Lec Phir11.26

Course: Physics I Code: PHIR11
# Lecture: 26
Topic: Nuclear and Particle Physics

by
Dr. Joy Prakash Das
Department of Physics
NIT Tiruchirappalli
Date: 25/01/2023 (Wed)
Nuclear properties – Stable nuclei
 Why some combinations of neutrons

and protons are more stable
than others?
 Not all combinations of neutrons and
protons form stable nuclei. In
general, light nuclei (A<20) contain
approximately equal numbers of
neutrons and protons, while in
heavier nuclei the proportion of
neutrons becomes progressively
greater.
 This is evident from the figure, which
is a plot of N (neutron number)
versus Z (proton number) for stable
nuclides. Neutron-proton diagram for stable
nuclides 2
 The tendency for N to equal Z follows from the existence of

nuclear energy levels.
 Nucleons, which have spins of ½, obey the exclusion principle. As
a result, each nuclear energy level can contain two neutrons of
opposite spins and two protons of opposite spins.
 Energy levels in nuclei are filled in sequence, just as energy levels
in atoms are, to achieve configurations of minimum energy and
therefore maximum stability.
 Thus the boron isotope
12
5
B has more energy
than the carbon isotope
12
6
C because one of its
neutrons is in a higher
energy level, and 12
5
B is
accordingly unstable.
3
 If created in a nuclear reaction, a 12 5

B nucleus changes by beta
decay into a stable 126
C nucleus in a fraction of a second.
 Secondly, protons are positively charged and repel one another
electrically. This repulsion becomes so great in nuclei with more
than 10 protons or so that an excess of neutrons, which produce
only attractive forces, is required for stability.
 Thus the curve of the earlier figure departs more and more from
the N=Z line as Z increases. Even in light nuclei N may exceed Z,
but (except in 11H and 32He) is never smaller; 12 5
B is stable, for
11
instance, but not C.
6
 Sixty percent of stable nuclides have both even Z and even N;
these are called “even-even” nuclides.
 Nearly all the others have either even Z and odd N (even-odd
nuclides) or odd Z and even N (odd-even nuclides), with the
numbers of both kinds being about equal. 4
 Only five stable odd-odd nuclides are known: 21H, 63 Li, 10

3
Be, 14
7
N,
and 180
73
Ta.
 Nuclear abundances follow a similar pattern of favoring even
numbers for Z and N.
 Only about one in eight of the atoms of which the earth is
composed has a nucleus with an odd number of protons, for
instance.
 These observations are consistent with the presence of nuclear
energy levels that can each contain two particles of opposite spin.
 Nuclei with filled levels have less tendency to pick up other
nucleons than those with partly filled levels and hence were less
likely to participate in the nuclear reactions involved in the
formation of the elements.
5
Nuclear properties – Nuclear decay
 Nuclear forces are limited in range, and as a result nucleons

interact strongly only with their nearest neighbors. This effect is
referred to as the saturation of nuclear forces.
 Because the coulomb repulsion of the protons is appreciable
throughout the entire nucleus, there is a limit to the ability of
neutrons to prevent the disruption of a large nucleus. This limit is
represented by the bismuth isotope 209 83
Bi, which is the heaviest
stable nuclide.
 All nuclei with Z > 83 and A > 209 spontaneously transform
themselves into lighter ones through the emission of one or more
alpha particles, which are 42He nuclei:
 This process is called alpha decay. 6

 If the resulting daughter nucleus after alpha decay has either too
small or too large a neutron/proton ratio for stability, it may beta
decay to one or more appropriate configuration.
 In negative beta decay, a neutron is transformed into a proton
and an electron is emitted.
 In positive beta decay, a proton becomes a neutron and a

positron is emitted.
 Thus negative beta decay decreases the proportion of neutrons

and positive beta decay increases it.
 A process that competes with positron emission is the capture of
an electron from its innermost shell by a nucleus. The electron is
absorbed by a nuclear proton which is thereby transformed into a
neutron.
7
 The figure shows how alpha

and beta decays permit an
unstable nucleus to reach a
stable configuration.
 Note: In a beta decay, the
conservation principles of
energy, linear momentum and
angular momentum are
apparently violated. Later it
was realized that besides
these products there is
neutrino (or anti-neutrino)
which is emitted, which takes
care of the conservation
principles. 8
Nuclear properties – Binding energy
 The hydrogen isotope deuterium, 21H, has a neutron as well as a

proton in its nucleus. Thus we would expect the mass of the
deuterium atom to be equal to that of an ordinary 11H atom plus
the mass of a neutron:
 However, the measured mass of the 21H atom is only 2.014102 u,

which is 0.002388u less than the combined masses of a 11H atom
and a neutron.
 The energy equivalent of the missing mass is
9
 We can perform experiments to see how much energy is needed

to break apart a deuterium nucleus into a separate neutron and
proton.
 The required energy indeed turns out to be 2.224 MeV.
 When less energy than 2.224 MeV is given to a 21H nucleus, the
nucleus stays together.
 When the added energy is more than 2.224 MeV, the extra
energy goes into kinetic energy of the neutron and proton as they
fly apart.
10
 Deuterium atoms are not the only ones that have less mass than
the combined masses of the particles they are composed of—all
atoms are like that.
 The energy equivalent of the missing mass of a nucleus is called
the binding energy of the nucleus. The greater its binding energy,
the more the energy that must be supplied to break up the
nucleus.
 The binding energy Eb in MeV of the nucleus 𝐴𝑍X, which has N=A-Z
neutrons, is given by
 Here m(11H) is the atomic mass of 11H, m(n) is the neutron mass,
and m(𝐴𝑍X) is the atomic mass of 𝐴𝑍X, all in mass units.
 Atomic masses and not nuclear masses are used in such
calculations, the electron masses subtract out. 11
Binding energy per nucleon
 The binding energy per nucleon for a given nucleus is an average

found by dividing its total binding energy by the number of
nucleons it contains.
 Thus the binding energy per nucleon for 21H is (2.2 MeV)/2 = 1.1
eV/nucleon, and for 209Bi it is (1640 MeV)/209 = 7.8 eV/nucleon.
83
12
Binding energy per nucleon
 The greater the binding energy per nucleon more stable the
nucleus is.
 If we can somehow split a heavy nucleus into two medium-sized
ones, each of the new nuclei will have more binding energy per
nucleon than the original nucleus did.
 Splitting a heavy nucleus, which is called nuclear fission, involves
100 million times more energy per atom than, say, the burning of
coal or oil.
 Joining two light nuclei together to give a single nucleus of
medium size also means more binding energy per nucleon in the
new nucleus.
 Such a process, called nuclear fusion, is also a very effective way
to obtain energy.
 In fact, nuclear fusion is the main energy source of the sun and
other stars.
13
Nuclear models – Liquid drop model
 It tries to provide a simple explanation for the binding energy

curve.
 First proposed by George Gamow and further developed by Niels
Bohr and John Archibald Wheeler.
 The nucleus is supposed to be spherical in shape as a liquid drop.
The spherical shape is due to attractive nuclear force between
the nucleons.
 There is a potential barrier on the surface of the nucleus. This is
similar to the force of surface tension which acts upon the liquid
drop.
 The molecules of the liquid drop interact with the neighboring
molecules only. It means the molecular force is a short ranged
force. Similarly the nucleons interact only with its neighboring
nucleons.
 The density of the liquid drop is independent of the volume.
Similarly, the nuclear density is independent of its volume. 14
Thank You
15

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Lec Phir11.26

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Course: Physics I Code: PHIR11

Topic: Nuclear and Particle Physics

Dr. Joy Prakash Das

 Why some combinations of neutrons

 The tendency for N to equal Z follows from the existence of

 If created in a nuclear reaction, a 12 5

 Only five stable odd-odd nuclides are known: 21H, 63 Li, 10

 Nuclear forces are limited in range, and as a result nucleons

 This process is called alpha decay. 6

 In positive beta decay, a proton becomes a neutron and a

 Thus negative beta decay decreases the proportion of neutrons

 The figure shows how alpha

 The hydrogen isotope deuterium, 21H, has a neutron as well as a

 However, the measured mass of the 21H atom is only 2.014102 u,

 We can perform experiments to see how much energy is needed

 The binding energy per nucleon for a given nucleus is an average

 It tries to provide a simple explanation for the binding energy

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