Solar Energy

Solar energy production

Solar luminosity

Solar radiation spectrum M =1.989·10

33 g R

=6.96·1010 cm L

=3.847·1033 erg/sec Tsurface 6000K

Math and Units

2

27

8

23

19

7

2

2

49.9311066.11

/10998.2

10022.6

106022.11

101

11

c

MeVkgamu

smc

particlesgA

JeV

Jerg

s

mkgJ

http://en.wikipedia.org/wiki/Electronvolt

s

JunitsinosityminLuL

m

WunitsinFluxF

WunitsinPowerS

JunitsinEnergyE

KunitsineTemperaturT

:

:

:

:

:

2

http://en.wikipedia.org/wiki/Electronvolt

Example

s

tons

s

kg

s

m

ss

mkg

sm

c

EmcmE

s

mkgJ

sJsergLsun

000,280,41028.4

103

/1085.3

11

/1085.3/1085.3

9

2

228

2

226

1

2

2

2

2

2633

Solar luminosity:

According to Einstein:

That amount of energy can only be generated by nuclear fusion processes!

Nuclear masses and energy

The mass difference is the binding energy B

Isotopes: nuclei with Z=constant, N varies!

22 cmNmZcM np

22 cmNmZcMB np

The mass M of the nucleus is smaller than the

mass of its proton and neutron constituents!

http://ie.lbl.gov/toimass.html

http://nucleardata.nuclear.lu.se/database/masses/

http://ie.lbl.gov/toimass.htmlhttp://nucleardata.nuclear.lu.se/database/masses/

Nuclear Binding Energy

Yield from nuclear fusion

Yield from nuclear fission

56Fe, 56Ni, maximum binding energy

Example: What is the binding energy of the oxygen isotope 18O?

mp= 1.007825 · 1.66 · 10-24 g

mn= 1.008665 · 1.66 · 10-24 g

M(18O) = 17.99916 · 1.66 · 10-24 g

Z=8, N=10

Atomic Mass Unit: 1 amu=1/12(M12C)=1.66 · 10-24 g

B = (Z · mp+ N · mn- M) · c2

B(18O) = 1.398 · 105 keV = 2.24·10-11 J

1g 18O contains 7.5·1011 J (W·s)

• Mass difference between initial particles and final particles is called:

Q-value (energy)

• If a reaction needs energy to take place it is called:

Endothermic (Q0)

A(a,b)B (mA+ma-mB-mb)·c2=Q

Projectile a (p, n, )

Target A (17N, 17O, 14C)

http://ie.lbl.gov/toi2003/MassSearch.asp

http://nucleardata.nuclear.lu.se/database/masses/

Nuclear Reactions and Q-values

Reaction occurs with a certain probability (cross section), which depends on the energy dependent Coulomb interaction and the probability for forming a new quantum system !

Product b

(p, n, )

Recoil B

http://ie.lbl.gov/toi2003/MassSearch.asphttp://nucleardata.nuclear.lu.se/database/masses/

Hydrogen & helium burning Calculate the energy release of solar hydrogen fusion:

4 1H1 4He

mp = 1.007825 · 1.66 · 10-24 g

m4He = 4.002603 · 1.66 · 10-24 g

MeVMeVQE

eVJcMQE

kgkgM

HeHHeH

HeHHeHHeH

HeH

7.2648.931002603.4007825.14

1067.21028.4

1076.41066.1002603.4007825.14

1414

7122

141414

2927

14

This is the energy release per fusion reaction

s

tons

s

reactionskgM

s

reactions

MeV

s

MeV

Rs

MeV

s

JL

H

sun

83727

37

39

3926

1002.61091066.1007825.14

1097.26

104.2104.21085.3

http://ie.lbl.gov/toi2003/MassSearch.asp

Stellar helium burning

MeVMeVQE

eVJcMQE

kgkgM

CHeCHe

HeHCHeCHe

CHe

27.748.93100.12002603.43

1027.71017.1

1030.11066.100.12002603.43

12124

12124

124

1313

6122

141313

2927

13

Helium burning process in red giant stars

3 4He 1 12C

m4He = 4.002603 · 1.66 · 10-24 g

m12C = 12.000000 · 1.66 · 10-24 g

Betelgeuse In Orion

Solar Energy Source

The energy generation rate in the pp chain, where XH is hydrogen mass fraction.

Particle density: Ni Avogadro’s number: NA=6.022·10

23 part/A g Hydrogen mass fraction: XH 0. 5, Solar core density (g/cm3): 160 g/cm3

Burning temperature (GK): T 0.015 GK

11380.33/2

243/1104.2

gserge

T

X THpp

A

HeHe

A

HH

A

iii

N

NX

N

NX

N

NAX

41

1H

3He

2H=D

1H

3He

1H

1H

4He

2H=D

1H 1H 1H

1H

pp-I

MeVQQHeH 7.2614 41

suncoresun

core

sun

pp

pp

THpp

MMgM

ggserg

sergM

sergL

gserg

gsergecmg

gsergeT

X

11.010989.1

1019.26.17

1085.3

1085.3

6.17

015.0

/1605.0104.2

104.2

33

32

11

133

133

11

11015.0380.3

3/2

324

11380.3

3/2

24

3/1

3/1

About 10% of the solar material is undergoing hydrogen burning reactions in the solar core !

Additional pp-chain sources

4He 4He

3He

7Be

4He

e-

7Li 1H

4He

4He

8B

8Be

1H

e-

pp-II pp-III

18%

Additional energy sources

11228.153/2

253/1104.4

gserge

T

ZX THCNO

The energy generation rate in the pp chain, where XH is hydrogen mass fraction and Z the average CNO mass fraction (metallicity).

02.01 ZZXXX HeHi

i

This requires CNO seed abundance as catalyst!

More massive stars in CNO mode

Vega in Lyra Distance 25 Ly Mvega=2.5Msun Lvega=50Lsun

Sirius in Canis Majoris Distance 8.6 Ly Mvega=2.0Msun Lvega=25Lsun

Homework 1

The solar hydrogen fuel will eventually get exhausted. The stellar core material contracts to increase the internal pressure to balance the gravitational forces. Assuming the stellar core material follows the ideal gas law, at what temperature will the CNO energy production be equal to the energy production by the pp-chains?.

CNOpp

GKT 017.0