12.1. THESCALEOFTHEWORLD 203
Toestimatetheenergyreleasedbyburningamoleofanything,assumethatthe
energyreleasedpermoleculeisoftheorderofmagnitudeofthebindingenergyofan
electronintheHydrogenatomgroundstate. Thisissurelynotveryaccurate,but
again,wearenotgoingtoworryaboutafewpowersoften. Thebindingenergyis
|E 1 |=
me^4
2 ̄h^2≈ 2 × 10 −^18 J (12.60)
ThenburningamoleofanythingwouldreleaseanenergyEontheorder
E∼NA|E 1 |∼ 1200 kJ (12.61)whichissufficienttoturnhalfakilogramof water, at 100 Cand 1 atmpressure,
completelyintosteam. Releasedinashorttimethiswouldmakeagoodbang,but
itscertainlynotenoughenergytoflattenacity.
Inthisway,wecanusequantummechanicstoestimatethe”scaleoftheworld;”
i.e. volumeper gram, energy releasedin chemical reactions,and so on. Infact,
witha bit more work,its possible to goon and estimatethe order-of-magnitude
size ofanimals andmountains!^3 Asexplained inLecture 6, the sizeandbinding
energyoftheHydrogenatomisultimatelyduetoaninterplaybetweentheattractive
CoulombpotentialandakineticenergycomingfromtheUncertaintyprinciple. It
isthisinterplaythatsetsthescaleoftheworld. Ofcourse,theargumentisalittle
incomplete: itrequiredasinputthemassesoftheelectronandproton,aswellasthe
electroncharge.^4 Wheredothesenumberscomefrom?Itisthereligiousbeliefofmost
physicists(includingyourprofessor)thatallsuchnumberswillonedaybederived
fromanultimate”TheoryofEverything,”whosecornerstonewillbetheprinciplesof
quantummechanics.^5
(^3) ThereisabeautifulessaybyV.Weisskopfonthissubject.
(^4) Nowadays,itspossibletocalculatethemassoftheprotonfromthetheoryofthestronginter-
actions(QCD),butthisstillrequiresinputofadimensionfulconstantknownas“QCDΛ.”
(^5) Anexcellentnon-technicaldiscussionisfoundinS.Weinberg’srecentbook,entitledDreamsof
aFinalTheory.