-p and n-n pairing
effects which are prominently observed in stable nuclei.
iv) The model ignores independent motions of nucleons,
magnetic moment effects etc.
v) The application of the model is limited to the nuclei with
medium mass. In light nuclei (A < 20) most nucleons are on the
surface where as in heavy nuclei (A > 150) columbic effects can not
be ignored.
e) Liquid Drop Model and Nuclear fission (Bohr-Wheeler Theory of nuclear
fission)
The liquid drop model can explain the phenomenon of nuclear fission. A liquid
drop has a spherical shape due to internal molecular forces responsible for
surface tension. On applying a large external force, the sphere may change into on
ellipsoid. If the external force is sufficiently large, ellipsoid may change into a
dumb -bell shape and may even break at the narrow end into two portions.
According to Bohr-wheeler theory, the nucleus behaves like a liquid drop. When
the nucleus captures a neutron falling on it, it forms a compound nucleus which is
highly energetic. The extra energy may set up a series of rapid oscillations in the
spherical compound nucleus labelled as ‘A’ in Fig below. As a result of these
oscillations, the shape of the nucleus may change at time form spherical to
ellipsoidal, labelled as ‘B’ in the same Fig. If the extra energy is large, oscillations
may be so violent that stage ‘C’ and ultimately stage ‘D’ may be approached. The
nucleus is now dumb-bell shaped and both parts of the dumb-bell which are not
necessarily of equal size carry positiv charge. The energy required to change the
nucleus from stage ‘A’ to stage ‘D’ is called as fission barrier. The nucleus is now in
critical state because once stage ‘D’ is reached, the final fission in to fragments
(stage ‘E’) is inevitable on account of repulsion between the two fragments.
 Nuclear chemistry B Sc III-SEM-VI
4. MESON THEORY OF NUCLEAR FORCE
Protons and neutrons are packed together in a very small nuclear
space (radius of nucleus is about 10-15 m). What is the nature of
the force which holds the protons and neutrons together in such a
small nucleus? If electrostatic forces alone would have operated
then the repulsion between the protons would render the nucleus
highly unstable. This does not happen except in case of heavier
elements which are radioactive. It is evident that there must be
some very strong attractive force operating between the
necluons, which must be stronger than the electrostatic repulsive
force between the protons. This attractive force which holds the
nucleons tightly inside the nucleus is called as nuclear force.
Although the exact nature of the nuclear force is not well
understood, it has been argued that just as atoms in a molecule
are held together by an exchange of electrons between them, a
similar mechanism involving the exchange of some particles
between neutrons and protons ought to work in a nucleus.
In 1935 H. Yukawa suggested that another fundamental particle,
called as meson oscillates between neighboring nucleons with a
velocity close to that of light. Mesons are 275 time heavier than
electron and may be electrically neutral, positive or negative. They
interact with protons and neutrons as result of which a proton may
change into a neutron and neutron may change into proton.
Proton + negative л-meson  neutron
Neutron + positive л-meson  Proton
Hence there is an exchange of meson back and forth between
neighbouring nucleons. This results in an attraction between neutron
and proton. Two protons or two neutrons attract each other by the
exchange of neutral π-meson.
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
5. NUCLEAR REACTIONS
Nuclear reaction is defined as a process in which one
nucleus changes into another nucleus. As per this
definition the disintegration of a radioactive (unstable)
nucleus by the emission of α, β or γ-rays is also a
nuclear reaction.
Nuclear reactions are carried out in the laboratory by
bombarding a nucleus (called as target nucleus) by a
particle like neutron, proton, deuteron or γ-rays
(called projectile). As a result of nuclear reaction, a
new nucleus (called as product or recoil nucleus) is
formed which is accompanied by the emission of a
particle or a γ-ray photon (called as ejectie).
5.1 REPRESENTATION OF A NUCLEAR REACTION
Like a chemical reaction, the nuclear reaction is represented by an
equation. On the left hand side of an arrow, the target nucleus and
projectile are written where as on the right hand side the product
nucleus and ejectile are written. A general nuclear reaction may be
written as
𝑍1
𝐴1
𝑋 + 𝑎 → 𝑍2
𝐴2
𝑌 + 𝑏
Target projectile product ejectile
Above reaction may also be represented by “Bethe notation” as
A1 X (a, b) A2Y
e. g. 7
14
𝑁 + 2
4
𝐻𝑒 → 8
17
𝑂 + 1
1
𝐻 may be written as 14 N (α,p) 17 O
5
10
𝐵 + 2
4
𝐻𝑒 → 6
13
𝐶 + 1
1
𝐻 may be written as 10 B (α, p) 13 C
5.2 CHARACTERISTICS OF NUCLEAR REACTIONS
i) The nuclear reactions are written like a chemical
equation. Reactants are written on the left hand side and
products on right hand side with an arrow in between.
ii) In nuclear reactions, nuclei are involved and not the
extranuclear electrons.
iii) In nuclear reaction total mass number and atomic
number are balanced on the two sides.
iv) Sum of the initial momenta of projectile and target is
equal to the sum of momenta of product and ejectile.
v) Nuclear reactions are accompanied by a large amount of
energy change which is expressed in MeV.
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
5.3 DIFFERENCE BETWEEN CHEMICAL REACTIONS AND NUCLEAR
REACTIONS
Chemical Reactions
i) During chemical reactions, elements do not lose their
identity. In these reactions, only the electrons in the outermost
shell of atoms participate whereas the nuclei of atoms remain
unchanged.
ii) Reactivity of an element towards chemical reactions
depends upon the oxidation state of the element. In ordinary
chemical reactions, Ra and Ra2+ behave quite differently.
iii) Different isotopes of an element have same chemical
reactivity.
iv) Rate of a chemical reaction is largely affected by
temperature and pressure.
v) A chemical reaction can be reversed.
vi) Chemical reactions are accompanied by relatively small
energy changes (of the order of eV).
Nuclear Reactions
i) During nuclear reactions, the nuclei of atoms undergo a
change and therefore new nuclei are formed as a result of such
reactions.
ii) Reactivity of an element towards nuclear reactions is nearly
independent of oxidation state of the element. For example, Ra
element or Ra+2 ion in RaC2 behave s similarly during nuclear
reactions.
iii) In nuclear reactions, isotopes behave quite differently. For
example, U-235 undergoes fission with thermal neutrons but U-238
does not.
iv) Rate of a nuclear reaction is independent of temperature and
pressure.
v) A nuclear reaction cannot be reversed.
vi) Nuclear reactions are accompanied by very large energy
changes (of the order of MeV).
5.4 EXAMPLES OF NUCLEAR REACTIONS
1. α - Induced Reaction- Nuclear reactions induced by α particles (2
4
𝐻𝑒)
i) (α, p) reactions-
a) 13
27
𝐴𝑙 + 2
4
𝐻𝑒 → 14
30
𝑆𝑖 + 1
1
𝐻 or 27 Al (α, p) 30 Si
b) 9
19
𝐹 + 2
4
𝐻𝑒 → 10
22
𝑁𝑒 + 1
1
𝐻 or 19 F (α, p) 22 Ne
ii) (α, n) reactions-
a) 4
9
𝐵𝑒 + 2
4
𝐻𝑒 → 6
12
𝐶 + 0
1
𝑛 or 9 Be (α, n) 12 C
b) 13
27
𝐴𝑙 + 2
4
𝐻𝑒 → 15
30
𝑃 + 0
1
𝑛 or 27 Al (α, n) 30 P
2. Proton Induced Reaction-Nuclear reaction induced by protons (1
1
𝐻)
i) (p, n) reaction-
5
11
𝐵 + 1
1
𝐻 → 6
11
𝐶 + 0
1
𝑛 or 11B (p, n) 11C
ii) (p, d) reaction
4
9
𝐵𝑒 + 1
1
𝐻 → 4
8
𝐵𝑒 + 1
2
𝐻 (𝐷𝑒𝑢𝑡𝑒𝑟𝑜𝑛) or 9Be ( p, d) 8Be
iii) (p, α) reaction-
7
14
𝑁 + 1
1
𝐻 → 6
11
𝐶 + 2
4
𝐻 or 14 N (p, α) 11C
iv) (p, γ) reaction
13
27
𝐴𝑙 + 1
1
𝐻 → 14
28
𝑆𝑖 + γ or 27Al (p, γ) 28Si
3. Deuteron Induced Reactions- Reactions induced by deuterons (1
2
𝐻)
i) (d, p) reaction-
1
2
𝐻 + 1
2
𝐻 → 1
3
𝐻 + 1
1
𝐻 or 2H (d, p) 3H
ii) (d, n) reaction
6
12
𝐶 + 1
2
𝐻 → 7
13
𝑁 + 0
1
𝑛 or 12C (d, n) 13N
iii) (d, α) reaction-
8
16
𝑂 + 1
2
𝐻 → 7
14
𝑁 + 2
4
𝐻𝑒 or 16O (d, α) 14N
4. Neutron Induced Reaction- Reactions induced by neutrons (0
1
𝑛)
i) (n, p) reaction
12
24
𝑀𝑔 + 0
1
𝑛 → 11
24
𝑁𝑎 + 1
1
𝐻 or 24Mg (n, p) 24Na
ii) (n, 2n) reaction
29
63
𝐶𝑢 + 0
1
𝑛 → 29
62
𝐶𝑢 + 20
1
𝑛 or 63Cu (n, 2n) 62 Cu
iii) (n, α) reaction
5
10
𝐵 + 0
1
𝑛 → 3
7
𝐿𝑖 + 2
4
𝐻𝑒 or 10B (n, α) 7Li
iv) (n, γ) reaction
18
40
𝐴𝑟 + 0
1
𝑛 → 18
41
𝐴𝑟 + 0
0
𝑟 or 40Ar (n, γ) 41Ar
5) Gamma Induced Reaction or photonuclear reactions-Reactions induced by
high energy (> 1MeV) γ-rays
i) (γ, p) reaction
12
25
𝑀𝑔 + γ → 11
24
𝑁𝑎 + 1
1
𝐻 or 25Mg (γ, p) 24 Na
ii) (γ, n) reaction
4
9
𝐵𝑒 + γ → 4
8
𝐵𝑒 + 0
1
𝑛 or 9Be (γ, n) 8Be
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
 Nuclear chemistry B Sc III-SEM-VI
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Nuclear chemistry B Sc III-SEM-VI

  • 1. Dr. Y. S. THAKARE M.Sc. (CHE) Ph D, NET, SET Assistant Professor in Chemistry, Shri Shivaji Science College, Amravati Email: yogitathakare_2007@rediffmail.com UNIT- VI PART-I Nuclear Chemistry
  • 2. 1. INTRODUCTION Chemical transformations involve the changes in valence electrons of the participating atoms while their atomic nuclei remain unaffected. In the beginning of 20th century other kinds of transformations, involving changes in the atomic nuclei were observed by the scientists, these transformations are called as nuclear reactions. The study of nuclear reactions led to the development of a new branch of chemistry called nuclear chemistry. Nuclear chemistry is defined as “the branch of chemistry which deals with the study of properties and structure of atomic nuclei, nuclear force and nuclear reactions. Nuclear chemistry originates in the discovery of natural radioactivity by Henry Becquerel in 1896. A good deal of knowledge was accumulated during the next few decades and this led to the discovery of artificial radioactivity. The release of a tremendous amount of energy in a nuclear fission reaction and the associated technological developments culminated in various peaceful applications of nuclear energy. As the fossil fuels are rapidly dwindling and the burning of which releases CO2 (a green house gas), nuclear energy turns out to be a good carbon free energy source. You were introduced to this novel branch of chemistry in XII standard where you have studied the fundamentals of nuclear chemistry. In this unit, you will learn nuclear properties, nuclear models and various aspects of nuclear reactions.
  • 3. 2. COMPOSITION OF NUCLEUS After the discovery of neutron in 1932, it became clear that the nucleus contains protons and neutrons. For lighter elements the number of protons is equal to number of neutrons but for heavier elements, the number of neutrons is more than the number of protons. A nucleus is characterized by the number of protons(Z) and the total number of protons and neutrons (A). Such a nucleus with known composition is called as nuclide and is represented by a symbol 𝑍 𝐴 𝑋 Where, ‘X’ is the chemical symbol of that element, 'Z’ is atomic number and ‘A’ is atomic mass number (A= Z+ N). Nuclides are classified as stable and unstable (radioactive). The number of stable nuclides is only 274 where as we have large number (>2000) of radioactive nuclides. Characteristic properties of the nuclei suggest that nucleus is not a structure less entity but must have definite structure.
  • 5. Nuclide OR Nucliede : Nucleus with known composition
  • 11. 3. THE NUCLEAR MODELS Nuclear properties clearly indicate that nucleus is very complex. In order to explain the observed nuclear properties, various theories of structure of nucleus have been put forward. Such theories are called as nuclear models which are the contributions of a large number of dedicated scientists. Complex nature of the nucleus nececiates the development of several nuclear models. We shall discuss below the silent features of nuclear shell model and liquid drop model.
  • 12. 3.1. THE NUCLEAR SHELL MODEL Inspiration for developing shell model of nucleus was derived from a very successful electronic shell model of atom. An electronic shell is completely filled (closed shell) when it contains a certain definite number of electrons. An atom with closed shell electronic configuration is very stable and exhibits chemical inertness(zero group elements). In the nuclear world, it was observed that nuclei with 2,8,20,50,82and 126 protons (Z) or neutrons (N) or both exhibit exceptional stability as compared to closed neighbours. Since no theoretical explanation was available for the extra stability associated with these numbers, these were called as magic numbers. Today we have the explanation in terms of nuclear shell model but still the name continues. In 1948, this model was mathematically developed by Mayer, Jensen, Hexel and Suess by applying quantum mechanics on the basis of certain assumptions (postulates).
  • 15. a) Postulates of Shell model i) Each nucleon moves in its own orbit which is determined by the nuclear potential ii) Nucleons are distributed in a series of discrete energy levels iii) As the capacity of each orbit is reached, a closed shell is formed. iv) A proton forms a pair with a proton. Similarly, a neutron forms a pair with a neutron but a proton can not form a pair with neutron. v) In case of odd N or odd Z (or both) nuclides, the nuclear properties like spin, parity and magnetic moment are due to the presence of unpaired nucleon. vi) This model is mainly applicable in the ground state of the nucleus.
  • 16. Nuclear energy levels in a shell model.
  • 17. 3.2. LIQUID DROP MODEL Liquid drop model is statistical in nature and was developed by N. Bohr and J Wheeler ( 1936) and independently by Frenkel on the basis of certain assumptions. a) Postulates of Liquid Drop Model- i) Nucleus is a homogeneous entity consisting of certain number of protons and neutrons. ii) Each nucleon interacts strongly with all its neighbours. iii) Considers the collective motion of all the nucleons. iv) The interaction force (nuclear force) is assumed to be a short range one tending to saturation. Thus, nuclear force is similar to that of intermolecular force of attraction in a liquid drop. v) Nuclear force is independent of charge and spin of the nucleons. vi) Behavior of nucleus is comparable to that of a liquid drop.
  • 18. Liquid Drop Nucleus 1) Consists of large number of molecules. 2) Homogeneous and incompressible 3) Density is independent of the size of the drop. 4) Intermolecular force of attraction is a short range force with saturation nature. 5) Liquid drop is spherical due to surface tension. 6) Large liquid drop captures a small droplet to form a compound drop. 7) Large drop when exited breaks into smaller droplets.(fission) 8) Small droplets fuse together to form a larger drop (fusion ) 9) Excited liquid drop may de-excite by cooling or by evaporation. 1) Consists of nucleons. 2) Homogeneous and incompressible. 3) Density is independent of mass number.(nuclear size). 4) Nuclear force is attraction is a short range force with saturation nature. 5) Nucleus also exhibits surface tension. 6) Large Nucleus captures a small projectile to form a compound nucleus. 7) Heavy nucleus when excited breaks into two smaller nuclei.(Nuclear fission) 8) Lighter nuclei fuse together to form a heavier nucleus. (Nuclear fusion) 9) Excited compound nucleus may de-excite by γ- ray emission or by the emission of particles(α, β, p, n etc) b) Comparison of the nucleus with that of a liquid drop-
  • 22. c) Advantages of Liquid drop model i) It provides basis for the equation of Weizsacker for calculating the accurate binding energies of nuclei and hence their atomic masses. ii) Radioactive decay could be predicted, correctly. iii) It could explain nuclear fission reaction. iv) It explains the mechanism of low energy nuclear reactions. v) It predicts α- and β-emission properties. vi) Capable of explaining nuclear properties in excited state.
  • 23. d) Limitations of Liquid drop Model i) The Periodicity in nuclear properties at magic numbers of protons and neutrons dose not find any satisfactory explanation in this model i.e. fails to explain magic numbers. ii) It fails to explain the stability of heavy nuclides. iii) This model is not consistent with the p-p and n-n pairing effects which are prominently observed in stable nuclei. iv) The model ignores independent motions of nucleons, magnetic moment effects etc. v) The application of the model is limited to the nuclei with medium mass. In light nuclei (A < 20) most nucleons are on the surface where as in heavy nuclei (A > 150) columbic effects can not be ignored.
  • 24. e) Liquid Drop Model and Nuclear fission (Bohr-Wheeler Theory of nuclear fission) The liquid drop model can explain the phenomenon of nuclear fission. A liquid drop has a spherical shape due to internal molecular forces responsible for surface tension. On applying a large external force, the sphere may change into on ellipsoid. If the external force is sufficiently large, ellipsoid may change into a dumb -bell shape and may even break at the narrow end into two portions. According to Bohr-wheeler theory, the nucleus behaves like a liquid drop. When the nucleus captures a neutron falling on it, it forms a compound nucleus which is highly energetic. The extra energy may set up a series of rapid oscillations in the spherical compound nucleus labelled as ‘A’ in Fig below. As a result of these oscillations, the shape of the nucleus may change at time form spherical to ellipsoidal, labelled as ‘B’ in the same Fig. If the extra energy is large, oscillations may be so violent that stage ‘C’ and ultimately stage ‘D’ may be approached. The nucleus is now dumb-bell shaped and both parts of the dumb-bell which are not necessarily of equal size carry positiv charge. The energy required to change the nucleus from stage ‘A’ to stage ‘D’ is called as fission barrier. The nucleus is now in critical state because once stage ‘D’ is reached, the final fission in to fragments (stage ‘E’) is inevitable on account of repulsion between the two fragments.
  • 26. 4. MESON THEORY OF NUCLEAR FORCE Protons and neutrons are packed together in a very small nuclear space (radius of nucleus is about 10-15 m). What is the nature of the force which holds the protons and neutrons together in such a small nucleus? If electrostatic forces alone would have operated then the repulsion between the protons would render the nucleus highly unstable. This does not happen except in case of heavier elements which are radioactive. It is evident that there must be some very strong attractive force operating between the necluons, which must be stronger than the electrostatic repulsive force between the protons. This attractive force which holds the nucleons tightly inside the nucleus is called as nuclear force. Although the exact nature of the nuclear force is not well understood, it has been argued that just as atoms in a molecule are held together by an exchange of electrons between them, a similar mechanism involving the exchange of some particles between neutrons and protons ought to work in a nucleus.
  • 27. In 1935 H. Yukawa suggested that another fundamental particle, called as meson oscillates between neighboring nucleons with a velocity close to that of light. Mesons are 275 time heavier than electron and may be electrically neutral, positive or negative. They interact with protons and neutrons as result of which a proton may change into a neutron and neutron may change into proton. Proton + negative л-meson  neutron Neutron + positive л-meson  Proton Hence there is an exchange of meson back and forth between neighbouring nucleons. This results in an attraction between neutron and proton. Two protons or two neutrons attract each other by the exchange of neutral π-meson.
  • 31. 5. NUCLEAR REACTIONS Nuclear reaction is defined as a process in which one nucleus changes into another nucleus. As per this definition the disintegration of a radioactive (unstable) nucleus by the emission of α, β or γ-rays is also a nuclear reaction. Nuclear reactions are carried out in the laboratory by bombarding a nucleus (called as target nucleus) by a particle like neutron, proton, deuteron or γ-rays (called projectile). As a result of nuclear reaction, a new nucleus (called as product or recoil nucleus) is formed which is accompanied by the emission of a particle or a γ-ray photon (called as ejectie).
  • 32. 5.1 REPRESENTATION OF A NUCLEAR REACTION Like a chemical reaction, the nuclear reaction is represented by an equation. On the left hand side of an arrow, the target nucleus and projectile are written where as on the right hand side the product nucleus and ejectile are written. A general nuclear reaction may be written as 𝑍1 𝐴1 𝑋 + 𝑎 → 𝑍2 𝐴2 𝑌 + 𝑏 Target projectile product ejectile Above reaction may also be represented by “Bethe notation” as A1 X (a, b) A2Y e. g. 7 14 𝑁 + 2 4 𝐻𝑒 → 8 17 𝑂 + 1 1 𝐻 may be written as 14 N (α,p) 17 O 5 10 𝐵 + 2 4 𝐻𝑒 → 6 13 𝐶 + 1 1 𝐻 may be written as 10 B (α, p) 13 C
  • 33. 5.2 CHARACTERISTICS OF NUCLEAR REACTIONS i) The nuclear reactions are written like a chemical equation. Reactants are written on the left hand side and products on right hand side with an arrow in between. ii) In nuclear reactions, nuclei are involved and not the extranuclear electrons. iii) In nuclear reaction total mass number and atomic number are balanced on the two sides. iv) Sum of the initial momenta of projectile and target is equal to the sum of momenta of product and ejectile. v) Nuclear reactions are accompanied by a large amount of energy change which is expressed in MeV.
  • 40. 5.3 DIFFERENCE BETWEEN CHEMICAL REACTIONS AND NUCLEAR REACTIONS Chemical Reactions i) During chemical reactions, elements do not lose their identity. In these reactions, only the electrons in the outermost shell of atoms participate whereas the nuclei of atoms remain unchanged. ii) Reactivity of an element towards chemical reactions depends upon the oxidation state of the element. In ordinary chemical reactions, Ra and Ra2+ behave quite differently. iii) Different isotopes of an element have same chemical reactivity. iv) Rate of a chemical reaction is largely affected by temperature and pressure. v) A chemical reaction can be reversed. vi) Chemical reactions are accompanied by relatively small energy changes (of the order of eV).
  • 41. Nuclear Reactions i) During nuclear reactions, the nuclei of atoms undergo a change and therefore new nuclei are formed as a result of such reactions. ii) Reactivity of an element towards nuclear reactions is nearly independent of oxidation state of the element. For example, Ra element or Ra+2 ion in RaC2 behave s similarly during nuclear reactions. iii) In nuclear reactions, isotopes behave quite differently. For example, U-235 undergoes fission with thermal neutrons but U-238 does not. iv) Rate of a nuclear reaction is independent of temperature and pressure. v) A nuclear reaction cannot be reversed. vi) Nuclear reactions are accompanied by very large energy changes (of the order of MeV).
  • 42. 5.4 EXAMPLES OF NUCLEAR REACTIONS 1. α - Induced Reaction- Nuclear reactions induced by α particles (2 4 𝐻𝑒) i) (α, p) reactions- a) 13 27 𝐴𝑙 + 2 4 𝐻𝑒 → 14 30 𝑆𝑖 + 1 1 𝐻 or 27 Al (α, p) 30 Si b) 9 19 𝐹 + 2 4 𝐻𝑒 → 10 22 𝑁𝑒 + 1 1 𝐻 or 19 F (α, p) 22 Ne ii) (α, n) reactions- a) 4 9 𝐵𝑒 + 2 4 𝐻𝑒 → 6 12 𝐶 + 0 1 𝑛 or 9 Be (α, n) 12 C b) 13 27 𝐴𝑙 + 2 4 𝐻𝑒 → 15 30 𝑃 + 0 1 𝑛 or 27 Al (α, n) 30 P
  • 43. 2. Proton Induced Reaction-Nuclear reaction induced by protons (1 1 𝐻) i) (p, n) reaction- 5 11 𝐵 + 1 1 𝐻 → 6 11 𝐶 + 0 1 𝑛 or 11B (p, n) 11C ii) (p, d) reaction 4 9 𝐵𝑒 + 1 1 𝐻 → 4 8 𝐵𝑒 + 1 2 𝐻 (𝐷𝑒𝑢𝑡𝑒𝑟𝑜𝑛) or 9Be ( p, d) 8Be iii) (p, α) reaction- 7 14 𝑁 + 1 1 𝐻 → 6 11 𝐶 + 2 4 𝐻 or 14 N (p, α) 11C iv) (p, γ) reaction 13 27 𝐴𝑙 + 1 1 𝐻 → 14 28 𝑆𝑖 + γ or 27Al (p, γ) 28Si
  • 44. 3. Deuteron Induced Reactions- Reactions induced by deuterons (1 2 𝐻) i) (d, p) reaction- 1 2 𝐻 + 1 2 𝐻 → 1 3 𝐻 + 1 1 𝐻 or 2H (d, p) 3H ii) (d, n) reaction 6 12 𝐶 + 1 2 𝐻 → 7 13 𝑁 + 0 1 𝑛 or 12C (d, n) 13N iii) (d, α) reaction- 8 16 𝑂 + 1 2 𝐻 → 7 14 𝑁 + 2 4 𝐻𝑒 or 16O (d, α) 14N
  • 45. 4. Neutron Induced Reaction- Reactions induced by neutrons (0 1 𝑛) i) (n, p) reaction 12 24 𝑀𝑔 + 0 1 𝑛 → 11 24 𝑁𝑎 + 1 1 𝐻 or 24Mg (n, p) 24Na ii) (n, 2n) reaction 29 63 𝐶𝑢 + 0 1 𝑛 → 29 62 𝐶𝑢 + 20 1 𝑛 or 63Cu (n, 2n) 62 Cu iii) (n, α) reaction 5 10 𝐵 + 0 1 𝑛 → 3 7 𝐿𝑖 + 2 4 𝐻𝑒 or 10B (n, α) 7Li iv) (n, γ) reaction 18 40 𝐴𝑟 + 0 1 𝑛 → 18 41 𝐴𝑟 + 0 0 𝑟 or 40Ar (n, γ) 41Ar
  • 46. 5) Gamma Induced Reaction or photonuclear reactions-Reactions induced by high energy (> 1MeV) γ-rays i) (γ, p) reaction 12 25 𝑀𝑔 + γ → 11 24 𝑁𝑎 + 1 1 𝐻 or 25Mg (γ, p) 24 Na ii) (γ, n) reaction 4 9 𝐵𝑒 + γ → 4 8 𝐵𝑒 + 0 1 𝑛 or 9Be (γ, n) 8Be