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ELEMENTARY PARTICLES
Classification :- The elementary particles are commonly classified in (i) Photons (ii)
Leptons (iii) Hadrons; Hadrons are again classified as (a) Meson (b)Baryons.[ baryons
means heavy, mesons means intermediate upto means small)

The following table shows basic properties of some common elementary particles.

Hypercharge
Multiplicity
Baryon no.

Strangeness
Lepton no.

3rd comp. 𝐼3

charge (𝑄)
̅̅̅̅
Charge
Symbol

Isospin (I)
Spin
Name

(M)
(B)

(L)

Average

(S)
Photons Photons γ 0 1 0 0 - - - - - -

L 𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛 e− −1 1
0 1 -
2
E
Muon μ− −1 1
0 1 -
2
P
Taun τ− −1 1
0 1 -
T 2

1
O Electron- γe 0 1 -
2
neutrino
N
1
Muon- γμ 0 0 1 -
2
neutrino
1
Taun- γτ 0 0 1 -
2
neutrino

H M 𝑃𝑖𝑜𝑛𝑠 + π+ +1 0 0 0 1

A E 𝑃𝑖𝑜𝑛𝑠 0 π0 0 0 0 0 3 1 0 0 0 0

D S 𝑃𝑖𝑜𝑛𝑠 − π− −1 0 0 0 −1
R O 𝐾𝑎𝑜𝑛+ K+ +1 0 0 0 1 1
2 2

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O N 𝐾𝑎𝑜𝑛0 K− 0 0 0 0 2 1 1 1 1
−
2 2
N S
𝐸𝑡𝑎0 n0 0 0 0 0 1 0 0 0 0 0
S
B Proton 𝑝 1 1
1 0 1 1
2
2 2
A 2 1 1 0
Neutron 𝑛 0 1
1 0 1 2
R 2 −
2
Y Lambda Λ0 0 1
1 0 1 0 0 −1
2
O
Sigma Σ+ +1 1
1 0 1
2
N
1 3 1
Sigma Σ0 0 1 0 0
S 2
0 0 −1
− 1
Sigma Σ −1 1 0 −1
2

Xi Ξ0 0 1
1 0 1 1 1
2 −
2 2 2
2 −1 −2
Xi Ξ −1
−1 1
1 0 1
2 −
2
Omega Ω− −1 1
1 0 1 0 0 −1 −1 -2
2

Quantum Numbers:-
1. Baryon numbers:- The behavior of nucleon and hadrons, i.e. of all baryons are
expressed by baryon quantum number (B).
𝐵 = 1 𝑓𝑜𝑟 𝐵𝑎𝑟𝑦𝑜𝑛𝑠
= −1 𝑓𝑜𝑟 𝑎𝑛𝑡𝑖 𝑏𝑎𝑟𝑦𝑜𝑛𝑠
= 0 𝑓𝑜𝑟 𝑛𝑜𝑛 𝑏𝑎𝑟𝑦𝑜𝑛𝑠
2. Lepton number:- The behavior of all leptons is assigned by Lepton quantum number
(L).
L=1 for leptons
=-1 for anti leptons

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=0 for non-leptons
3. Multiplot number M:- Some elementary particles with nearly some mass but
different by charge are assigned to multiplot number M. e.g. nucleons 𝑃(+1) , 𝑛(0)
have multiplicity →2; pions (𝜋 + , 𝜋 0 , 𝜋 − ) have multiplicity →3; for single eta (𝑛0 )
multiplicity →1.
4. Iso-spin quantum number:- In case of atomic energy state, multiplicity due to spin
state “S” is defined as 2S+1; we define iso-spin quantum number (I) which is
𝑀−1
related with multiplicity M as 𝑀 = 2𝐼 + 1 𝑖. 𝑒. 𝐼 = .
2
“I” is treated as vector of magnitude √I(I + 1) like angular momentum.
2−1 1
For e.g. For nucleons m=2; 𝐼 = =
2 2
1
∴𝐼 = 𝑓𝑜𝑟 𝑝
2
1
= − 𝑓𝑜𝑟 𝑛
2
3−1
For pions M=3; 𝐼 = =1
2
∴ I=+1 for 𝜋 +
= 0 𝑓𝑜𝑟 𝜋 0
= −1 𝑓𝑜𝑟 𝜋 −1
̅ of a particle in a multiple group is defined as
5. Hyper charge :- The average charge Q
∑𝑄
𝑄̅ = 𝑖 M multiple numbers ; ∑ 𝑄𝑖 is the sum of charges of each number of the
𝑀
group.
The hyper charge (Y) quantum number is defined as 𝑌 = 2𝑄̅
6. Strangeness :- This quantum number was introduced to explain strange behavior of
K-mesons and hyperons which were found to be produced by strong interaction but
decay only in weak interactions.
The strangeness quantum number is defined as, 𝑆 = 𝑌 − 𝐵
e.g. For proton. 𝑌 = 1; 𝐵 = 1 𝑆 = 1
For Σ 0 𝑌 = 0; 𝐵 = 1 𝑆 = −1
For K + Y = 1, B = 0 S = 1 etc.

• Fundamental interaction:- In order to understand behavior of the elementary

particles i.e. their formation and decay, one need to understand different types of
interactions between particles, which fall into the following four categories,
1. Gravitational interaction,
2. Electromagnetic interactions

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3. Strong interaction
4. Weak interaction.

1. Gravitational interaction:- It is the weakest of four types of interaction and act

between all bodies having mass and is described by the long range inverse square
type. This interaction is believed to be mediated through the quantum of interaction
is called gravitation, which is yet to be discovered.
The gravitation interaction however becomes negligible when the interaction of
elementary particles, nuclei and atoms are considered.

2. Electromagnetic interaction:- All the charged particles are acted upon by e.m.
interaction. This interaction is attractive as well as repulsive. This inverse square
interaction is mediated through photon exchanged. It is stronger than gravitational
force. The formation of electron-positron pair from a γ- photon is an example of an
e.m. interaction.

3. Weak interaction:- This fundamental interaction involves lepton and hadrons. The
β-decay of radioactive nuclei is atypical weak interaction. This interaction is
mediated through bosons. The intrinsic strength of weak interaction is 10−10 times
the e.m. interaction. In weak interaction the strengthness q.n. and charge
conjugation are not conserved. The parity may be violated in some cases.

4. Strong interaction:-This is the strongest force in nature and occurs between the
nucleons. This short range attractive force is charge independent and is mediated
through π-meson. It explains the interaction between the hadrons.
Since proton, neutron, π-mesons are thought to be built up by quarks- the strong
forces believed to be mediated through gluons which is exchanged by quarks.

• Conservative laws:-
• Exact law:-
1. Energy conservation:- The total energy including the rest mass energy is
conserved in any interaction.
2. Conservation of linear momentum:- The total linear momentum is conserved for
all interaction.

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3. Conservation of angular momentum:- This is also conserved for all types of

interactions. The spin and orbital angular momentum may not be separately
conserved.
4. Conservation of charge:- The net charge is conserved for all the interactions.
e.g. 𝑛 → 𝑝+ + 𝑒 − + 𝛾𝑒
𝜋 − → 𝜇− + ̅̅̅𝛾𝜇
𝜋 + → 𝑒 + + 𝛾̅𝑒
𝜋 − → 𝜋 0 + 𝑒 − + 𝛾̅𝑒
In all the cases initial total charge final total charge.
5. Conservation of Baryon number:- In any interaction the initial baryon number is
the as the final baryon number is the total number of baryon (or anti baryon) is
conserved for all interaction.
e.g. (i) Λ + 𝑛 → 𝑝 + 𝑛 + 𝜋 0
𝐵 => 1 1 1 1 Δ𝐵 = 0
(ii) 𝑝 + 𝑛 → 𝜋 0 + ̅𝜋̅̅0̅
B=>1 1 0 0 Δ𝐵 ≠ 0
In reaction (i) baryon number is conserved hence it is allowed but in (ii) baryon
number is not conserved hence it is not allowed.
6. Conservation of lepton number:- Total lepton number before and after any
reaction must be the same.
e.g. (i) 𝜋 + → 𝜇+ + 𝛾𝜇
𝐿 => 0 − 1 + 1 [ 𝑎𝑙𝑙𝑜𝑤𝑒𝑑] ∆𝐿 = 0
(ii)𝜋 + → 𝑒 + + 𝛾
0 − 1 0 [ 𝑛𝑜𝑡 𝑎𝑙𝑙𝑜𝑤𝑒𝑑] ∆𝐿 ≠ 0

Approximation laws:-
7. Conservation of iso-spin:- Iso-spin is conserved for strong interactions but is
violated in electromagnetic and weak interaction.
[The Z-component of isospin (𝐼3 ) is conserved in strong and e.m. interaction, not
in weak intearction]
8. Conservation of hyper- charge:- For any strong and electromagnetic interaction,
the hypercharge is conserved in weak interaction.
e.g. 𝑝 + 𝑝 → Λ0 + 𝐾 0 + 𝑝 + 𝜋 +
𝑌: 1 + 1 0 + 1 + 1 + 0 Δ𝑌 = 0

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9. Strangeness quantum number conservation:- total strangeness number S is

conserved in strong and e.m. reactions. In weak interaction S cannot change ±1.
i.e. ∆S=0, ±1 ; it is known as selection rule.
e.g. (i) 𝜋 − + 𝑝 → 𝛴 − + 𝐾 +
𝑆∶ 0 + 0 − 1 + 1; Δ𝑆 = 0
(ii) 𝜋 + 𝑝 → Λ0 + 𝐾 0
𝑆: 0 0 − 1 + 1; Δ𝑆 = 0
(iii) 𝜋 − + 𝑝 → 𝛴 + + 𝐾 −1
0 + 0 − 1 − 1 ; Δ𝑆 = 2
Here (i) & (ii) are allowed but (iii) is forbidden.
• There are few more quantum numbers and conservation laws which are useful in
deciding different types of interactions.
10. Parity:- It is purely quantum mechanical concept related with invariance of
physical laws under inversion of space co-ordinate (𝑟⃗ → −𝑟
⃗⃗⃗⃗⃗⃗); in other word, it
deals with right handed or left-handedness in natural phenomena. Every particle
with a non-zero mass has intric parity (Π) which may be either+1 (even) or -
1(odd) and total parity is definned by their product.
Parity is conserved in strong and e.m. interaction but not conserved in weak
interaction.
11. Charge conjugation:- Charge conjugation means reversal of the signs of all
types of charge electronic baryonic and leptonic of the particles conservation of
charge conjugation(or charge parity) indicates that interactions or the processes
are unchanged when every particle is replaced by their antiparticle.
Strong and e.m. interactions are charge conjugate invariant. But weak
interactions like β- decay does not obey charge conjugation.

12. Time reversal (T):- The operator T i.e. time reversal means replacing t by –t in
the all equation of motion (reflection of t-axis at the origin of time co-ordinate in
space rime continuum.
If time reversal invariance holds (i.e. T is conserved,) then time reversed
equation of motion is also equation of motion. T is conserved in all types of and
electromagnetic interactions.

• CPT theorem:- It states that all interactions in nature are invariant under joint
operations of charge conjugation(C), Parity (P), and reversal of time (T).

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i.e. if any interaction in not invariant under any of C,P,T operations, its effect gets
compensated by the joint effect of the other two.
Although its validity is universal, exception has been found for K.decay into 𝜋 + +
𝜋 −.
• Quark Model :- According to this model each hadrons are made up of basic units
called quarks which are point particles with no internal structure and unlike
anything else in nature are supposed to have fractional charge.
The original three quarks were leveled as 𝑢(𝑢𝑝), 𝑑(𝑑𝑜𝑤𝑛 ), 𝑆(𝑠𝑡𝑟𝑎𝑛𝑔𝑒) and
correspond anti quarks 𝑢̅, 𝑑̅ , 𝑆̅, respectiely. Basic properties of these quarks and anti
quarks are listed below.

QUARK q B S Spin 𝐼 𝐼3 𝑄̅ 𝑌

U 2 1 0 1 1 1
+
3 3 2 2 2
1 1
D 1 1 0 1 1 1 6 3
− −
3 3 2 2 2
S 1 1 −1 1 0 0 1 2
− − −
3 3 2 3 3
u̅ 2 1 0 1 1 1
− − −
3 3 2 2 2
1 1
− −
d̅ 1 1 0 1 1 1 6 3
−
3 3 2 2 2
S̅ 1 1 1 1 0 0 1 2
− −
3 3 2 3 3
1
u the quarks are assigned 𝑠𝑝𝑖𝑛 ; i.e. these are fermions and obey Fermi-Dirac
2
statistics.

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• Quark content of some baryon and mesons are listed below.

Baryons Mesons

Name QUARK Name QUARK CONTENT

CONTENT

𝑝 𝑢𝑢𝑑 𝜋± 𝑢𝑑̅ , 𝑑𝑢̅

𝑛 𝑢𝑑𝑑 𝜋0 𝑢𝑢̅

Λ 𝑢𝑑𝑠

𝐾± 𝑢𝑆̅ 𝑆𝑢̅

Σ+ 𝑢𝑢𝑠

Σ0 𝑢𝑑𝑠 ̅̅̅̅0
𝐾 0, 𝐾 𝑑𝑆̅ 𝑆𝑑̅

Σ− 𝑑𝑑𝑠

Ξ0 𝑢𝑠𝑠

Ξ− 𝑑𝑠𝑠

Ω− 𝑠𝑠𝑠

Eight folds way (octet Symmetry ):- Based on abstract group theory, several scheme were
developed to classify strongly interacting particles e.g. baryons and mesons. This
classification is based on the values 𝐼3 and Y of the particles and is known as octet
symmetry or eight fold way.

Here is the third component of iso-spin (𝐼3 ) is plotted along x-axis and the hypercharge is
plotted along Y- axis. In this plot eight baryon are fitted in a hexagonal array called
baryon octet. For meson is called Meson octet.

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Decuplet Symmetry:- Weight diagram in the 𝑌 − 𝐼3 plane can be constructed for the

resonance(Baryons) particles. The existence of a baryonic decuplet was predicted by SU3

symmetry. Its weight diagram is an equilateral triangle shown by the diagram. It consists
of quadruplet of Δ, triplet of Σ, doublet of Ξ and the singlet Ω.

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Discovery of positron : The positron was the first evidence of antimatter and was
discovered when Anderson allowed cosmic rays to pass through a cloud chamber and a
lead plate. A magnet surrounded this apparatus, causing particles to bend in different
directions based on their electric charge. The ion trail left by each positron appeared on
the photographic plate with a curvature matching the mass-to-charge ratio of an
electron, but in a direction that showed its charge was positive.

Resonance particles:-
Apart from the stable and semi-stable particles, many other particles have been
discovered, which have mean lives comparable to the characteristic nuclear time, which
the time is taken by a pion to travel past a proton (~4 × 10−24 𝑠) . These are known as
particle resonance. Their means lives are too short to be measured directly.

The term resonance comes from the fact that these particles are recognized by
resonance peaks in the graph showing the variation of cross section [Fig] of different
types of events during high energy collisions at certain different energies.

The mass of a resonance particle is obtained from

the position of the peak and the mean life from the
width of the peak through the uncertainly
relation 𝜏 = ℏ/∆𝐸.

Particle resonances have been discovered both

among the hyperons and mesons. They are produced
in high energy collisions between hadrons by strong
interactions and are observed during scattering or
reactions initiated by very high energy elementary
particles obtained from particle accelerators.

Color hypothesis

Requirement: One of the main problems in formulating the quark structure of the
hadrons is the apparent failure of Pauli’s exclusion principle.

Since the quark are spin ½ particles they obey Fermi-Dirac statistics. The proposed
quark structure of the baryon 𝑝(𝑢 𝑢 𝑑) and neutron 𝑛(𝑢 𝑑 𝑑) or baryon

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∆++ (𝑢 𝑢 𝑢)requires more than two spin 1/2 particles together in a single state. Obviously
such a combination violates Pauli’s exclusion principle.

Qurk theory: To get over this difficulty, a new property of the quark (or quantum
number) known as the colour, was proposed by Gell-Mann and Zweing in1963. It is
assumed that the quarks can have three primary colours –Red(R); Green (G); and Blue (B)
respectively. An antiquark can take one of three anticolors: called anti red (𝑅̅), anti green
(𝐺̅ ), and antiblue (𝐵̅) (represented as cyan, magenta and yellow, respectively). Those
particles or quark bound states exist in nature which are color-less

In this scheme the ∆ particle would be represented as

∆++ = 𝑢𝑅 𝑢𝐺 𝑢𝐵

𝑃𝑟𝑜𝑡𝑜𝑛, 𝑝 = 𝑢𝑅 𝑢𝐺 𝑢𝐵 and so on

i.e i)Baryons are colorless due to the 𝑅 − 𝐺 − 𝐵 combinations.

ii) Hence any meson must have the combination 𝑅 𝑅̅ , 𝐺𝐺̅ 𝑜𝑟 𝐵 𝐵̅.

iii) Gluons are mixtures of two colors, such as red and anti-green, which constitutes their
color charge. QCD considers eight gluons of the possible nine color–anti-color
combinations to be unique.

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NUCLEO SYNTHESIS: -
The Big bang theory is the prevailing cosmological model for early development of the
universe. According to this theory, the Big Bang occurred approximately 13.798 ± 0.037
billion years ago, which is thus considered as the age of the universe.

At this time the universe was in an extremely hot and dense state and began to expand
rapidly. After initial expansion the universe cooled sufficiently to allow energy to convert
into various subatomic particles including protons, neutrons, and electrons.

The 1st step in building up complex atom is the formation of deuterium nucleus, from the
combination of proton and a neutron as

𝑛+𝑝 →𝑑+𝛾

Once deuterons are formed, they readily react with protons and neutrons as

𝑑 + 𝑛 → 𝐻13 + 𝛾
𝑑 + 𝑝 → 𝐻𝑒23 + 𝛾

Finally 𝐻13 , 𝐻𝑒23 also react with protons and neutrons and create 𝛼 − particles

𝐻13 + 𝑝 → 𝐻𝑒24 + 𝛾
2 𝐻𝑒 3 + 𝑛 → 𝐻24 + 𝛾

Because 𝐻𝑒24 has the greater stability, we assume that nearly all deuterons are converted
to 𝐻𝑒 4 .

Though simple atomic nuclei formed within 1st few minutes after the big bang thousand
years passed before formation of neutral atom of Hydrogen and Helium when proton and
𝛼 −particles combine with electrons.

Thus majority of atoms that were produced by Big Bang are 𝐻, 𝐻𝑒 atoms. Giant cloud of
these primordial elements later coalesced through gravity to form stars and galaxies, and
heavier elements were formed within the stars.

• Formation of Heavy elements:-

During the period, the star remains in the main sequence, they convert Hydrogen into
Helium by fusion reaction and release of energy balances the inward gravitational force.

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After a star has used up its supply of hydrogen and becomes mostly Helium, it began to
contract, which increases the temperature. It results fusion of 𝐻𝑒 4 𝑖𝑛𝑡𝑜 𝐶 12 as,

3𝐻𝑒24 → 𝐶612 + 𝛾

Once 𝐶 12 is formed, we can have additional 𝐻𝑒 4 reactions as,

𝐶612 + 𝐻𝑒24 → 𝑂816 + 𝛾

𝑂816 + 𝐻𝑒24 → 𝑁𝑒1020
+𝛾
20
𝑁𝑒10 + 𝐻𝑒24 → 𝑀𝑔1224
+ 𝛾 𝑎𝑛𝑑 𝑠𝑜 𝑜𝑛

These reactions have increasingly high coulomb barriers and hence require increasing
temperatures. Eventually these reactions reach the peak of binding energy curve (𝐴 = 56)
for 𝐹𝑒 56 . Beyond this point, energy is no longer released in fusion reactions.

Now a nucleus in the interior of a star can capture neutrons until its neutron excess is
sufficient to convert it into a proton by beta decay.

For example

𝐹𝑒 56 + 𝑛 → 𝐹𝑒 57 + 𝛾
𝐹𝑒 57 + 𝑛 → 𝐹𝑒 58 + 𝛾
𝐹𝑒 58 + 𝑛 → 𝐹𝑒 59 + 𝛾

Though 𝐹𝑒 57 , 𝐹𝑒 58 are stable, 𝐹𝑒 59 is radioactive, and can decay as

59 59
𝐹𝑒26 → 𝐶𝑜27 + 𝛾 + 𝑒−

This 𝐶𝑜 59 can also capture neutron to become 𝐶𝑜 60 which is radioactive and may decay
60
to 𝑁𝑖28 . Continuing in this way we can think of production of all the heavier elements
through neutron capture beta

Energy produced in star:

Two sets of thermonuclear reactions have been proposed as source of energy in Sun and
other stars of the universe in their main sequence. One set is called p-p cycle and other is
known as CNO cycle.

𝑷 − 𝑷 𝒄𝒚𝒄𝒍𝒆: − There are three branches of p-p cycle.

𝑝 − 𝑝 𝑐𝑦𝑐𝑙𝑒 (𝐼): − It consists of the following reactions,

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𝐻11 + 𝐻11 → 𝐻12 + 𝛽 + + 𝛾𝑒 (× 2)

𝐻11 + 𝐻12 → 𝐻𝑒23 + 𝛾(× 2)
𝐻𝑒23 + 𝐻𝑒23 → 𝐻𝑒24 + 2𝐻11

For the 3rd reactions to occur the 1st two relations must occur twice. The effect of the
reactions is

4𝐻1 → 𝐻𝑒 4 + 2𝛽 + + 2𝛾𝑒 + 2𝛾 + 26.7 𝑀𝑒𝑣

Thus is the most probable p-p cycle (≈ 85%)

𝒑 − 𝒑 𝑪𝒚𝒄𝒍𝒆 (𝑰𝑰): − It consists of the following reactions,

𝐻11 + 𝐻11 → 𝐻12 + 𝛽 + + 𝛾𝑒

𝐻11 + 𝐻12 → 𝐻𝑒23 + 𝛾

𝐻𝑒23 + 𝐻𝑒24 → 𝐵𝑒47 + 𝛾

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𝐵𝑒47 + 𝛽 − → 𝐿𝑖37 + 𝛾𝑒 + 𝑟

𝐿𝑖37 + 𝐻11 → 2𝐻𝑒24

Its probability is ≈ 15%

𝒑 − 𝒑 𝒄𝒚𝒄𝒍𝒆(𝑰𝑰𝑰): − Here the reactions are,

𝐻11 + 𝐻11 → 𝐻12 + 𝛽 + + 𝛾𝑒

𝐻11 + 𝐻12 → 𝐻𝑒23 + 𝛾
𝐻𝑒23 + 𝐻𝑒24 → 𝐵𝑒47 + 𝛾

𝐵𝑒47 + 𝐻11 → 𝐵58 + 𝛾

𝐵58 → 𝐵𝑒48 + 𝛽 + + 𝛾
𝐵𝑒48 → 𝐻𝑒24 + 𝐻𝑒24

It probability is ≈ 0.1%

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𝑁𝑜𝑡𝑒: −

1. The end result of each reaction is four protons together from a helium nucleus with
release of 26.7 𝑀𝑒𝑣 energy.
2. 𝑝 − 𝑝 (𝐼𝐼) 𝑎𝑛𝑑 𝑝 − 𝑝(𝐼𝐼𝐼) reactions are dominate only about 107 𝐾
3. The protons gradually depleted and the Concentra of helium builds up.

CNO Cycle:-
For the mown sequence stars having higher temperature, Bethe proposed a set of
reaction, called Carbon-Nitrogen-oxygen cycle in account for energy production. The
𝐶, 𝑁, 𝑂 nucleus behaves as catalyst in these reaction in which 4 protons are converted into
helium nucleus and about 26 𝑀𝑒𝑣 energy is released.

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The Sequence of reactions is

𝐶612 + 𝐻11 → 𝑁713 + 𝛾

𝑁713 → 𝐶613 + 𝑒10 + 𝛾
6
𝐶13 + 𝐻11 → 𝑁714 + 𝛾
𝑁714 + 𝐻11 → 𝑂815 + 𝛾
𝑂815 → 𝑁715 + 𝑒10 + 𝛾
𝑁715 + 𝐻11 → 𝐶612 + 𝐻𝑒24

Adding up above reaction the order all reaction will be

4𝐻11 → 𝐻𝑒24 + 2𝑒10 + 2𝛾 + 3𝛾 + 26.72 𝑀𝑒𝑣

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Conclusion:-

1. It is thought that CNO cycle is the dominant mechanism for synthesis of He in stars
more massive than the Sun. For the stars having masses less than the Sun, p-p chain
is the dominant mode.
2. The CNO cycle produces only 1.5% of energy of the sun.

Formation of Stars:-
Once neutral atoms are formed, there are essentially no free charged particles left in
universe. This is the time of decoupling of matter and radiation field. After decoupling of
matter and radiation, the matter (consisting of hydrogen and Helium) was subjected to
only gravitational force. Recent precise observation have shown that distribution of
matter was slightly non uniform. Regions of higher density began to condense into matter
of ever increasing density. As each much portions contracted under its own gravity, its
temperature rose until it becomes that enough to initiate fusion reaction. This is how its
generation stars formed.

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How are the shape of the stars maintained:-

A star is a sphere of gas held together by its own gravity. The force of gravity is
continually trying to cause the star to collapse, but this is counteracted by the pressure of
hot gas and radiation in the stars interior. This is called Hydrostatic support. During most
of the life time of a star the interior heat and radiation is provided by nuclear radiations
near the Centre this phase of stars life is called the main sequence and stars maintain their
shape.

𝑮𝒐𝒐𝒅 𝒕𝒐 𝒌𝒏𝒐𝒘: − Before the main sequence, the star is contracting and is not yet hot
enough or dense enough in its interior for the nuclear reactions to begin. During this
phase, hydrostatic support is provided by the heat generated during contraction.

After the main sequence, most of the nuclear fuel in the core has been used up. The star
now requires a series of less efficient nuclear reactions for internal heat. (It results
subsequent higher neutral elements). Eventually when these reactions no longer
generate, sufficient heat to support the star against its own gravity, the star will collapse.

• Why the life time of a star is so long?

Studies of our own main sequence star e.g. the Sun reveals that energy comes from a
series of nuclear reaction mainly called p-p chain as

𝐻11 + 𝐻11 → 2𝐻12 + 𝑒 + + 𝛾𝑒

𝐻11 + 𝐻12 → 𝐻𝑒24 + 𝛾
𝐻𝑒23 + 𝐻𝑒23 → 𝐻𝑒24 + 2𝐻11 + 𝛾

The probability of the 1st reaction is very slow.

Since

(1) It is a weak interaction

(2) The (+) vely charge protons interacts in most of the cases by quantum
mechanical tunneling.

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Now the time scale for any nuclear reaction chain is set by its slowest step. Thus whole
process is very slow, thus energy is produced in the above reactions for a long time.

NECLEOSYNTHESIS
[The Big Bang]

↓ 1second from the big bang

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[Protons, neutrons emerges from the cooling quark soup]

↓ 250 second from BB

[Simple atomic nuclei are formed. 74% H, 25% He, 1% other]

↓ 300,000 years from BB

[Electrons combine with H, He and other nuclei to form neutral atoms]

↓ Billions of years
[Gravity causes the diffuse 𝐻2 /𝐻𝑒 gas to form clouds which collapse into stars]

↓Billions of years

[Stars ignite by burning 𝐻1 𝑎𝑛𝑑 𝐻𝑒 4 . The cosmos lights up]

↓ Millions of years (Nucleosynthesis)

[Heavy stars, late in their lives, burn to form isotopes up to 𝐹𝑒 56 before exploding as
supernova. Isotopes heavier than 𝐹𝑒 56 are produced during expression]

↓ Years of seconds (Nucleosynthesis)

[Hot radioactive fallout explodes into the interstellar medium where it rapidly cools]

↓ Millions of years
[The fallout’s activity decays until it consists of 266 isotopes]

↓ Millions of years
[The rich stardust (clinker) incorporates into emerging solar systems]

↓ Millions of years
[Where it forms planets…]

↓
[And biology begins…]

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2017

1. A hadron has a quark content ddu. Find the charge and strangeness of this hadron.
2. How is the CNO cycle in stars different from the pp chain?
3. Which of the following reaction can occur? State the conservation principles
violated by the others
(𝑖)𝑝 + 𝑝 → 𝑛 + 𝑝 + 𝜋 + , (𝑖𝑖)𝑝 + 𝑝 → 𝑛 + 𝜋 0 (𝑖𝑖𝑖)𝜋 + + 𝑝 → 𝜋 + + 𝑝 + 𝜋 − + 𝜋 0
4. What is color hypothesis? Which type of interaction is supported by this
hypothesis?
5. Find the missing particles in the following interactions:
(𝑖)𝜇− → 𝑒 − + 𝛾𝑒 + ⋯ (𝑖𝑖)𝛾𝑒 + 𝑛 → 𝑝+ … . (𝑖𝑖𝑖)𝑒 + + 𝑒 − → 𝜇− + ⋯
6. All resonance particles have very short lifetimes. Why does this suggest they must
be hadrons?
2016

1. A hadron has a quark content SSS. Find the baryon number, charge, spin and
strangeness of this hadron.
2. What are the differences between the p-p chain and the CNO cycle in reference to
primordial nucleosynthesis?
3. Explain with reason whether the following reactions are allowed or forbidden:
(𝑖)𝑝 → 𝜋 + + 𝜋 − + 𝑒 − (𝑖𝑖)𝜋 + + 𝑛 → 𝜋 0 + 𝑘 + (𝑖𝑖𝑖)𝑝 + 𝜋 − → 𝑛 + 𝜋 0
4. Using conservation laws, identify the missing particles:
(𝑖)𝜇− + 𝑝 → 𝑛 + ⋯ (𝑖𝑖)𝜋 − + 𝑛 → 𝑘 0 + ⋯
5. How do you write the 𝛽- decay of a neutron in terms of quark decay?
What is meant by eightfold way? Explain with reference to the octet symmetry

2015

1. Explain the type of interaction of the following process:

𝑝 + 𝑝 → 𝐻12 + 𝑒 + + 𝑣𝑒
2. Are the following reactions allowed or forbidden?
(𝑖)𝜋 − + 𝑝 → 𝜋 0 + 𝑛
(𝑖𝑖)𝜋 + + 𝑛 → 𝑝 + 𝑣𝑒

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1
3. What is hypercharge? Show the multiplate of spin − baryons on a plot of
2
hyperchange versus isospin projection.
4. Define lepton number and baryon number. Write down the equation for muon
decay. How is lepton number conserved in this process?

2014

1. A hadron has a quark content ddu. Find the baryon number, charge, spin and
strangeness of this hadron.
2. Consider the following reactions:
𝜋− + 𝑝 → 𝑛 + 𝜋0
𝜋 0 → 2𝛾
𝜋− + 𝑝 → 𝑛 + 𝛾
Show that the intrinsic parities of 𝜋 − 𝑎𝑛𝑑 𝜋 0 are the same and it is odd.
3. The decay ≡− → 𝐴0 + 𝜋 − is observed in nature, whereas the apparently similar
decay ≡− → 𝑛0 + 𝜋 − is never observed. Why?
4. Write down an equation for moun decay. How is lepton number conserved in this
interaction?
3+
5. A hadron is symbolized by ∆++ ( ). Is it a fermion or a boson? What re its spin,
2
parity and isospin?
6. How are the ions introduced into the Dees near the center of a cyclotron?
7. Show that in a decreases in radius with increase in its kinetic energy.
8. What are the design parameters for cyclotron that would accelerate 𝛼 particles to a
maximum energy of 20 MeV? The does are to have a diameter of 1m.
9. How is the CNO cycle in stars different from the pp chain?
2013

1. Explain whether the following reaction can occur or not

𝑒 + + 𝑒 − → 𝜇+ + 𝜋
2. A hadron has a quark content 𝑢𝑑⃗. Find the baryon number, charge, spin and
strangeness of this hadron. Name the hadron.
3. What is parity? Name a reaction in which parity is not conserved. Which class of
interaction does this reaction belong to?
4. What do you mean by “charge conjugation”?
5. Which does act as mediator in ‘electromagnetic interaction’?
2012

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1. Define hyper change. Plot the hyper change against isospin for the quark triplet and
the baryon decuplet, with the respective particles and their quark contents properly
indicated for the latter.
2. Why does a free neutron not decay into an electron and a positron? Explain.

2011
1. Check whether the following processes are allowed or forbidden. If they are
forbidden, mention why?
(𝑖)𝜋 − + 𝑝 → 𝜋 0 + ⋀0 (𝑖𝑖)𝐾 − + 𝑝 → 𝐾 0 + 𝑛

1. Define baryon number and lepton number.

2. Write down an equation for much decay. How is lepton number conserved in this
interaction?
3. Identify the unknown particle in each case, using the conservation
(𝑖)𝜇− + 𝑝 → 𝑛+?
(𝑖𝑖)𝜋 − + 𝑝 → 𝐾 0 +?
4. Explain why you do not see (i) a baryon with strangeness -2 and electric charge +1;
(ii) a meson with strangeness +1 and electric charge -1.

2010

1. Consider the decay 𝑛 → 𝑝 + 𝑒 − + 𝜈⃗. Show that both baryon and lepton numbers
are conserved in this process.
2. A hadron has a quark content us. Find the baryon number, charge, spin and
strangeness of this hadron. Can you identify this hadron?
3. Explain why a ⋀ hyperon does not decay into a 𝜋 + 𝑎𝑛𝑑 𝑎 𝜋 − meson?
4. Are the following reactions possible? Give reasons.
(𝑖)𝑝 → 𝑛 + 𝑒⃗ + 𝜈⃗𝑒
(𝑖𝑖)𝑝 + 𝑝 → 𝑛 + 𝑝 + 𝜋 ⨁

2009

1. What are quarks?

2. Outline the basic assumptions and properties of quarks.
3. Express neutron and antineutron in terms of quark model.

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A 𝜇− days at rest and emits an electron. Which other particles will be emitted in above
decay? Use the conservation laws to establish your answer.

2008

1. What are Baryons and Leptons?

2. What is the intrinsic parity of pion? What are its spin and isopin values?
3. What is strangeness? Define hypercharge.
2007

1. A hadron has a quark content 𝑢𝑑⃗. Find the baryon number, charge, spin and
strangeness of this hadron. Can you identify the hadron?
2. Draw the 𝐼3 − 𝑌 plot of the octet of pseudo scalar mesons indicating the respective
particles.
3. Name a reaction in which parity is not conserved. Which class of interaction does
this reaction belong to?
4. What do you mean by charge conjugation?
2006

1. Give an example of a reaction in which strangeness is not conserved. What type of

interaction does it involve?
2. Define hypercharge. Plot the hypercharge against isospin for the quark triplet and
the baryon decuplet, with the respective particles and their quark contents properly
indicated for the latter.
2005

1. What are Baryon number and Lepton number?

2. Explain what do you mean by strangeness quantum number.
3. What is eight fold way?
4. Are the following processes possible? Give reasons:
(𝑖)𝜇+ → 𝑒 + + 𝑣 + 𝑣⃗
(𝑖𝑖)𝑣⃗𝜇 + 𝑝 → 𝑛 + 𝜇+
(𝑖𝑖𝑖)𝑛 → 𝑝 + 𝑒 − + 𝛾
(𝑖𝑣)𝑝 → 𝜋 + + 𝜋 − + 𝑒 +
(𝑣)𝜇+ → 𝑒 + + 𝛾

2004

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1. Explain Quark model

2003

1. What is position. How did Anderson prove that the particle is not a proton?
2. Explain what do you mean by strangeness quantum number.
3. What is eight fold way?
4. Are the following processes possible? Give reasons in support of your answer
⃗⃗𝜇 + 𝑃 → 𝑛 + 𝜇+
(𝑖)𝜋 + + 𝑛 → ⋀0 + 𝑘 + (𝑖𝑖)𝑉

2002

1. Briefly outline one cycle of reactions which can serve as the source of energy of a
star.
2. What is the quark model? Display the quark content of any four of the baryons
1
forming the spin + even parity octet.
2
3. From the reaction 𝑝 + 𝜋 → 𝑘 0 + Å, which occurs via strong interactions, deduce
the strangess S of Å, given S=1 for 𝐾 0 . Now comment on the fact that the decay
Å → 𝑝 + 𝜋 −1 does occur in nature.
4. Are the following processes possible? Give reasons
(𝑖)𝑛 → 𝑝 + 𝑒 − + 𝛾 (𝑖𝑖)𝑛 + 𝛾 → 𝑝 + 𝑒 −
5. Write down an equation representing muon decay. How is lepton number
conserved in this equation?

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