Nuclear Processes
At one point in time matter was considered to be made up of “atoms” only, which were
considered to be the fundamental particles. It was soon discovered that the atoms are made up
of elementary particles. Thus the physical world is composed of a combination of various sub-
atomic or fundamental particles.
Thus an atom is denoted as "!𝑋 where
• “Z” is the proton number, or the atomic number. Just a reminder that protons are
positively charged.
• “A” is the number of nucleons, the number of protons plus the neutrons and is known
as the mass number.
The electron(𝑒 # ) are negatively charged particles and carry a charge of 1.6 × 10#$%
Coulomb. The mass of an electron is approximately 9.1 × 10#&$ Kg. Electrons are Fermions
i.e they have an half integer spin and hence they open Fermi-Dirac statistics / distribution.
We do encounter a “positive electron” known as the “positron”, which is identical to an electron
in all respects, except that it is positively charged.
From Einstein’s energy-mass equivalence, we know that the rest-mass of an electron / positron
is 511 keV. According to Einstein’s theory of relativity, the mass of a particle depends upon
it’s speed (relative to a stationary observer). The rest mass corresponds to the situation wherein
the particle is at rest. “keV” refers to kilo-electron-volt, and is the unit of energy conventionally
used in nuclear physics.
It corresponds to the energy gained by an electron when accelerated across a potential
difference of 1 volt.
1 𝑒𝑉 = (1.6 × 10#$% ) × 1 Coulomb –Volt = 1.6 × 10#$% Joule
It is customary to use the following larger units
1 𝑘𝑒𝑉 = 10& 𝑒𝑉 ; 1 𝑀𝑒𝑉 = 10' 𝑒𝑉
,In the above context, the rest mass of an electron is
𝐸( = 𝑚) × 𝑐 * = (9.11 × 10#&$ ) × (3 × 10+ )* = 8.2 × 10#$, Joule
+.* ×$)!"#
𝐸( = $.'×$)!"$
= 0.511 MeV
Protons(𝝅) are positively charged, with a charge equal in magnitude to that of an electron. It’s
mass is 𝑚0 = 1.6 × 10#*1 kg.
The neutron(𝝂) is an electrically neutral particle, and has a mass slightly heavier than that of
proton. This small mass difference between the neutron and the proton has a significant bearing
on us being what we are today. The neutron is not a stable particle i.e it is stable inside the
nucleus, however a free neutron has a mean life of about 14 minutes and 42 seconds or a half
life of about 10 minutes and 11 seconds.
A neutron decays to a proton and the conservation laws demand that this reaction proceed as
𝑛$ ⟶ 𝑝$ + 𝑒 #$ + 𝜈̅ , where𝜈̅ , is an anti-neutrino
The neutrino is a particle with rest-zero mass and no charge and is required from conservation
laws.
The atomic dimensions are of the order of Angstrom (1𝐴) = 10#$) 𝑚), whereas the nuclear
dimensions are of the order of Fermi (1𝐹 = 10#$2 𝑚).
The radius of the nucleus is related to the total number of nucleons present viz. the mass number
as
$3
𝑅 = 𝑅( × 𝐴 & Fermi, where 𝑅( = 1.2 fm.
The nuclear density is constant across the nuclear landscape, and
𝑚𝑎𝑠𝑠 𝐴(𝑎𝑚𝑢) 𝐴 × 1.6 × 10#*1 𝑘𝑔 𝐴 × 1.6 × 10#$%
𝜌4567 = = , = & 𝑚& = ,
𝑣𝑜𝑙𝑢𝑚𝑒 𝜋𝑅 & , $ × 𝜋 × 𝑅( × 𝐴
& × 𝜋 × K𝑅( × 𝐴 3& L &
&
Hence,
, 𝜌4567 ≈ 10$+ 𝑘𝑔⁄𝑚&
Thus we can conclude that
• The density of nuclear matter is very high
• The nuclear density is independent of A, i.e all nuclei have almost identical density.
Therefore, this suggests that nuclei are very similar to liquid drops, which have the same
density irrespective of the size of the drop. This has resulted in the development of a
macroscopic model known as the “Liquid Drop Model” of the nucleus (as described /discussed
later)
Alternatively we know that
$3 &
𝑉𝑜𝑙𝑢𝑚𝑒 ∝ 𝑅& ∝ S𝐴 &T ∝𝐴
8(759:
Hence, "
= 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Therefore, number of nucleons per unit volume is constant for all nuclei.
Atomic Mass Unit (AMU, u)
The mass of nucleons is usually expressed as Atomic Mass Unit (AMU, 𝑢). It is a relative
scale, where the mass of a neutral 12C atom is taken precisely as 12 units. i.e
𝑚( $*'𝐶 ) = 12 𝑢
9= "&%> ?
1 amu is hence considered as 1⁄12;< the mass of 12C atom, 1 𝑎𝑚𝑢 =
$*
We know that 1 mole of a substance contains Avagrados number of atoms (6.023 × 10*& ).
i.e one mole of a substance contains the same number of atoms / molecules.
∴ 1 mole of 12C contains 12 gm of the isotope, on the other hand 1 mole of natural O2 contains
2 × 15.99938 = 31.99876 gm.
∴ 12 gm of 12C has 6.023 × 10*& atoms.
$* × $)!'
∴ 1 atom of 12C weighs '.)*& × $)&' 𝑘𝑔
12 × 10#& 1
∴ 1 𝑎𝑚𝑢 = × = 1.66053 × 10#*1 𝑘𝑔
6.023 × 10*& 12
∴ from energy-mass equivalence, we have the energy associated with 1 𝑢 as
𝐸$5 = 1.66053 × 10#*1 × (3 × 10+ )* Joule
At one point in time matter was considered to be made up of “atoms” only, which were
considered to be the fundamental particles. It was soon discovered that the atoms are made up
of elementary particles. Thus the physical world is composed of a combination of various sub-
atomic or fundamental particles.
Thus an atom is denoted as "!𝑋 where
• “Z” is the proton number, or the atomic number. Just a reminder that protons are
positively charged.
• “A” is the number of nucleons, the number of protons plus the neutrons and is known
as the mass number.
The electron(𝑒 # ) are negatively charged particles and carry a charge of 1.6 × 10#$%
Coulomb. The mass of an electron is approximately 9.1 × 10#&$ Kg. Electrons are Fermions
i.e they have an half integer spin and hence they open Fermi-Dirac statistics / distribution.
We do encounter a “positive electron” known as the “positron”, which is identical to an electron
in all respects, except that it is positively charged.
From Einstein’s energy-mass equivalence, we know that the rest-mass of an electron / positron
is 511 keV. According to Einstein’s theory of relativity, the mass of a particle depends upon
it’s speed (relative to a stationary observer). The rest mass corresponds to the situation wherein
the particle is at rest. “keV” refers to kilo-electron-volt, and is the unit of energy conventionally
used in nuclear physics.
It corresponds to the energy gained by an electron when accelerated across a potential
difference of 1 volt.
1 𝑒𝑉 = (1.6 × 10#$% ) × 1 Coulomb –Volt = 1.6 × 10#$% Joule
It is customary to use the following larger units
1 𝑘𝑒𝑉 = 10& 𝑒𝑉 ; 1 𝑀𝑒𝑉 = 10' 𝑒𝑉
,In the above context, the rest mass of an electron is
𝐸( = 𝑚) × 𝑐 * = (9.11 × 10#&$ ) × (3 × 10+ )* = 8.2 × 10#$, Joule
+.* ×$)!"#
𝐸( = $.'×$)!"$
= 0.511 MeV
Protons(𝝅) are positively charged, with a charge equal in magnitude to that of an electron. It’s
mass is 𝑚0 = 1.6 × 10#*1 kg.
The neutron(𝝂) is an electrically neutral particle, and has a mass slightly heavier than that of
proton. This small mass difference between the neutron and the proton has a significant bearing
on us being what we are today. The neutron is not a stable particle i.e it is stable inside the
nucleus, however a free neutron has a mean life of about 14 minutes and 42 seconds or a half
life of about 10 minutes and 11 seconds.
A neutron decays to a proton and the conservation laws demand that this reaction proceed as
𝑛$ ⟶ 𝑝$ + 𝑒 #$ + 𝜈̅ , where𝜈̅ , is an anti-neutrino
The neutrino is a particle with rest-zero mass and no charge and is required from conservation
laws.
The atomic dimensions are of the order of Angstrom (1𝐴) = 10#$) 𝑚), whereas the nuclear
dimensions are of the order of Fermi (1𝐹 = 10#$2 𝑚).
The radius of the nucleus is related to the total number of nucleons present viz. the mass number
as
$3
𝑅 = 𝑅( × 𝐴 & Fermi, where 𝑅( = 1.2 fm.
The nuclear density is constant across the nuclear landscape, and
𝑚𝑎𝑠𝑠 𝐴(𝑎𝑚𝑢) 𝐴 × 1.6 × 10#*1 𝑘𝑔 𝐴 × 1.6 × 10#$%
𝜌4567 = = , = & 𝑚& = ,
𝑣𝑜𝑙𝑢𝑚𝑒 𝜋𝑅 & , $ × 𝜋 × 𝑅( × 𝐴
& × 𝜋 × K𝑅( × 𝐴 3& L &
&
Hence,
, 𝜌4567 ≈ 10$+ 𝑘𝑔⁄𝑚&
Thus we can conclude that
• The density of nuclear matter is very high
• The nuclear density is independent of A, i.e all nuclei have almost identical density.
Therefore, this suggests that nuclei are very similar to liquid drops, which have the same
density irrespective of the size of the drop. This has resulted in the development of a
macroscopic model known as the “Liquid Drop Model” of the nucleus (as described /discussed
later)
Alternatively we know that
$3 &
𝑉𝑜𝑙𝑢𝑚𝑒 ∝ 𝑅& ∝ S𝐴 &T ∝𝐴
8(759:
Hence, "
= 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Therefore, number of nucleons per unit volume is constant for all nuclei.
Atomic Mass Unit (AMU, u)
The mass of nucleons is usually expressed as Atomic Mass Unit (AMU, 𝑢). It is a relative
scale, where the mass of a neutral 12C atom is taken precisely as 12 units. i.e
𝑚( $*'𝐶 ) = 12 𝑢
9= "&%> ?
1 amu is hence considered as 1⁄12;< the mass of 12C atom, 1 𝑎𝑚𝑢 =
$*
We know that 1 mole of a substance contains Avagrados number of atoms (6.023 × 10*& ).
i.e one mole of a substance contains the same number of atoms / molecules.
∴ 1 mole of 12C contains 12 gm of the isotope, on the other hand 1 mole of natural O2 contains
2 × 15.99938 = 31.99876 gm.
∴ 12 gm of 12C has 6.023 × 10*& atoms.
$* × $)!'
∴ 1 atom of 12C weighs '.)*& × $)&' 𝑘𝑔
12 × 10#& 1
∴ 1 𝑎𝑚𝑢 = × = 1.66053 × 10#*1 𝑘𝑔
6.023 × 10*& 12
∴ from energy-mass equivalence, we have the energy associated with 1 𝑢 as
𝐸$5 = 1.66053 × 10#*1 × (3 × 10+ )* Joule
