Physics
438
13.1 INTRODUCTION
In the previous chapter, we have learnt that in every atom, the positive
charge and mass are densely concentrated at the centre of the atom
forming its nucleus. The overall dimensions of a nucleus are much smaller
than those of an atom. Experiments on scattering of
α
-particles
demonstrated that the radius of a nucleus was smaller than the radius
of an atom by a factor of about 10
4
. This means the volume of a nucleus
is about 10
–12
times the volume of the atom. In other words, an atom is
almost empty. If an atom is enlarged to the size of a classroom, the nucleus
would be of the size of pinhead. Nevertheless, the nucleus contains most
(more than 99.9%) of the mass of an atom.
Does the nucleus have a structure, just as the atom does? If so, what
are the constituents of the nucleus? How are these held together? In this
chapter, we shall look for answers to such questions. We shall discuss
various properties of nuclei such as their size, mass and stability, and
also associated nuclear phenomena such as radioactivity, fission and fusion.
13.2 ATOMIC MASSES AND COMPOSITION OF NUCLEUS
The mass of an atom is very small, compared to a kilogram; for example,
the mass of a carbon atom,
12
C, is 1.992647 × 10
–26
kg. Kilogram is not
a very convenient unit to measure such small quantities. Therefore, a
Chapter Thirteen
NUCLEI
2020-21
439
Nuclei
different mass unit is used for expressing atomic masses. This unit is the
atomic mass unit (u), defined as 1/12
th
of the mass of the carbon (
12
C)
atom. According to this definition
12
mass of one C atom
1u =
12
26
1.992647 10 kg
12
×
=
27
1.660539 10 kg
= ×
(13.1)
The atomic masses of various elements expressed in atomic mass
unit (u) are close to being integral multiples of the mass of a hydrogen
atom. There are, however, many striking exceptions to this rule. For
example, the atomic mass of chlorine atom is 35.46 u.
Accurate measurement of atomic masses is carried out with a mass
spectrometer, The measurement of atomic masses reveals the existence
of different types of atoms of the same element, which exhibit the same
chemical properties, but differ in mass. Such atomic species of the same
element differing in mass are called isotopes. (In Greek, isotope means
the same place, i.e. they occur in the same place in the periodic table of
elements.) It was found that practically every element consists of a mixture
of several isotopes. The relative abundance of different isotopes differs
from element to element. Chlorine, for example, has two isotopes having
masses 34.98 u and 36.98 u, which are nearly integral multiples of the
mass of a hydrogen atom. The relative abundances of these isotopes are
75.4 and 24.6 per cent, respectively. Thus, the average mass of a chlorine
atom is obtained by the weighted average of the masses of the two
isotopes, which works out to be
=
100
× + ×
= 35.47 u
which agrees with the atomic mass of chlorine.
Even the lightest element, hydrogen has three isotopes having masses
1.0078 u, 2.0141 u, and 3.0160 u. The nucleus of the lightest atom of
hydrogen, which has a relative abundance of 99.985%, is called the
proton. The mass of a proton is
27
1.00727 u 1.67262 10 kg
p
m
= = ×
(13.2)
This is equal to the mass of the hydrogen atom (= 1.00783u), minus
the mass of a single electron (m
e
= 0.00055 u). The other two isotopes of
hydrogen are called deuterium and tritium. Tritium nuclei, being
unstable, do not occur naturally and are produced artificially in
laboratories.
The positive charge in the nucleus is that of the protons. A proton
carries one unit of fundamental charge and is stable. It was earlier thought
that the nucleus may contain electrons, but this was ruled out later using
arguments based on quantum theory. All the electrons of an atom are
outside the nucleus. We know that the number of these electrons outside
the nucleus of the atom is Z, the atomic number. The total charge of the
2020-21
Physics
440
atomic electrons is thus (–Ze), and since the atom is neutral, the charge
of the nucleus is (+Ze
). The number of protons in the nucleus of the atom
is, therefore, exactly Z, the atomic number.
Discovery of Neutron
Since the nuclei of deuterium and tritium are isotopes of hydrogen, they
must contain only one proton each. But the masses of the nuclei of
hydrogen, deuterium and tritium are in the ratio of 1:2:3. Therefore, the
nuclei of deuterium and tritium must contain, in addition to a proton,
some neutral matter. The amount of neutral matter present in the nuclei
of these isotopes, expressed in units of mass of a proton, is approximately
equal to one and two, respectively. This fact indicates that the nuclei of
atoms contain, in addition to protons, neutral matter in multiples of a
basic unit. This hypothesis was verified in 1932 by James Chadwick
who observed emission of neutral radiation when beryllium nuclei were
bombarded with alpha-particles (
α
-particles are helium nuclei, to be
discussed in a later section). It was found that this neutral radiation
could knock out protons from light nuclei such as those of helium, carbon
and nitrogen. The only neutral radiation known at that time was photons
(electromagnetic radiation). Application of the principles of conservation
of energy and momentum showed that if the neutral radiation consisted
of photons, the energy of photons would have to be much higher than is
available from the bombardment of beryllium nuclei with
α
-particles.
The clue to this puzzle, which Chadwick satisfactorily solved, was to
assume that the neutral radiation consists of a new type of neutral
particles called neutrons. From conservation of energy and momentum,
he was able to determine the mass of new particle ‘as very nearly the
same as mass of proton’.
The mass of a neutron is now known to a high degree of accuracy. It is
m
n
= 1.00866 u = 1.6749×10
–27
kg (13.3)
Chadwick was awarded the 1935 Nobel Prize in Physics for his
discovery of the neutron.
A free neutron, unlike a free proton, is unstable. It decays into a
proton, an electron and a antineutrino (another elementary particle), and
has a mean life of about 1000s. It is, however, stable inside the nucleus.
The composition of a nucleus can now be described using the following
terms and symbols:
Z - atomic number = number of protons [13.4(a)]
N - neutron number = number of neutrons [13.4(b)]
A - mass number = Z + N
= total number of protons and neutrons [13.4(c)]
One also uses the term nucleon for a proton or a neutron. Thus the
number of nucleons in an atom is its mass number A.
Nuclear species or nuclides are shown by the notation
X
A
Z
where X is
the chemical symbol of the species. For example, the nucleus of gold is
denoted by
197
79
Au
. It contains 197 nucleons, of which 79 are protons
and the rest118 are neutrons.
2020-21