The
Atomic Nucleus:
The protons and Neutrons
are the constituent particles of the Nucleus. There nuclear constituent
particular are in general called nucleons which follow the Fermi – Dirac
statistics.
Ø The nucleus
contains Z protons (Z denotes the atomic Number) and N neutrons to give the
mass number A (=Z + N). For a particular value of Z, because of the different
numbers of N, the isotopes appear. The neutron- proton ratio and their oddness
and evenness are very much important in determining the stability of the
nucleus.
Ø The emission
of
particles i.e. electrons, from the nucleus does not
contradict the proton – neutron model of the nucleus. It is now believed that
the trans formation of a neutron into a proton leads to the ejection of a
particle.(Important
topic for Chemistry JAM Coaching)
In this
proton – neutron model, it is now believed that they are continuously changing
one into another through the exchange of common property. Thus, within the
nucleus, it is not appropriate to define a particle either as a proton or as a
neutron. They are really indistinguishable within the nucleus due to the
exchange phenomenon. This is why, within the nucleus, the constituent particles
are reasonably referred to as nucleons, and they can be characterized as protons
neutrons when they emerge form the nucleus. Important topic for Chemistry JAM Coaching
Many question
are asked from this topic. Hence it is a important topic for GATE chemistry coaching
Fermions
and Bosons
Ø
Maxwell
–Boltzmann statistics is well documented to explain the properties (e.g.
velocity distribution, energy distribution, etc) for the assemblies (i.e. large
number) of molecules of a gas. However, this classical mechanics is not
applicable for the elementary particles like electron, protons, neutrons,
meson, neutrinos, etc and atomic nuclei. To deal with these particles, two
quantum mechanical statistics, namely, Fermi-Dirac statistics and Bose
–Einstein statistics are developed. The particles having half integral spins
(e.g. electrons , protons, neutrons, positrons, etc) which follow the Fermi –Dirac statistics are
called fermions while the particular having the integral spins
(e.g. photons, mesons, α particles, etc) which follow the Bose –Einstein statistics are called bosons.
The fermions follow the
Pauli’s exclusion principle while the bosons do not
Nuclear
Forces: àWhat
is the nature of the forces which hold the protone and neutrons together in
such a small nucleus?
If electrostatic
forces (Coulombic forces) alone were involved, the repulsion between the
protons would have rendered the nucleus highly unstable and labile to
disintegration. Since this does not happen except in the case of heavier
elements which are radioactive it is evident that there must be some attractive
force between protone and neutron, neutron and neutron and even between proton
and proton. This must be stronger than the repulsive forces due to positive
charges on the protone. These attractive forces are called nuclear forces.
These forces are short range forces (i.e. 10-16m). There are not
follow the inverse square law.
Hideki Yukawa suggested that pi mesons oscillate between
neighboring nucleons (protons and neutrons) with a velocity close to that of light.
Proton + negative pi meson
Neutron
Neutron + positive pi meson
Proton
There is thus an exchange of pi mesons back and forth
between neighboring nucleons. This results in an allraction between neutron and
proton. Important topic for Chemistry
JAM Coaching
Nuclear Size:
Some indication about the size of the nucleus was obtained
from Ruther ford’s experiments on scattering of alpha particles. More accurate
information has now been obtained from experiments on scallering of neutrons.
The results can be summarized by the equation.
Where r
= radius of a nucleus A = Mass Number
R0 = Constant =
Nuclear radius is
generally measured in Fermi units
Example: Estimate the radius of
nucleus.
Solution The radius
Where R = 1.5 f and
A = 27
Then
it is a important topic for GATE chemistry coaching
Atomic mass Unit (a.m.u)
According to the latest convention, the mass of the standard
carbon atom
is taken to be
12 a.m.u. Thus one amu, is exactly 1/12th of the mass of an
atom.
1amu =
where is
Avogadro’s number
=
Nuclear Density: à
As mentioned above, the radius (r) of a nucleus is extremely
small being of the order of
. Since the nucleus is believed to be spherical, its
volume
would be for
too smaller, being to the order of
. As a result, the density (mass/ volume) of the
nucleus would be tremendously high. It is independent of the nature and size of
the nuclei.
Where m = mass (in kg)
r = Radius (in m)
it is a important topic for GATE chemistry coaching
Shape of the Nucleus: à
In our previous consideration, the spherical nature of the
nucleus has been considered. But the actual shape of the nucleus depends on the
total angular quantum number or simply, the nuclear spin I and the electric
quadrupole moment (=Q) of the nucleus under consideration.
The parameter, electric quadrupole moment (Q) describes the
interaction of the nucleus with the electric field gradient
. Thus the term Q can be expressed as follows.
Where e is the unit of electrostatic charge,
(r) gives the electric charge density at a distance r
from the centre of the nucleus with x,y,z as its coordinates whose origin also
lies at the centre of the nucleus –Q give a measure of deviation of nuclear
charge distribution from the spherical symmetry. If the charge is spherically
and symmetrically distributed then it leads to.
In such case (i.e. spherically symmetrical) e Q = 0, i.e. Q=
0. The positive value of Q indicates that the nucleus is elongated in the Z-
direction and negative value indicates that the nucleus is contracted in the z
– direction.
It has been found that the systems having I
1 and eQ
are deviated from the spherical shape. On the other
hand, the nuclei having I = 0. ½ and e Q = 0, are perfectly spherical. In this
parameter e is the unit of electrostatic charge and Q gives the measure of
deviation from sphericality of the nucleus. If eQ is positive, ie eQ >0,
then the nucleus becomes a prelate spheroid (ie egg shaped) while for eQ <0,
the nucleus becomes an oblate spheroid (ie. discus or pumpkin shaped). These
are shown in Fig.
The dimension of quadrupole moment (Q) is cm2 and
it is very often expressed in the unit of
(=1barn). The value for deuteron is
m barn (milli barn)
Important topic for Chemistry JAM Coaching
Equivalence of a.m.u. and Energy: à
According to Einstein’s mass energy relationship, E = mc2
where m is mass in kg, C is velocity of light in ms-1 and E is
energy in joules. Therefore. energy equivalent to one a.m.u is given by
it is a
important topic for GATE chemistry coaching
Packing fraction:
It has been observed that isotopic masses of element are
close to but not exactly equal to whole numbers. The mass numbers, however, are
invariably whole number. Aston expressed the variation of isotopic mass from
mass number of the isotope in terms of a quantity called packing fraction.
Packing fraction may have a negative an a positive sign. The
negative sign of the packing fraction means that the isotopic mass is less than
the mass number of the isotope. In such cases, some mass gets transformed into
energy in the formation of that nucleus. In accordance with Einstein’s
equation, E = mc2. Such nuclei therefore are more stable. A positive
packing fraction. On the other hand would imply a tendency towards instability.
But this is not correct especially for elements of low atomic masses.
Mass Defect: Binding Energy of Nucleus:à
It has been found that the actual isotopic mass of an
element is almost invariably less than the sum of masses of protons. Neutrons
and electrons present in it. The difference between the two is known as mass
defect.
Suppose A is the mass number and Z is the atomic Number
(nuclear charge) of an element. Evidently its atom contains Z protons, (A-Z)
neutrons and Z electrons. Let mp be the mass of a proton, mn
that of a neutron and me that of an electron. The atomic mass M’ of
the isotope, therefore should be given by.
Where
is mass of
Hydrogen atom.
The actual atomic mass of the element, however, is found to
be less than M’ suppose it is M. Then
Mass defect = M’ – M = ΔM = Z
+ (A-Z) Mn
– M
The quantity ΔM represents the loss of mass in the formation
of the nucleus of the atom. The loss of mass is equivalent of the energy
released in the formation of the given nucleus from individual protons and
neutrons. The release of energy results in the stability of the nucleus.
The energy released in the formation of a nucleus from its
constituent nucleons is called the binding energy of the nucleus. it is a
important topic for GATE chemistry coaching
This binding energy of a nucleus when divided by the number
of nucleons gives the means binding energy per nucleon. The binding energy per nucleon is a measure
of stability of the nucleus. The greater the binding energy per nucleon is a
measure of stability of the nucleus. it is a important topic for GATE chemistry
coaching
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