4
1 Nuclear Chemistry
6. Excitation energy needed for nuclei belonging to the magic number is greater for
its first excitation state.
The stability of isotopes can be better understood by a mathematical model. In
general, an element “X” is represented as
A X Z , where A is the total mass of the
element (i.e., the total number of protons and neutrons) and Z is the atomic number
(i.e., the total number of protons).
Useful information can be obtained by studying the so-called binding energy
which controls the stability of nuclei. A proton (
1 H 1 ) has a unit positive charge and
mass of one H atom (i.e., one proton and one electron), viz., 1.00782522 a.m.u.,
while a neutron (
1 n 0 ) is an electrically neutral particle of mass slightly greater than
that of the proton, viz., 1.00866544 a.m.u. Like charges repelling each other, the
forces which bind protons and/or neutrons together in a nucleus must be other than
an electrostatic force.
1.5 Binding Energy of Nucleus
It is observed that the mass of an atom is less than the combined masses of separate
constituents of the atom. This difference in mass is called the “mass defect” and may
be expressed in terms of “energy” by using the well-known Einstein’s mass–energy
relation, i.e.,
E = mc
2
,
where “c” is the velocity of light and “m” the mass. This energy is responsible for
binding nucleons together in the nucleus and is called the “binding energy”.
For example, a He atom (
4 He 2 ) with a mass of 4.00260361 a.m.u. can be considered to explain the binding energy. The separate constituents of He may be considered
to be two H atoms (or two protons and two electrons) and two neutrons. The mass
of these particles, sometimes called “nucleons”, is expressed either in the unit of kg
or in atomic mass unit (a.m.u.). One atomic mass unit (a.m.u.) = 1.66054 × 10
−27
kg. This mass can be converted into energy by using Einstein’s relation (E = mc
2 ).
If mass is expressed in kg, and velocity of light in ms
−1 , then energy (in the unit
of mega electron volt, MeV) produced from one unit of a.m.u. can be obtained by
multiplying mc
2 by a conversion factor of 62.41539 × 10
−5 . Thus,
1 a.m.u. = (1.66054 × 10
−27 kg) × (2.99792458 × 10
8 m/s or ms
−1
)
× 2 × (62.41539 × 10
−5
)
= 931.5 MeV.
1 Nuclear Chemistry
6. Excitation energy needed for nuclei belonging to the magic number is greater for
its first excitation state.
The stability of isotopes can be better understood by a mathematical model. In
general, an element “X” is represented as
A X Z , where A is the total mass of the
element (i.e., the total number of protons and neutrons) and Z is the atomic number
(i.e., the total number of protons).
Useful information can be obtained by studying the so-called binding energy
which controls the stability of nuclei. A proton (
1 H 1 ) has a unit positive charge and
mass of one H atom (i.e., one proton and one electron), viz., 1.00782522 a.m.u.,
while a neutron (
1 n 0 ) is an electrically neutral particle of mass slightly greater than
that of the proton, viz., 1.00866544 a.m.u. Like charges repelling each other, the
forces which bind protons and/or neutrons together in a nucleus must be other than
an electrostatic force.
1.5 Binding Energy of Nucleus
It is observed that the mass of an atom is less than the combined masses of separate
constituents of the atom. This difference in mass is called the “mass defect” and may
be expressed in terms of “energy” by using the well-known Einstein’s mass–energy
relation, i.e.,
E = mc
2
,
where “c” is the velocity of light and “m” the mass. This energy is responsible for
binding nucleons together in the nucleus and is called the “binding energy”.
For example, a He atom (
4 He 2 ) with a mass of 4.00260361 a.m.u. can be considered to explain the binding energy. The separate constituents of He may be considered
to be two H atoms (or two protons and two electrons) and two neutrons. The mass
of these particles, sometimes called “nucleons”, is expressed either in the unit of kg
or in atomic mass unit (a.m.u.). One atomic mass unit (a.m.u.) = 1.66054 × 10
−27
kg. This mass can be converted into energy by using Einstein’s relation (E = mc
2 ).
If mass is expressed in kg, and velocity of light in ms
−1 , then energy (in the unit
of mega electron volt, MeV) produced from one unit of a.m.u. can be obtained by
multiplying mc
2 by a conversion factor of 62.41539 × 10
−5 . Thus,
1 a.m.u. = (1.66054 × 10
−27 kg) × (2.99792458 × 10
8 m/s or ms
−1
)
× 2 × (62.41539 × 10
−5
)
= 931.5 MeV.