ADummy'sGuideto
Science
Doyoueverfeelconfusedbyexpertcolleagues,andtooashamedtoaskwhattheymean
byradioactivity,agene,aterafloporabarrelofoil?Ordoyoueverfeeltheneedtoget
backtobasicswhenhelpingwiththatsciencehomework?Ifso,youmightfindthe
helpfulinformationinthisnote,whichincludesinformationabout:
• TheMeasurementSystem
• Conversionfactors
• DerivedUnits
• SoundandLight
• Geology,theEarthetc.
• Atoms,radiation
• Sub-atomicparticles
• Biology
TheMeasurementSystem
Inprinciple,allphysicalmeasurementscanbereducedtoacombinationofthe
following7SI*BaseUnits:
Mole(amountofsubstance)
Metre(length)
Kilogram(mass)
Kelvin(temperature)
Ampere(electriccurrent)
Candela(luminosity)&
Second(time).
*SIstandsforSystemeInternationald’Unites
Allothermeasurements,suchasNewtons,Pascals,ohmsetccanbereducedtothe
aboveunits.Someexamplesarelaterinthisnote.
Thefollowingprefixescanalsobeaddedtotheaboveunits.
yocto y
10-24
zepto z
10-21
atto a
10-18
femto f
10-15
pico p
10-12
nano n
10-9
micro
μ
10-6
milli m
10-3
centi c
10-2
deci d
10-1
1
deca
hecto
kilo
mega
giga
tera
peta
exa
zetta
yotta
da
h
k
M
G
T
P
E
Z
Y
101
102
103
106
109
1012
1015
1018
1021
1024
-thatisathousand
-thatisamillion
-abillion
-atrillion
Thehigheroftheseprefixesareincreasinglyoftenfoundindescriptionsofcomputer
speed,storageetc.So:-
o 1bitisoneunitofstorageinacomputer(i.e.a“0”ora“1”).
o Abyteis8bits(suchas10011001-andcontainsenoughinformationto
identify,forinstance,onesymbol;suchasaletterofthealphabet).
o Akilobyteis1000bytes,andsoonuptoapetabyte.
o A“flop”isameasureofcomputerspeed–beingonecomputationasecond.
o Ateraflopistherefore1012(atrillion)computationsasecond–thespeed
reachedbythefastestsupercomputersinthemid-2000s
ConversionFactors
Length,Area&Volume
1inch=2.54cm
1metre=39.4inches
1mile=1.609km
1metre/sec=3.60km/hr=2.24mph
1nauticalmile=1.15miles
9.46x1015metres=1light-year
3.086x1016metres=1parsec
1hectare=10,000sq.metres(i.e.100metressq.)=2.471acres
1acre=4840sq.yds(i.e.c70ydssq.)
1litre=0.22galls=1.76pints=0.001cubicmetre
1UKgallon=1.20USgall
1cubicmetre=35.3cubicfeet
1unitofalcohol=10millilitres(Thereforeone-thirdofabottle(250ml)ofa10%proof
winecontains2.5unitsofalcohol.)
Oil
1barrel=159litres=35UKgalls=42USgalls
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1tonneofoil=7.48barrels=1.19cubicmetres
N.B.1barrelperday=58cubicmetrespa=48.8tonnespa
(i.e.typicaldensityofoil=0.87)
Gas
1000cubicmetresofgas=1cubicmetreofoilequivalent
1cubicmetrecontainsapprox.9000kcal
1barrelofoilequivalent=159cumetresgas=5900cubicfeetgas
Non-gasLiquids
1tonneNGL=1.3cubicmetresoilequivalent
Force
1Newton=100,000dynes
Pressure
1Pascal=1Newton/squaremetre
1hecto-Pascal=1millibar
Energy
1Joule=10,000,000ergs
1Calorie=4.186joules
1kcal=3.92BTU
1Kilowatt-hour=3.6millionjoules
(i.e.1000joules/secforanhour)
1Megajoule=0.278Kilowatt-hrs
1.6x10-19joules=1electron-volt(theenergygainedbyanelectronacceleratedthrough
anelectrostaticpotentialdifferenceofonevolt)
Power
1watt=1joule/second
1horsepower=746watts.
Weight
1gram=0.0353ounce(strictlyavoirdupoisounce;1gramis0.0322troyounce–a
slightlyheavierunitmainlyusedformeasuringtheweightofpreciousmetals)
1kg=2.205lb.
1ton=1.016tonne
1tonne=1000kg
1mlwaterweighs1g.
1litrewaterweighs1kg
Temperature
degreeskelvin=degreesCelsius+273
degreesFahrenheit=degreesCelsiusx1.8+32
OldEnglish
3
1quart=2pints
1pint=4gills=20fluidounces
1tablespoon=18.5ml
1dessertspoon=12.3ml
1teaspoon=6.2ml
1breakfastcup=284ml
1standardcup=250ml
1yard=3feet=36inches
DerivedUnits:
Contents:-
• Volume:thelitre
• Force:theNewton
• Pressure:thePascal
• Energy:thejoule
• Power:thewatt
OneofthemostcommonderivedunitsisVolume.ThebasicSIunitis1metre3.Butas
thisisfairlylarge,itismuchmoreusualtouse1litrewhichis0.001m3or1millilitre
whichis0.001litres.
AnotherderivedunitisForce.Whatdoesaforcedo?Itcausesabodytostarttomove
andthen,ifthereisnoresistance,togofasterandfaster–i.e.toaccelerate.Sothebasic
unitistheforcethatmakesamassof1kilogramacceleratetoavelocityof1
metre/secondiftheforceisappliedfor1second.(AllthemeasurementsinitalicsareSI
BaseUnits.)Putmoreshortly,thebasicunitofforceiskilogramsxmetres/secondsx
secondswhichshortenstokg.m/sec2.Asthisisrathercomplicated,itisalsoknown
moresimplyasaNewton.
ANewtonisquitealargeforce.Afterall,anyforcethatcanaccelerate1kgtoaspeedof
1m/sec(3.6km/hr)inonly1secondisquitepowerful.
TheGravitationalForceattractingtwomasseswhicharermetresapartisGMm/r2,
whereGis6.67x10-11Nm2/kg2.
OntheEarth,amassof1kgissubjecttoagravitationalforceofc9.8Newtons:-i.e.it
weighs9.8Newtons.Soifitfallsforonesecond,itreachesaspeedof9.8metres/secor
35km/hour.Itisinterestingtonotethatitdoesnottravel9.8metresinthatfirst
secondoffalling,butstartsat0.0m/secandthenonlyreachesthespeedof9.8m/sec
afteronesecond.Itsaveragevelocityisthereforeonlyhalfof9.8m/sec,i.e.4.9m/sec.
Thisinturnmeansthatifyoujumpoffa4.9-metre-highwallyouwillhittheground
onlyonesecondlater,andwillbetravellingat9.8m/sec(or35kphor22mph)when
youdoso:-Notagoodidea!
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GravitationalAccelerationvariesslightlyfromplacetoplace.Itis9.83m/sec2at
groundlevelattheNorthPole,but(a)itdecreaseswithaltitude,and(b)itdecreases
towardstheequator(whereitis9.78m/sec2)becausetheEarthisslightlybroader
aroundtheequator.
BecausetheNewtonissuchalargeforce,itisoftenconvenienttouseamuchsmaller
unitofforce,thedyne,whichistheforcewhichaccelerates1gramby1cm/sec/sec.
Therearetherefore100,000dynesinaNewton.
Pressureistheamountofforceactingoveranarea,soitsbasicunitisforce/m2i.e.
Newtons/squaremetre.ThisunitisalsoknownasaPascal.ReducedtoSIbasicunits,
thedimensionsarekg.m/sec2m2=kg/m.sec2.
Themassof1m3ofairatsealevelisc1kg.Thegravitationalforceactingonitis
thereforec10Newtons,sothatametre’sdepthofairappliesapressureatsealevelof
around10Pascals.Thetotalpressureofthecolumnofairaboveseallevelisaround105
Pascals,i.e.103hectopascals(or103millibarsor1bar).
Anincreaseinpressureofonehectopascal/millibarwilllowersealevelbyc1cm.Tide
tablesassumeastandardpressureof1013hectopascals,soanincreaseto1040
hectopascalswilllowersealevelbyc30cm–whichcanbenoticeable.
Theatmospherethinsexponentially(atlowerlevels)withahalf-heightofabout5600
metres.Thereisthereforeonly25%oftheatmosphereaboveyou(witha
correspondingdecreaseinavailableoxygen)at11200metres(36400feet):-the
cruisingheightofmanyjetsandalittlehigherthanthesummitofEverest.
AnotherwayoflookingatforceistothinkofitasthewayinwhichEnergyis
transferredfromoneformtoanother.Forinstancearocketmotoruseschemical
energytoforcetherockettogainkineticenergy.Thebasicunitofenergyistheenergy
thatisusedwhenabasicunitofforcepushesthroughadistanceof1metre.Thebasic
unitistherefore
(kg.m/sec2)xm=kg.m2/sec2.ThisunitisknownasaJoule.
Notethatthedimensionsofenergyaremassxvelocity2.Thisisconsistentwith
Einstein’ssuggestionthatmassmcanbeconvertedintoenergyEandthatwhenthis
happensthenE=mc2,wherec=thespeedoflight.Itcanalsobecalculatedthatamass
ofmgramtravellingatvcm/sechaskineticenergyof0.5mv2joules.
Thereareofcourseseveraldifferentformsofenergy,withlotsofdifferentnames.
Soundandheatarebothformsofkineticenergyofatomsandmolecules.
Potentialenergyderivesfromthepositionofanobject:-i.e.aweightthatisliftedaway
fromthecentreoftheEarthhasgravitationalpotentialenergy,whilstastretchedor
compressedspringhaselasticpotentialenergy.
Kineticandpotentialenergyarebothinturndifferentformsofmechanicalenergy.
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Otherformsofenergyincludechemical,electrical,nuclearandradiant(inc.light
andradiowaves).
LiketheNewton,theJouleisquitealargeunit.Itisthereforesometimesusefultouse
theergwhichistheworkdonewhen1dyneoperatesthrough1cm.Asthereare
100,000dynesinaNewton,and100cmsinametre,thereare10millionergsinajoule.
Heatenergyismoreoftenmeasuredincalories.1calorieistheheatrequiredtoraise
thetemperatureof1gramofwaterby1degreeCelsius.1calorieisequivalentto4.186
joules.
(Amassof1kgfallingthrough1metreonEarththereforereleases9.8joules
ofpotentialenergy–i.e.justover2caloriesofenergy.Thisisenoughenergy
toheat1gramofwaterby2degreesC,oritself(1kg)by0.002degreesC.)
Poweristherateatwhichenergytransferredfromoneformtoanother.1wattisthe
sameas1joule/second.
A100wattlightbulbthereforegenerates100jouleseverysecondor24caloriesevery
second.Inotherwordsitcouldraisethetemperatureof1gramofwaterby24degrees
Ceverysecond–andboilitinabout4seconds.AnRB211aeroenginegenerates30
megawatts,i.e.30millionjoules/second(thesortofpowerneededbyatownofabout
60,000people).
Sound&Light
Imaginestandingstillaswavesgopastyou.If10wavecrestsgopastyoueveryminute,
andthedistancebetweenthecrestsis2metres,thenthewavesmustbetravellingat20
metresaminute.Inotherwordsthespeedofawaveisitslengthxitsfrequency.
Thespeedofsounddependsuponthemediumthroughwhichitistravellingandonthe
temperature.Inair,atroomtemperature,thespeedofsoundis300m/sec.Soagapof
3or4secondsbetweenlightningandthundermeansthatitisabout1kmaway.
Thespeedofsoundismuchfaster(1500m/sec)inwaterandfasterstill(6000m/sec)in
steel:-whichiswhyyoucanhearatraincomingalongwayawayifyouputyourearto
therail.
Thespeedoflight(indeed,thespeedofallelectromagneticradiation)inavacuumis3x
108m/sec.(Itgoesslowerifnotinavacuum,whichiswhylightisbentwhenentering
waterorglassatanangle–Thisiscalledrefraction.)Andasspeed=frequencyx
wavelength,thelatterincreasesastheformerfalls.Theresultisthe…
ElectromagneticSpectrum
Frequency Wavelength
Hertz
metres
6
(i.e.cycles/sec)
Gammarays 3x1019
10-11
17
-9
Xrays 3x10 10 Ultra-violet 3x1015
10-7
14
Violetlight 7x10 4x10-7
Redlight
4x1014
7x10-7
13
Infra-red
3x10 10-5
Microwaves 3x1010
10-2
8
9
UHFradio 3x10 –3x10 10-1–1
ProfessionalVHFradio
1.08–1.36x108
2.2–2.7
(i.e.aircraft,police,taxis)
BroadcastVHFradio0.88–1.08x108
2.7–3.4
(frequencymodulated)
TV
5.5–8.7x107 3.5–5.5
Shortwaveradio 0.6-3x107
1–5x101
Mediumwaveradio 0.5–1.7x106 1.8–6x102
(amplitudemodulated) 5
Longwaveradio
1.5–3x10
1–2x103
1
Electro-magneticwaves
5–6x10 5–6x106
(e.g.nearpowerlines)
Asnotedabove,lightgoesmoreslowlyifnotinavacuum.Theextremecaseiswhenit
travelsatverylowtemperaturesthroughaweirdsubstancecalledaBose-Einstein
condensatewhenitsspeedhasbeenreducedto17metres/sec–thespeedofasports
cyclist!
Geology,theEarthetc.
TheEarth’sradiusis6357kmattheNorthPole.Itisslightlylarger(becauseofthe
Earth’sspin)at6378kmattheequator.
ThemassoftheEarthisc.6x1024kg
Thedensityofairis1.22kg/m3atgroundleveland0.47kg/m3at9000m.
Igneousrocksareformedfrommoltenrock(magma)thatbecomessolidwhenitcools.
• Lavasetc.areextrusiveandcoolveryquickly,formingverysmallcrystals.
• Others,(e.g.granite)areintrusive,i.e.formeddeepunderground.Slowcooling
formsmuchbiggercrystals.Suchrocksareexposedasaresultoferosion.
Sedimentaryrocksarelaiddowninlayers.
• Sandonabeachandmudonariverbedcreatese.g.sandstones.
• Marineorganismscreatelimestones,inc.chalk.
Metamorphicrocksareexistingrocksthathavechangedformunderhighpressure
and/ortemperature,e.g.afterdeepburialintheEarth.
• Theserocks(e.g.schist,slateandmarble)arealsocrystalline,butthecrystals
forminthesolidstate.
• Slatewasoriginallyfinemud.
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•
Marbleisformedfromlimestone.Itdoesnothaveabandedstructureandsocan
breakinanydirection,makingitidealforsculpture.
Allthreetypesofrockcanturnintotheothertwotypesthroughburial,extrusionand
erosion/deposition.
Atoms,radiationetc.
Thereare6x1023atomsin1moleofasubstance(i.e.1gramofHydrogen,12gramsof
Carbon).
Therestmassofaprotonis1.67x10-27kg.
Thechargeonanelectronis1.6x10-19coulombs.
ThemassofsubatomicparticlesismoreusuallyquotedinGigaElectronVolts(GeV)or
atomicmassunits.Aprotonweighs1amuor0.93GeV.1GeVis1.783x10-27kg.
Theheaviestnaturallyoccurringelementisuraniumwhichhas92protons.Heavier
elementshavebeencreatedinlaboratories,uptotheasyetun-namedelement118.
Atomicdisintegrationscreatethreetypesofradioactivity:-Alphaparticlesarethe
nucleiofheliumatoms,Betaparticlesareelectrons,andGammaraysare
electromagneticradiationwithveryshortwavelength.
1Becquerel=1atomicdisintegration/sec.
Manufacturedsubstancesmustbetreatedasradioactive,andcarefullystoredetc.,if1
kilogramofthesubstanceproducesmorethan380disintegrationsasecond–i.e.their
radioactivityexceeds380Becquerel/kilogram(Bq/kg).
Thecommonestnaturallyoccurringradioactiveelementispotassium.Thereisenough
radioactivepotassiuminthefollowingsubstancestoproducethefollowing
radioactivity:
Humans:
140Bq/kg
Coal: 250Bq/kg
Tea: 830Bq/kg
Coffee:
1640Bq/kg.
Note,therefore,thatteaandcoffeewouldneedtobestoredinspecialcontainers,
carryingtheabovesign,iftheywerenotnaturallyoccurringsubstances!
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SubatomicParticles
Asmassandenergyaretwosidesofthesamecoin(rememberE=mc2)scientistssay
thatordinarymatter-gas,stars,planetsandgalaxies-makesupjust5%ofthe
Universe.Darkenergymakesupabout68%,anddarkmatter-whichdoesnotreflector
emitdetectablelight-accountsfor27%.Butifwediscounttheenergypartofthe
universe,andjustlookatmass,thentheUniverseis85%darkmatterand15%normal
orbaryonicmatter.
DarkmattermayconsistofWIMPs(weaklyinteractingmassiveparticles)and/or
Axions.
Allordinarymatterconsistsoffermionsboundtogetherbymessengerparticlescalled
bosons.
Thereare12fermions:6leptons(electron,muon,tau,electronneutrino,muon
neutrinoandtauneutrino)and6quarks(up,charm,top,down,strange&bottom).
Therearebelievedtobe6elementarybosons(aswellasanumberofcompositeones).
TheexistenceoftheHiggsbosonandthefourgaugebosons(photons,gluons,andtheW
andZbosons)hasbeenconfirmed.Theexistenceofthegravitonisnotyetconfirmed.
TheHiggsbosongivesparticlestheirmass.Theotherbosonsprovidefourtypesof
forceorinteraction:
Gravity–theattractiveforce-carriedbygravitons
Electromagnetism–theinteractionbetweenbodieswithelectriccharge-carriedby
photons
TheStrongNuclearForce–keepsprotonsandneutronstogetherinanatom’snucleus
-carriedbygluons
TheWeakNuclearForce–governsthingslikeradioactivedecay-carriedbyWandZ
bosons
Non-fundamentalparticlessuchasprotonsandneutronsconsistofanumberofquarks
invariouscombinations.Forinstance,aprotonismadeof2Upquarksand1Down.
Everyfundamentalparticlehasacorrespondinganti-particlewiththesamemassbut
oppositecharge.
Biology
Thisisalistofthecurrentlylivingthingswhoseancestorsbranchedawayfromtheline
whicheventuallybecameman(homosapiens).
Itisnotyetknownhowchemicalsmanagedtodeveloplife-likeproperties,butbiology
thenbeganwithtwoenormouslydiversegroupsofsinglecelledmicroorganisms
(microbes)knownasBacteriaandArchaea.
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Amergerbetweenthesetwoancientcelltypes,billionsofyearslater,isthoughttohave
createdEukaryotes,whichareorganismswhosecellscontaincomplexstructures
enclosedwithinmembranes.Thedefiningmembrane-boundstructureisthenucleus,or
nuclearenvelope,withinwhichthegeneticmaterialiscarried.Allspeciesoflarge
complexorganismsareeukaryotes,includinganimals,plantsandfungi.
Thefollowingarelistedintheorderinwhichtheyarebelievedtohavebranchedoffthe
homosapiensline.
Variouseukaryotes,inc.seaweeds,slimemoulds,someamoeba,werenextleave,
leaving…
Plants,inc.red&greenalgae
SomeotherAmoeba
Fungi(someofwhichassociatewithalgaeorcyanobacteriatoformlichens)
DRIPs
Choanoflagellates–leavingAnimals:-
Sponges
Placozoans
Ctenophores
Corals,seaanemones,jellyfish
Acoelomorphflatworms–leavinganimalswithbodycavitiesandanuses
Worms,insects(beetles,flies,crickets–6legs),centipedes,spiders(8legs),
crustaceans(crabs,lobsters,woodlice),molluscs(slugs,snails,mussels,
octopus,cuttlefish,squid),etc.
Starfish,seaurchinsetc.
Seasquirts
Lancelets
Lampreysandhagfish–jawlessfish
Sharks,skates,raysetc:leavingbonyanimals:
Ray-finnedfish
Coelacanths
Lungfish:leaving…
Tetrapods,whicharevertebrateanimalshavingfourlimbs.Amphibians,
reptiles,birdsandmammalsarealltetrapods;evensnakesandotherlimbless
reptilesandamphibiansaretetrapodsbydescent.
Amphibians:frogs,toads,salamanders,newts
Birds(warmblooded)andreptilesinc.dinosaurs,crocodiles,lizards,snakes,
turtles
Duckbilledplatypus:leaving(warmblooded)mammals:
Marsupials:leavingplacentalmammals:
Elephants,dugongs,manatees,aardvarks
Armadillos,slothsandanteaters
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Dogs,cats,bears,seals,horses,deer,hipposandwhales
Rabbitsandrodents
Treeshrewsandcolugos
Lemurs,bushbabies,lorisesandpottos
Tarsiers
NewWorldmonkeys
OldWorldmonkeys-baboonsetc.
Gibbons
OrangUtans
Gorillas
Chimpanzees
Otherinformation
Allhumancells(excepteggs,spermandredbloodcells)containanucleusand2setsof
genome.Eachgenomecontains23chromosomesconsistingofanintertwinedpair(i.e.
adoublehelix)ofverylongDNAmolecules,offwhichareseveralthousandsiderungs
calledgenes.Eachgeneitselfconsistsofmanythousandsofcodons,eachwhichinturn
containsthree(offouravailable)bases–adenine,cytosines,guanineandthymine
(usuallyabbreviatedtoA,C,G&T).
Cellsdividetoenableustogrow,andtheycarryondividingafterwehavereached
adulthood,partlysoastorepairdamage.RandomDNAcopyingmistakesduringcell
divisioncancausecancer.Basalskincellsdivide10trilliontimesinalifetime,andare
thereforerelativelylikelytocauseskincancer,atleastincomparisonto,say,pelvic
bonecellswhichonlydividearound1milliontimesinalifetime.
GenesaretranslatedintoproteinsbyRNA.Proteinsarerelativelylargeorganic
compoundsmadeupofaminoacids.Theyareessentialpartsofalllivingorganisms
andparticipateineveryprocesswithincells.Manyproteinsareenzymesthatcatalyse
biochemicalreactionsinthebody.Otherproteinshavestructuralormechanical
functions,suchastheproteinswhichformasystemofscaffoldingthatmaintainscell
shape.Proteinisalsoanecessarycomponentinourdiet,sinceanimalscannot
synthesisealltheaminoacidstheyneedandmustobtainsomeessentialonesfromfood.
Throughtheprocessofdigestion,animalsbreakdowningestedproteinintofreeamino
acidsthatcanbeusedforproteinsynthesis.
Virusesaregeneticentitiesthataremetabolicallyinertexceptwhentheyinfectahost
cell,whenthevirusinsertsitsowngeneticmaterialandliterallytakesoverthehost’s
finctions.
Thelifespanofmammalsisroughlyinproportiontotheanimal’smasstothepowerof
0.25.Andmetabolicrate(e.g.heartrate)isroughlyinproportiontomasstothepower
of–0.25.Totalenergyconsumptionisroughlyinproportiontomasstothepowerof
0.75.
A10,000kgelephantwillthereforelive10timesaslong,andhaveaheartrate1/10thof,
a1kghen.
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A100kgmanburnsenergyattherateofc.100watts–or24cals/sec–or2mcals/day
i.e.2000kcals/day.
©MartinStanley
[email protected]
Pleasefeelfreetocopyfromthisnote,butpleasecreditthesource:-
http://www.regulation.org.uk
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