NUCLEI
SIR LIANZELA
COMPOSITION OF THE NUCLEUS
The nucleus of an atom contains protons and neutrons which are
collectively known as nucleons.
The number of protons in a nucleus is called its atomic number.
The total number of protons and neutrons in a nucleus is called its
mass number.
𝑍 = Atomic number
𝐴 = Mass number
𝑁 = (𝐴 − 𝑍) is number of neutrons.
SYMBOL OF THE ELEMENT
𝒁𝑿
𝑨 or 𝑨𝒁𝑿
e.g.: 6𝐶 12 , 8𝑂16 , 17𝐶𝑙 35.47 , 197
79𝐴𝑢 , …
ATOMIC MASS UNIT
One atomic mass unit is defined as 1/12𝑡 of the mass of carbon
12𝐶 atom.
Mass of a carbon atom is 1.992647 × 10;26 𝑘𝑔
1.992647×10−26 𝑘𝑔
∴ 1u =
12
𝟏𝐮 = 𝟏. 𝟔𝟔𝟎𝟓𝟑𝟗 × 𝟏𝟎;𝟐𝟕 𝒌𝒈
Mass of neutron, 𝑚𝑛 = 1.6749 × 10;27 𝑘𝑔 = 1.00866 u
Mass of proton, 𝑚𝑝 = 1.67262 × 10;27 𝑘𝑔 = 1.00727 u
Mass of electron, 𝑚𝑒 = 9.1094 × 10;31 𝑘𝑔 = 0.00055 u
1u = 931.5 MeV/c 2
ISOTOPES
Atomic species of the same element differing in mass are called isotopes
e.g., 1𝐻1 , 1𝐻2 , 1𝐻3
ISOBARS
All nuclides with same mass number are called isobars.
e.g., 1𝐻3 and 2𝐻𝑒 3
ISOTONES
Nuclides with same neutron number but different atomic number are
called isotones.
e.g., 197
79𝐴u and 80𝐻𝑔
198
EINSTEIN’S MASS-ENERGY EQUIVALENCE
𝐸 = 𝑚𝑐 2
𝑐 = velocity of light in vacuum ≈ 3.0 × 108 𝑚𝑠 ;1
SIZE OF THE NUCLEUS
Volume of the nucleus is proportional to its mass number 𝐴
𝑉∝𝐴
4
𝜋𝑅 3 ∝ 𝐴
3
1
𝑅∝𝐴 3
1
𝑅 = 𝑅0 𝐴 3
Where 𝑅0 = 1.2 × 10;15 𝑚 = 1.2 fm
NUCLEAR DENSITY
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑛𝑢𝑐𝑙𝑒𝑢𝑠
𝜌=
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑛𝑢𝑐𝑙𝑒𝑢𝑠
Density of nucleus is constant irrespective of mass number or size.
𝜌 = 2.3 × 1017 𝑘𝑔 𝑚;3
MASS DEFECT
The difference in mass of the nucleus and its constituents is call the
mass defect.
∆𝑚 = 𝑍𝑚𝑝 + 𝐴 − 𝑍 𝑚𝑛 − 𝑀
BINDING ENERGY
Binding energy is the minimum amount of energy required to break
the nucleus into its constituent particles.
𝐵𝐸 = ∆𝑚𝑐 2
𝐵𝐸 = ∆𝑚 × 931.5 𝑀𝑒𝑉
$ 1𝑒𝑉 = 1.6 × 10;19 𝐽
$ 1 𝑀𝑒𝑉 = 1.6 × 10;13 𝐽
BINDING ENERGY PER NUCLEON
𝐵𝐸
𝐵𝐸 =
𝐴
Larger the binding
energy per nucleon, the
greater the work that
must be done to remove
the nucleon from the
nucleus, the more stable
is the nucleus.
The maximum 𝐵𝐸 occurs around 𝐴 = 50. 𝐹𝑒 56 is located close to the
peak with 𝐵𝐸 value of approximately 8.75 𝑀𝑒𝑉. 𝐹𝑒 56 is one of the
most stable nuclides that exist.
𝐵𝐸 is lower for both light nuclei (𝐴 < 30) and heavy nuclei
(𝐴 > 170)
The constancy of 𝐵𝐸 in the range 30 < 𝐴 < 170 is a consequence of
the fact that the nuclear force is a short-ranged.
STABILITY OF NUCLEUS ON NUMBERS OF NUCLEONS
Even number of protons and even number of neutrons is most likely to be
stable
Odd numbers of protons and odd number of neutrons is most likely to be
unstable
NUCLEAR FORCE
Nuclear forces are strongest forces in
nature. Its magnitude is about 102 times
electrostatic force and 1038 times the
gravitational force.
The potential energy between two
nucleons is a minimum at a distance 𝑟0
of about 0.8 fm. This means that the
force is attractive for distances larger
than 0.8 fm and repulsive if they are
separated by distances less than
0.8 fm.
$ Nuclear force between
There is no mathematical form of
𝑛-𝑝 = 𝑛-𝑛 = 𝑝-𝑝
nuclear force. {Range ~ 4.2 fm}
RADIOACTIVITY
Radioactivity is the spontaneous disintegration of nuclei of some nuclides
(called radionuclides) with the emission of 𝛼-particles or 𝛽-particles and
some accompanied by 𝛾-ray emission.
𝒅𝑵
Radioactive decay law : = −𝝀𝑵 𝜆 = decay constant
𝒅𝒕
𝑁 = 𝑁𝑜 𝑒 ;𝜆𝑡
𝛼-decay : Helium nucleus 24𝐻𝑒 is emitted.
𝛽-decay : Electrons or positrons are emitted.
𝛾-decay : High energy photons are emitted.
Half-life Mean-life
0.693 1
𝑡1 2 = 𝑡𝑎 =
𝜆 𝜆
Fraction of nuclei left undecayed after 𝒏 half live is
𝑡
𝑁 1 𝑛 1 𝑡1 2
= = #𝑡 = 𝑛𝑡1 2
𝑁0 2 2
ACTIVITY OF A RADIOACTIVE SAMPLE
The number of disintegrations per seconds.
𝑑𝑁
𝑅=−
𝑑𝑡
Activity law, 𝑹 = 𝑹𝟎 𝒆;𝝀𝒕
where 𝑅0 = 𝜆𝑁0 is decay rate at 𝑡 = 0 and 𝑅 = 𝜆𝑁
Activity SI unit is becquerel ( Bq) : 1 𝐵𝑞 = 1 decay/sec
Traditional unit of activity is curie
1 curie = 1 Ci = 3.70 × 1010 decay/sec = 37 𝐺𝐵𝑞
The other unit of radioactivity is rutherford
1 rutherford = 106 disintegrations/sec
Kinetic energy of daughter nuclei and 𝜶-particle
Parent nuclei 𝑋 having mass number 𝐴 breaks down into daughter nuclei
𝑌 and 𝛼-particle.
Applying conservation of momentum.
𝑃𝑌 = 𝑃𝛼 ⇒ 2𝐾𝑌 𝑚𝑌 = 2𝐾𝛼 𝑚𝛼
𝑚𝑌 𝐾𝑌
𝐾𝛼 = (i)
𝑚𝛼
Using energy conservation, 𝐾𝑌 + 𝐾𝛼 = 𝑄 (ii)
From (i) and (ii), we get
𝑚𝑌 𝐴;4
𝐾𝛼 = 𝑄 ⇒ K𝛼 = 𝑄 and
𝑚𝛼 :𝑚𝑌 𝐴
𝑚𝛼 4
𝐾𝑌 = 𝑄 ⇒ 𝐾𝑌 = 𝑄
𝑚𝛼 :𝑚𝑌 𝐴
NUCLEAR REACTION (Q-Value)
In nuclear reaction, mass number, electric charge, energy, linear
momentum, angular momentum, spin angular momentum are conserved.
A nuclear reaction can be represented by
𝐴+𝐵 =𝑋+𝑌+𝑄
𝑄 is the energy released in the process.
𝑄 = 𝑚𝐴 + 𝑚𝐵 − 𝑚𝑋 − 𝑚𝑌 𝑐 2
Also, 𝑄 = difference in binding energies
𝑄 = 𝐵𝐸𝑓 − 𝐵𝐸𝑖 = Δ𝑚𝑥 + Δ𝑚𝑦 − Δ𝑚𝐴 − Δ𝑚𝐵 𝑐 2
If 𝑄 is positive, the reaction is exothermic (exoergic) and
If 𝑄 is negative the reaction is endothermic (endoergic).
NUCLEAR FISSION
The phenomenon of splitting a heavy nucleus into two or more lighter
nuclei is called nuclear fission.
Examples :
1 144 89
i. 0𝑛 + 235
92𝑈 →
236
92𝑈 → 56𝐵𝑎 + 36𝐾𝑟 + 3 10𝑛
1 133
ii. 0𝑛 + 235
92𝑈 →
236
92𝑈 → 51𝑆𝑏
99
+ 41 𝑁𝑏 + 4 10𝑛
1 235 236 140 94 1
iii. 0 𝑛 + 92𝑈 → 92𝑈 → 54𝑋𝑒 + 38𝐾𝑟 + 2 0𝑛
The energy released ( the 𝑄 value) in fission reaction of nuclei like
uranium is of the order of 200 𝑀𝑒𝑉 per fissioning nucleus.
The source of energy in nuclear reactors, which produce electricity, is
nuclear fission. The enormous energy released in an atom bomb comes
from uncontrolled nuclear fission.
NUCLEAR FUSION - energy generation in stars
The phenomenon of fusion of two or more lighter nuclei into a heavier
nucleus is called nuclear fusion.
The fusion reaction in the sun is a multi-step process in which hydrogen in
burned into helium. Thus, the fuel in the sun is the hydrogen in its core.
The 𝑝𝑟𝑜𝑡𝑜𝑛-𝑝𝑟𝑜𝑡𝑜𝑛 (𝑝, 𝑝) cycle in star is
1 1 2 :
1𝐻 + 1𝐻 → 1𝐻 + 𝑒 + 𝜈 + 0.42 𝑀𝑒𝑉 (i)
𝑒 : + 𝑒 ; → 𝛾 + 𝛾 + 1.02 𝑀𝑒𝑉 (ii)
2 1 3
1𝐻 + 1𝐻 → 2𝐻𝑒 + 𝛾 + 5.49 𝑀𝑒𝑉 (iii)
3
2𝐻𝑒 + 3
2 𝐻𝑒 → 4
2 𝐻𝑒 + 1
1 𝐻 + 1
1𝐻 + 12.86 𝑀𝑒𝑉 (iv)
If we consider the combination 2 i + 2 ii + 2 iii + iv , the net
effect is
4 11𝐻 + 2𝑒 ; → 42𝐻𝑒 + 2𝜈 + 6𝛾 + 26.7 𝑀𝑒𝑉
Thus, four hydrogen atoms combine to form helium atom with a release
of 26.7 𝑀𝑒𝑉 of energy.
The age of the sun is about 5 × 109 years and it is estimated that there
is enough hydrogen to keep it going for another 5 billion years. After
that, the hydrogen burning will stop and the sun will begin to cool and
will start to collapse under its own gravity, which will raise the core
temperature. The outer envelope of the sun will expand, turning it into
the so called Red giant.
ELECTRON CAPTURE
It is a rare process in which nucleus captures one of the atomic electrons,
most likely from the 𝐾 shell. A proton in the nucleus combines with the
electron and converts itself into a neutron.
1 0 1
1𝑝 + ;1𝑒 = 0𝑛 + 𝜈 + 𝑄
Neutrinos (𝜈) are the most abundant particles that have mass in the
universe. They are also known as Ghost Particles.
Neutron production factor (𝑲)
1 144 89
0𝑛 + 235
92𝑈 → 236
92𝑈 → 56𝐵𝑎 + 36𝐾𝑟 + 3 1
0𝑛 + 𝑄
The nuclear chain reaction is controlled by
rate of production of neutrons
𝐾=
rate of loss of neutrons
CONTROLLED NUCLEAR FISSION
To maintained a sustained controlled nuclear reaction, for every 2
or 3 neutrons released, only one must be allowed to strike another
uranium nucleus. If this ratio is less than 1 then the reaction will die
out; if its more than 1 it will grow uncontrolled ( an atomic
explosion)
CRITICAL MASS
The minimum amount of fissile substance needed to maintained a
nuclear chain reaction (self-sustaining).
A spherical critical mass of pure or weapon’s grade Uranium-235
is 52 kilograms.
NUCLEAR REACTOR
𝛼 𝑒+ 𝛽− 𝑒−
1. 290
82𝑋 𝑌 𝑍 𝑃 Q
In the nuclear emission stated above, the mass number and
atomic number of the product 𝑄 respectively are
A. 288, 82 B. 286, 81
C. 280,81 D. 286, 80
2. The following fusion reaction takes place :
2 2 3
1𝐻 + 1𝐻 2𝐻𝑒 + 10𝑛 + 3.27 𝑀𝑒𝑉
If 2 𝑘𝑔 of deuterium is subjected to above reaction, the energy
released is used to light a 100 𝑊 lamp, how long will the lamp glow?
A) 2 × 106 years B) 3 × 105 years
C) 5 × 104 years D) 7 × 103 years
3. Two protons attract each other when
A) The distance between them is 10;2 𝑚
B) The distance between them is 10;9 𝑚
C) The distance between them is 10;15 𝑚
D) This will never happen
4. The nucleus 𝑛𝑋 𝑚 emits one 𝛼 and one 𝛽 particles. The resulting
nucleus is
A) 𝑛𝑋 𝑚;4 B) 𝑛;2𝑋 𝑚;4
C) 𝑛;3𝑋 𝑚;4 D) 𝑛;1𝑋 𝑚;4
5. If the binding energy per nucleon of deuterium is 1.115 𝑀𝑒𝑉,
its mass defect in atomic mass unit is
A) 0.0048 B) 0.0024
C) 0.0012 D) 0.0006
6. The half-life of 𝑃𝑜218 is 3 minutes. What fraction of a 10 𝑔𝑟𝑎𝑚
sample of 𝑃𝑜218 will remain after 15 minutes?
1 1
A) B)
32 64
1 1
C) D)
25 15
7. The radius of 29𝐶𝑢64 nucleus will be
A. 1.2 × 10;15 𝑚
B. 2.4 × 10;15 𝑚
C. 3.6 × 10;15 𝑚
D. 4.8 × 10;15 𝑚
8. Of the three basic forces gravitational, electrostatic and nuclear,
which are able to provide an attractive force between two neutrons
A) electrostatic and gravitational only
B) electrostatic and nuclear only
C) nuclear and gravitational only
D) nuclear only.
9. The correct relation between the packing fraction 𝑓 and mass
number 𝐴 is
𝑀;𝐴 𝑀:𝐴
A) 𝑓 = B) 𝑓 =
𝐴 𝐴
𝐴 𝐴
C) 𝑓 = D) 𝑓 =
𝑀;𝐴 𝑀:𝐴
10. If 𝐹𝑝𝑝 , 𝐹𝑝𝑛 and 𝐹𝑛𝑛 are the magnitude of nuclear forces
between proton-proton, proton-neutron and neutron-neutron
respectively then
A) 𝐹𝑝𝑝 = 𝐹𝑝𝑛 = 𝐹𝑛𝑛
B) 𝐹𝑝𝑝 < 𝐹𝑝𝑛 < 𝐹𝑛𝑛
C) 𝐹𝑝𝑝 > 𝐹𝑝𝑛 > 𝐹𝑛𝑛
D) 𝐹𝑝𝑝 < 𝐹𝑝𝑛 < 𝐹𝑛𝑛
11. The mass of proton is 1.0073 u and that of neutron is
1.0087 u. What will be the binding energy of 24𝐻𝑒?
A) 0.0305 𝐽 B) 0.0305 𝑒𝑟𝑔
C) 28.4 𝑀𝑒𝑉 D) 0.061 u
12. The binding energy per nucleon of deuteron 1.1 𝑀𝑒𝑉 and that
of helium is 28 𝑀𝑒𝑉. If two deuterons are fused to form one 24𝐻𝑒
then the energy released is
A) 25.8 𝑀𝑒𝑉 B) 23.6 𝑀𝑒𝑉
C) 19.2 𝑀𝑒𝑉 D) 30.2 𝑀𝑒𝑉
13. The radius of Germanium (𝐺𝑒) nuclide is measured to be twice
the radius of 49𝐵𝑒. The number of nucleons in 𝐺𝑒 are
A) 73 B) 74
C) 75 D) 72
14. The ratio of the radii of the nuclei 13𝐴l27 and 54𝑇𝑒
125
is
A) 13: 52 B) 27: 125
C) 3 3: 5 5 D) 3: 5
15. Assertion : The mass of a nucleus is always less than the sum of
the masses of nucleons present in it.
Reason : The whole mass of the atom is concentrated in the
nucleus.
A) Both assertion and reason are true and reason
is the correct explanation of assertion.
B) Both assertion and reason are true but reason is
not the correct explanation of assertion.
C). Assertion is true but reason is false
D) Both assertion and reason is false.
THANK YOU
