- An atom has a nucleus. The nucleus is positively charged. The radius
of the nucleus is smaller than the radius of an atom by a factor of
104
. More than 99.9% mass of the atom is concentrated in the nucleus
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- On the atomic scale, mass is measured in atomic mass units (u). By
definition, 1 atomic mass unit (1u) is 1/12th mass of one atom of 12C;
1u = 1.660563 × 10–27 kg
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- A nucleus contains a neutral particle called neutron. Its mass is almost
the same as that of proton
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- The atomic number Z is the number of protons in the atomic nucleus
of an element. The mass number A is the total number of protons and
neutrons in the atomic nucleus; A = Z+N; Here N denotes the number
of neutrons in the nucleus.
A nuclear species or a nuclide is represented as X
A
Z , where X is the
chemical symbol of the species.
Nuclides with the same atomic number Z, but different neutron number
N are called isotopes. Nuclides with the same A are isobars and those
with the same N are isotones.
Most elements are mixtures of two or more isotopes. The atomic mass
of an element is a weighted average of the masses of its isotopes and
calculated in accordance to the relative abundances of the isotopes.
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- A nucleus can be considered to be spherical in shape and assigned a
radius. Electron scattering experiments allow determination of the
nuclear radius; it is found that radii of nuclei fit the formula
R = R0 A
1/3
,
where R0
= a constant = 1.2 fm. This implies that the nuclear density
is independent of A. It is of the order of 1017 kg/m3
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- Neutrons and protons are bound in a nucleus by the short-range strong
nuclear force. The nuclear force does not distinguish between neutron
and proton.
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- The nuclear mass M is always less than the total mass, Sm, of its
constituents. The difference in mass of a nucleus and its constituents
is called the mass defect,
DM = (Z mp
- (A – Z )mn
) – M
Using Einstein’s mass energy relation, we express this mass difference
in terms of energy as
DEb
= DM c2
The energy DEb
represents the binding energy of the nucleus. In the
mass number range A = 30 to 170, the binding energy per nucleon is
nearly constant, about 8 MeV/nucleon.
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- Energies associated with nuclear processes are about a million times
larger than chemical process.
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- The Q-value of a nuclear process is
Q = final kinetic energy – initial kinetic energy.
Due to conservation of mass-energy, this is also,
Q = (sum of initial masses – sum of final masses)c
2
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- Radioactivity is the phenomenon in which nuclei of a given species
transform by giving out a or b or g rays; a-rays are helium nuclei;
b-rays are electrons. g-rays are electromagnetic radiation of wavelengths
shorter than X-rays.\
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- Energy is released when less tightly bound nuclei are transmuted into
more tightly bound nuclei. In fission, a heavy nucleus like 235
92 U breaks
into two smaller fragments, e.g., 235 1 133 99 1
92 0 51 41 U+ n Sb Nb + 4 n → + 0
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- In fusion, lighter nuclei combine to form a larger nucleus. Fusion of
hydrogen nuclei into helium nuclei is the source of energy of all stars
including our sun.
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- The density of nuclear matter is independent of the size of the nucleus.
The mass density of the atom does not follow this rule.
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- The radius of a nucleus determined by electron scattering is found to
be slightly different from that determined by alpha-particle scattering.
This is because electron scattering senses the charge distribution of
the nucleus, whereas alpha and similar particles sense the nuclear
matter.
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- After Einstein showed the equivalence of mass and energy, E = mc
2
,
we cannot any longer speak of separate laws of conservation of mass
and conservation of energy, but we have to speak of a unified law of
conservation of mass and energy. The most convincing evidence that
this principle operates in nature comes from nuclear physics. It is
central to our understanding of nuclear energy and harnessing it as a
source of power. Using the principle, Q of a nuclear process (decay or
reaction) can be expressed also in terms of initial and final masses.
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- The nature of the binding energy (per nucleon) curve shows that
exothermic nuclear reactions are possible, when two light nuclei fuse
or when a heavy nucleus undergoes fission into nuclei with intermediate
mass.
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- For fusion, the light nuclei must have sufficient initial energy to
overcome the coulomb potential barrier. That is why fusion requires
very high temperatures.
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- Although the binding energy (per nucleon) curve is smooth and slowly
varying, it shows peaks at nuclides like 4He, 16O etc. This is considered
as evidence of atom-like shell structure in nuclei.
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- Electrons and positron are a particle-antiparticle pair. They are
identical in mass; their charges are equal in magnitude and opposite.
(It is found that when an electron and a positron come together, they
annihilate each other giving energy in the form of gamma-ray photons.)
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- Radioactivity is an indication of the instability of nuclei. Stability
requires the ratio of neutron to proton to be around 1:1 for light
nuclei. This ratio increases to about 3:2 for heavy nuclei. (More
neutrons are required to overcome the effect of repulsion among the
protons.) Nuclei which are away from the stability ratio, i.e., nuclei
which have an excess of neutrons or protons are unstable. In fact,
only about 10% of knon isotopes (of all elements), are stable. Others
have been either artificially produced in the laboratory by bombarding
a, p, d, n or other particles on targets of stable nuclear species or
identified in astronomical observations of matter in the universe.