NUCLEAR BINDING ENERGY
Mass defect
The sum of the masses of the constituent nuclei is always more than the actual mass of the resulting nucleus. The difference between the masses of the constituent nucleons and the actual mass of the nucleus is called the mass defect. Let M be the mass of the nucleus having the mass number A and atomic number Z.
Mass defect,∆m= [Zmp+(A-Z)mn]-M
Where mp is the mass of the proton and mn is the mass of the neutron
Binding energy
When protons and neutrons combine to form a nucleus, the mass that disappear (mass defect) is converted into equivalent amount of energy. This energy is called binding energy of the nucleus.
Binding energy =mass defect x c2=∆mxc2=[Zmp+(A-Z)mn-M]c2
The binding energy determines the stability of the nucleus. If the binding energy is large the nucleus is stable and vice versa. The binding energy must be supplied to the nucleus to split into completely into its constituent nucleons.
MASS-ENERGY RELATION
Einstein’s mass-energy relation, relationship between mass (m) and energy (E) in the special theory of relativity of Albert Einstein, embodied by the formula E = mc2, where c equals 300,000 km (186,000 miles) per second—i.e., the speed of light.
NUCLEUS AND ITS COMPOSITION
NUCLEUS AND ITS COMPOSITION
Nucleus and Nuclear Particles:
Nucleus is small and positively charged part of an atom at the center where entire mass of the atom is concentrated. E. Rutherford and his co-workers conducted a series of scattering experiments, on the basis of which the existence of the nucleus was first proposed in1911. These experiments helped to understand the arrangement of sub atomic particles (electrons, protons and neutrons) in an atom. From the experimental observations it was concluded that the protons and neutrons are present in the nucleus where as electrons are present in the empty space around the nucleus.
ATOMIC NUMBER: It is the numbers of electrons present outside the nucleus or the number of protons present inside the nucleus. It is denoted by (Z).
Atomic Number (Z) = Number of electrons (e) OR Number of Protons (p)
NUCLEONS: The sub atomic particles (protons and neutrons) of nucleus are collectively called nucleons. The total number of nucleons is denoted byA and is called mass number of the nucleus.
Mass Number (A) = Number of Protons (p) + Number of Neutrons (n)
REPRESENTATION OF NUCLIDE: The nucleus of any atom is represented by specifying the atomic number as a subscript at the left hand bottom of the atomic symbol and mass number as a superscript at the left hand top of the symbol. For example, carbon atom, its symbol is C; atomic number is 6, mass number is12. It is represented as12c .Such symbols are called as nuclides.
NUCLEAR DIMENSIONS:
The radius of the nucleus is of the order of 10-12 and that of atom is 10-8
•
The radii of the various nuclei can be calculated by the following relation
r= R0A1/3
Where; r= radius of nucleus
A= mass number
R0 = constant (1.4 x 10-24cm)
•
Nuclear Dimensions are expressed in Fermi units, 1Fermi = 10-13cm.
•
Area of cross section of nucleus is measured in unit called barn
(1barn = 10-24cm2)
•
Radius of nucleus is 105 times smaller than that of atom.
•
Density is of the order of 1014gcm-3.
•
Volume is of the order of 10-38 cm3.
ISOTOPES, ISOBARS, ISOTONES,
Isotopes:
These are the atoms having same atomic number but different mass numbers.
They contain same number of protons but different number of nucleons.
Isobars:
The atoms having different atomic numbers but same mass number are called isobars. They contain same number of nucleons but different number of protons.
Calcium and Argon are isobars of each other having same mass number but different atomic number.
Similarly Lead and Bismuth are isobars of each other.
Isotones:
These are the atoms having same number of neutrons but different number of nucleons. But by appearance they have different number atomic number and different mass number but the number of neutrons is same all these nuclides have different mass number and atomic number. But if we calculate the number of neutron in each case it is coming out to bethe16.
Because Number of neutrons = mass number (A) – atomic number (Z)
Atomic mass
One way scientists measure the size of something is by its mass. Scientists can even measure very, very tiny things like atoms. One measure of the size of an atom is its "atomic mass". Almost all of the mass of an atom (more than 99%) is in its nucleus, so "atomic mass" is pretty much a measure of the size of the nucleus of an atom.
The nucleus of an atom is made up of protons and neutrons. Protons and neutrons are almost exactly the same size. If you add up the number of protons and neutrons in the nucleus of an atom, you get that atom's atomic mass. A simple hydrogen atom has just one proton and zero neutrons. Its atomic mass is 1. The most common kind of carbon atom has 6 neutrons and 6 protons. It has an atomic mass of 12.
All atoms of a certain element have the same number of protons. Oxygen atoms always have 8 protons; carbon atoms all have 6 protons. Most atoms come in different types called isotopes. Isotopes have different numbers of neutrons. The most common isotope of carbon has 6 neutrons and 6 protons. Its atomic mass is 12. A rare, radioactive isotope of carbon has 8 neutrons. Its atomic mass is 14 ( = 6 protons + 8 neutrons).
Mass defect
The sum of the masses of the constituent nuclei is always more than the actual mass of the resulting nucleus. The difference between the masses of the constituent nucleons and the actual mass of the nucleus is called the mass defect. Let M be the mass of the nucleus having the mass number A and atomic number Z.
Mass defect,∆m= [Zmp+(A-Z)mn]-M
Where mp is the mass of the proton and mn is the mass of the neutron
Binding energy
When protons and neutrons combine to form a nucleus, the mass that disappear (mass defect) is converted into equivalent amount of energy. This energy is called binding energy of the nucleus.
Binding energy =mass defect x c2=∆mxc2=[Zmp+(A-Z)mn-M]c2
The binding energy determines the stability of the nucleus. If the binding energy is large the nucleus is stable and vice versa. The binding energy must be supplied to the nucleus to split into completely into its constituent nucleons.
MASS-ENERGY RELATION
Einstein’s mass-energy relation, relationship between mass (m) and energy (E) in the special theory of relativity of Albert Einstein, embodied by the formula E = mc2, where c equals 300,000 km (186,000 miles) per second—i.e., the speed of light.
NUCLEUS AND ITS COMPOSITION
NUCLEUS AND ITS COMPOSITION
Nucleus and Nuclear Particles:
Nucleus is small and positively charged part of an atom at the center where entire mass of the atom is concentrated. E. Rutherford and his co-workers conducted a series of scattering experiments, on the basis of which the existence of the nucleus was first proposed in1911. These experiments helped to understand the arrangement of sub atomic particles (electrons, protons and neutrons) in an atom. From the experimental observations it was concluded that the protons and neutrons are present in the nucleus where as electrons are present in the empty space around the nucleus.
ATOMIC NUMBER: It is the numbers of electrons present outside the nucleus or the number of protons present inside the nucleus. It is denoted by (Z).
Atomic Number (Z) = Number of electrons (e) OR Number of Protons (p)
NUCLEONS: The sub atomic particles (protons and neutrons) of nucleus are collectively called nucleons. The total number of nucleons is denoted byA and is called mass number of the nucleus.
Mass Number (A) = Number of Protons (p) + Number of Neutrons (n)
REPRESENTATION OF NUCLIDE: The nucleus of any atom is represented by specifying the atomic number as a subscript at the left hand bottom of the atomic symbol and mass number as a superscript at the left hand top of the symbol. For example, carbon atom, its symbol is C; atomic number is 6, mass number is12. It is represented as12c .Such symbols are called as nuclides.
NUCLEAR DIMENSIONS:
The radius of the nucleus is of the order of 10-12 and that of atom is 10-8
•
The radii of the various nuclei can be calculated by the following relation
r= R0A1/3
Where; r= radius of nucleus
A= mass number
R0 = constant (1.4 x 10-24cm)
•
Nuclear Dimensions are expressed in Fermi units, 1Fermi = 10-13cm.
•
Area of cross section of nucleus is measured in unit called barn
(1barn = 10-24cm2)
•
Radius of nucleus is 105 times smaller than that of atom.
•
Density is of the order of 1014gcm-3.
•
Volume is of the order of 10-38 cm3.
ISOTOPES, ISOBARS, ISOTONES,
Isotopes:
These are the atoms having same atomic number but different mass numbers.
They contain same number of protons but different number of nucleons.
Isobars:
The atoms having different atomic numbers but same mass number are called isobars. They contain same number of nucleons but different number of protons.
Calcium and Argon are isobars of each other having same mass number but different atomic number.
Similarly Lead and Bismuth are isobars of each other.
Isotones:
These are the atoms having same number of neutrons but different number of nucleons. But by appearance they have different number atomic number and different mass number but the number of neutrons is same all these nuclides have different mass number and atomic number. But if we calculate the number of neutron in each case it is coming out to bethe16.
Because Number of neutrons = mass number (A) – atomic number (Z)
Atomic mass
One way scientists measure the size of something is by its mass. Scientists can even measure very, very tiny things like atoms. One measure of the size of an atom is its "atomic mass". Almost all of the mass of an atom (more than 99%) is in its nucleus, so "atomic mass" is pretty much a measure of the size of the nucleus of an atom.
The nucleus of an atom is made up of protons and neutrons. Protons and neutrons are almost exactly the same size. If you add up the number of protons and neutrons in the nucleus of an atom, you get that atom's atomic mass. A simple hydrogen atom has just one proton and zero neutrons. Its atomic mass is 1. The most common kind of carbon atom has 6 neutrons and 6 protons. It has an atomic mass of 12.
All atoms of a certain element have the same number of protons. Oxygen atoms always have 8 protons; carbon atoms all have 6 protons. Most atoms come in different types called isotopes. Isotopes have different numbers of neutrons. The most common isotope of carbon has 6 neutrons and 6 protons. Its atomic mass is 12. A rare, radioactive isotope of carbon has 8 neutrons. Its atomic mass is 14 ( = 6 protons + 8 neutrons).
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