1Class 26Thermonuclear fusion in the Sun Conversion of mass to energy Conservation laws The actual reactions…Notation… we need some compact way ofdiscussing nucleiAtomic number= number of protonsSymbol for element(set by atomicnumber)Total number ofnucleons =protons+neutrons2I : Conversion of mass to energy Essential result of the nuclear processes in the Sun is Let’s add up the masses… Initial state… Mass of 1H = 1.67262x10-27kg So… mass of 4 1H = 6.69048x10-27kg Final state Mass of 4He = 6.64466x10-27kg Mass positron = 9.10938x10-31kg So, total mass is 4He + 2e+ = 6.64648x10-27kg There is a mass difference of 4.4x10-29kg Where has this mass gone? Einstein discovered an equivalence between mass andenergy The “missing mass” has been converted into energy…this is how the Sun is powered! About 4 million tonnes/second is converted from massto energy to power the Sun Need to convert about 600 million tonnes/second ofhydrogen into helium Define the “efficiency” of the process by… For fusion of hydrogen to helium, efficiency is about 0.007(0.7%)… about 106 times more efficient that chemicalburning!3A hydrogen bombII : Conservation laws To understand nuclear reactions, we need tokeep in mind the following familiar laws ofphysics… Conservation of energy Conservation of momentum Conservation of electrical charge There’s also important and less familiar laws… Conservation of “lepton number”… total numberof electron-like particles is conserved Conservation of “baryon number”… total numberof nucleons (protons & neutrons) is conserved Anti-particles count negatively towards the leptonand baryon number4III : Fusion reactions in the Sun We cannot fuse 4 hydrogen atoms intoone helium atom in one step? [Why?] Discussion on the board…The proton-proton (pp) chain5Without the clutter…P1There are other “side reactions”P26 The rate that energy is produced per unit timeper unit volume scales with density andtemperature… Where x≈4 for the Sun Explains why fusion reactions only occur in the corewhere density and temperature is highest. Eventually, all of the hydrogen will be used upin the core… what then? Will discuss next class how structure of Sun changeswhen H is used up… result is core compresses, heatsup, and a new reaction starts…7Triple-alpha processKicks in at about 100 million