Lecture notes
Nuclear physics
- Module
- Physics (PHYS)
- Institution
- Clackmannan College Of Further Education
Lecture notes of 40 pages for the course Physics at Clackmannan College of Further Education (Nuclear physics)
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Department of PhysicsTaki Government College
STUDY MATERIAL
FOR SEM-4 CORE
NUCLEAR PHYSICS
Sources of the Materials:
1.http://www.brainkart.com/article/Classification-of-nuclei-and-Properties-of-nucleus-Nuclear-
size_2954/
2. https://www.soton.ac.uk/~ab1u06//teaching/phys3002/notes.html
3. https://ocw.mit.edu/courses/nuclear-engineering/22-02-introduction-to-applied-nuclear-physics-
spring-2012/lecture-notes/MIT22_02S12_lec_ch7.pdf
,Nucleus
The nucleus consists of the elementary particles, protons and neutrons which are
known as nucleons. A proton has positive charge of the same magnitude as that of
electron and its rest mass is about 1836 times the mass of an electron. A neutron is
electrically neutral, whose mass is almost equal to the mass of the proton. The
nucleons inside the nucleus are held together by strong attractive forces called
nuclear forces.
A nucleus of an element is represented as ZXA, where X is the chemical symbol
of the element. Z represents the atomic number which is equal to the number of
protons and A, the mass number which is equal to the total number of protons and
neutrons. The number of neutrons is represented as N which is equal to A −Z. For
example, the chlorine nucleus is represented as 35.
17Cl It contains 17 protons and 18
neutrons.
1Classification of nuclei
(i) Isotopes
Isotopes are atoms of the same element having the same atomic number Z but
different mass number A. The nuclei 1H 1, 1H2 and 1H3 are the isotopes of hydrogen.
In other words isotopes of an element contain the same number of protons but
different number of neutrons. As the atoms of isotopes have identical electronic
structure, they have identical chemical properties and placed in the same location in
the periodic table.
(ii) Isobars
Isobars are atoms of different elements having the same mass number A, but
different atomic number Z. The nuclei 8O16 and 7N16 represent two isobars. Since
isobars are atoms of different elements, they have different physical and chemical
properties.
(iii) Isotones
Isotones are atoms of different elements having the same number of neutrons.
14 and 8O16 are some examples of isotones.
6C
,2.General properties of nucleus
Nuclear size
According to Rutherford's α−particle scattering experiment, the distance of the
closest approach of α − particle to the nucleus was taken as a measure of nuclear
radius, which is approximately 10−15 m. If the nucleus is assumed to be spherical, an
empirical relation is found to hold good between the radius of the nucleus R and its
mass number A. It is given by
R ∝ A1/3
R = roA1/3
where ro is the constant of proportionality and is equal to 1.3 F (1 Fermi, F =
10−15 m)
Nuclear density
The nuclear density ρN can be calculated from the mass and size of the nucleus.
ρN = Nuclear mass / Nuclear volume
Nuclear mass = AmN
where, A = mass number
and mN = mass of one nucleon and is approximately equal to 1.67 x 10−27 kg
Nuclear volume = 4/3 πRR3
ρN = mN / ( 4/3 πRr03)
Substituting the known values, the nuclear density is calculated as 1.816 x 10 17
kg m−3 which is almost a constant for all the nuclei irrespective of its size.
The high value of the nuclear density shows that the nuclear matter is in an
extremely compressed state.
Nuclear charge
The charge of a nucleus is due to the protons present in it. Each proton has a
positive charge equal to 1.6 x 10−19 C.
The nuclear charge = Ze, where Z is the atomic number.
, Atomic mass unit
It is convenient to express the mass of a nucleus in atomic mass unit (amu),
though the unit of mass is kg. One atomic mass unit is considered as one twelfth of
the mass of carbon atom 6C 12. Carbon of atomic number 6 and mass number 12 has
mass equal to 12 amu.
1 amu = 1.66 x 10−27 kg
The mass of a proton, mp = 1.007276 amu
This is equal to the difference in mass of the hydrogen atom which is 1.007825
amu and the mass of electron.
The mass of a neutron, mn = 1.008665 amu
The energy equivalence of one amu can be calculated in electron-volt
Einstein's mass energy relation is, E = mc2 Here, m = 1 amu =
1.66 x 10−27 kg
c = 3 x 108 ms−1
E = 1.66 x 10−27 x (3 x 108)2 J
One electron-volt (eV) is defined as the energy of an electron when it is
accelerated through a potential difference of 1 volt.
1 eV = 1.6 x 10−19 coulomb x 1 volt, 1 eV = 1.6 x
10−19 joule
Hence, E = 1.66 x 10 − 27 x (3 x10 8 ).6 x10-19 eV
= 931 million electronvolt = 931 MeV
Thus, energy equivalent of 1 amu = 931 MeV
Nuclear mass
As the nucleus contains protons and neutrons, the mass of the nucleus is
assumed to be the mass of its constituents.
Assumed nuclear mass = ZmP + Nmn,
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