Energy production in star
For 3rd year physics honours
Sukla Debnath
Early universe
Formation of star
Primordial nucleosynthesys
Primordial nucleosynthesys
As the Universe expand and temperature fall the reaction rate
decreased Below 109 k the nutron and proton combined to form
deuterium nucleus a number of reaction then led to the formation
of helium nucleus, the mostTightly bound nucleus involved in
nucleosynthesys.
Energy production in star
The three possible source of energy are –
 Chemical Reaction
 Gravitational contraction
 Thermonuclear reaction
Chemical reaction : Coal burning
Burning is conversion of chemical energy into electromagnetic
reaction
• Coal burning yield 4 × 108 J/Kg which is not sufficient
•For our SUN , if the Sun is made of coal of 2×1038 Kg it give energy
2× 1030×4×108 J = 8×1038 J
Sun has radiate 1.2×1043 J energy in 109 year
Gravitational Contraction
The Gravitational potential energy is given by ,
V=-3/5 (GM2 /R)
The energy radiated during collapse would be
ΔE = -Ef = 3/10 (GM2/R)
o For Sun ΔE = 2× 1041 J
Thermonuclear reaction
In the special theory of relativity, Einstein
demonstrate that the total mass energy was conserved.
The relaton between mass and energy is,
E = m c2
Where E=energy equivalent to mass
m=mass
c=speed of light
The rest energy of proton,
E= (1.67× 10-27 )(3×108)2 J
=940 MeV
What is the source of enormous energy of stars
Nuclear fission or fusion ?
Binding energy curve :
What is the source of enormous energy of stars
Nuclear fission or fusion ?
From binding energy curve it is seen that the nuclei atomic number nearer
to A=60 is most stable.
If the heavy nuclei split apart into smaller nuclei having masses nearer to
A=60,they produces energy and this is fission process.
When the lightest element like hydrogen and helium combined to form a
Comparably heavy nuclei up to A=60,the process is nuclear fusion and fusion
Can release enormous energy.
Both fission and fusion reaction have the potential to convert a small amount
of mass into large amount of energy.
However stars are made from light element. Thus nuclear fusion is quite
possible source of energy of the star.
Nuclear time scale
The rest energy of proton,
E= (1.67× 10-27 )(3×108)2 J
=940 MeV
For Sun
E= Ms C2 =1.8 ×1047 J
At current luminosity of sun this would be spent in
Teinstein = E/L =1.4 ×1013 year
Classical approach
The repulsive force between like Charged particles
results a potential barrier that gets stronger as the
Particle get closer
Coulomb potential barrier
The coulombic potential is given by,
u(r)=1/4πε0 (z1z2e2/r)
Z1 , z2 are the no of proton in each nuclei and r is their distance.
The K.E of the reduced mass µ ,
½ µ v2 =3/2 KTclassical
Fusion is possible if the average particle K.E is equals to or greater
than the coulomb potential energy.
For proton z=1, r=10-15m
Tclassical =1.1×1010 k
The central temperature of the sun 107 k much lower than 1010 k. So
classical physics is unable to explain the phenomena.
Maxwell-Boltzmann statistics does not help
If the gas is in thermal equillibrium with
Temperature T, the atoms have a range of
Velocities described by Maxwell-Boltzmann
Distribution function.
The central temperature of the sun is
T≈2×107 K
The K.E of a proton at this temp. is≈2 keV
The electrostatic P.E of two protons 10-15
Apart is 1MeV.
The relative fraction of proton with thermal energy of 1MeV is only
exp(- 1MeV/2keV) = exp(-500)
Quantum mechanics to rescue
Heisenberg uncertainty principle state
That the position and momentum of a particle are not
Precisely defined,
ΔxΔ
The uncertainty in position
means that if two proton can
get close enough to each other
There is some probability
that they will be found within
the coulomb barrier. This is
known as tunneling
Quantum tunneling
The tunneling is possible if the protons come within 1 de Broglie
wavelenth for each other
λ=
The temperature require to sustain the nuclear reaction is, Tquantum
Tq ≈107 k
The temperature required for nuclear reaction is consistent with the estimated
temperature of the sun. So without the quantum effect fusion would not be
possible in the sun and such high luminosities could never be achieved.
Proton-proton cycle
Proton-proton cycle
The reactions are -
The CNO cycle
For more massive stars the pp chain can still occur, but there is
another sequence of Reactions that become more favorable
for converting hydrogen to helium that is Called CNO cycle.
CNO cycle
The reactions are-
Thank you