The Nucleus Of The Atom - Michigan State University

The nucleus of the atom In 1919, Rutherford starts tocollect the first data indicatingthat there is another structurewithin the nucleus- the proton. Two years later, JamesChadwick and E.S. Bielerconclude that some strongforce holds the nucleustogether. Why? If protons in nucleus(and not electrons) thenwhat keeps the repulsiveforce from driving thenucleus apart? Nucleus confined to a verysmall volume ( 10-14 m indiameter), 0.01% ofdiameter of atom density is 1017 kg/m3

So here we are in 1930 There were three fundamentalparticles- electron, proton, andphoton. There were three fundamentalforces- gravity,electromagnetic, and thestrong nuclear force. Gravity we know is muchweaker than the other forces strong force is about 100Xstronger than EM force naturally occuringelements only have up to100 protonsstrong force betweenprotons saturates but EMrepulsive force doesn’tfor more than 100protons repulsive forcewins There were still some“details” to work out butmany felt like Max Born,who said, "Physics as weknow it will be over in sixmonths." Who is Max Bornsgranddaughter ?

Olivia Newton-John as far as I know, JohnTravolta is not relatedto any famousphysicist

The nucleus The nucleus hadceased to befundamental. It wascomposed ofpositively chargedprotons and neutrallycharged neutrons(not actuallydiscovered until 1931by Chadwick).

Characterizing atoms Nuclei of atoms consistof protons and neutrons Surrounding the nucleusare the electrons Characterize nuclei byfollowing characteristics Atomic number Z: # ofprotons in nucleus (alsoequal to # electrons fornormal atom)Neutron number N: # ofneutrons in nucleusMass number A: # ofnucleons (protons neutrons) in nucleus: X is symbol forelement, A is atomicmass and Z is atomicnumber Isotopes of an elementhave the same atomicnumber but differentatomic weight A XZ same number of protonsand electrons same chemical propertiesdifferent number ofneutrons different nuclearproperties

MassesER mc2note the factor of 2000differenceunified mass unit: 12C has amass of 12 amu1 u 1.660559 X 10-27 kg

Radius of nucleus Rutherford found anexpression for how closean alpha particle cancome to a nucleus For a head-on collisionall of kinetic energy ischanged to potentialenergy 1 2dd is the distance of closestapproach2mv k(2e)(Ze)

Solve for d 4kZe2d mv2 or a distance of about 3.2 X10-14 m for alpha particles ona gold nucleus From these results, Rutherfordconcluded that the positivecharge in a nucleus isconcentrated in a spherewhose radius is no greaterthan 10-14 m or about 10fermis (1 fermi 1 X 10-15 m) Nuclear radii go as: r roA1/3A is the # of nucleons andro 1.2X10-15 mall nuclei have roughly thesame density

Stable nuclei The nucleus can exist onlybecause the strong nuclearforce between nucleons in anucleus is stronger than theelectrostatic repulsive forcebetween the protons Light elements have roughlythe same number of protonsand neutrons Heavier elements have moreneutrons than protons(neutrons contribute to thestrong binding force inside thenucleus but not to therepulsive EM force) Isotopes within the shadedregion are stable

Unstable nuclei The heavier elements in theuniverse were all made insupernova explosions Unstable isotopes areproduced (too many neutrons)which then decay to the stableisotopes One of areas of concentrationof NSCL (and of RIA)

Binding Energy The total mass of anucleus is less than thesum of the masses of theprotons and neutronsthat comprise it This difference is calledthe binding energy of thenucleus and can bethought of as the energythat must be added to anucleus to break it apartiron has the highestbinding energy

Radioactivity In 1896, Henri Becquerel, whileinvestigating fluoresence inuranium salts, accidentallydiscovered radioactivity Work by Curies and othersshowed that radioactivity was theresult of the decay ordisintegration of unstable nuclei Up til that point, atoms werebelieved to be indestructible andforever Cleared up a major question as towhy the interior of the Earth wasstill molten Shared the 1903 Nobel prize withthe Curies Work by Curies and othersshowed that radioactivity was theresult of the decay ordisintegration of unstable nuclei

Radiation Alpha particles arehelium nuclei (2 p, 2n): Beta particles arespeedy electrons: Gamma radiation is astream of photons:these are supposed tobe x’s

Half-life If a radioactive samplecontains N radioactive nucleiat some instant, the number ofnuclei that decay in a time Δtis proportional to N ΔN/Δt α N ΔN -λNΔt where λ is a decayconstant R ΔN/Δt λN rate of which atoms decay N Noe-λt T1/2 (half-life) is time it takesfor half of sample to decay Decay constants vary greatlyfor different radioactivedecays and thus so do halflives

Alpha decay AXZA-4Z-24Y 2He X is called the parent nucleusand Y the daughter nucleus Example is Radium, decayinginto Radon and an alphaparticle In order for alpha emission tooccur, mass of the parentmust be greater thancombined mass of daughterand alpha particle excess mass converted intokinetic energy, most of whichis carried by the alpha particle

Beta decay When a radioactivenucleus undergoes betadecay, the daughternucleus has the samenumber of nucleons asthe parent nucleus buthe atomic number ischanged by 1 AXZX eZ-1A A neutron turns into aproton emitting anelectron 1 n0One problem: expect the electronto carry away almost all of thekinetic energy but it doesn’t1 p1 e-It has a range of energies.

Problemo, big problemo Is Momentum Conserved? How can we account for thediscrepancies? Wolfgang Pauli suggested abizarre idea, another particle, onenot yet seen, was carrying themissing energy and could beused to solve the momentumissue. For Conservation of Charge, thenew particle would have to beneutral. According to other experiments,the particle would have to beincredibly light, perhaps even bemassless!

A joke name but it stuck Due to thosecharacteristics, theItalian physicistEnrico Fermisuggested calling itNeutrinoItalian for “littleneutral one.”-zeroelectric charge-very small mass (if any)-a spin of 1/2-very weak interaction with matter,making it difficult to detect

New interaction force Since the beta decayhappened to freeneutrons outside thenucleus, the StrongNuclear Force could notbe responsible. Thus physicists were ledto consider anotherfundamental force- theWeak Nuclear Force. At this point, there were Five FundamentalParticles: electron, proton,neutron, electron, photon,and neutrino.and Four FundamentalForces (or Interactions):Gravity, Electromagnetic,Strong Nuclear Force, andWeak Nuclear Force. The Weak Force isweaker thanElectromagnetic orStrong, but is strongerthan Gravity.

Mass of neutrinos Not until 1956 was thereconvincing experimental evidencethat neutrinos really existed. Anexperiment at a nuclear reactorconducted by Fred Reines wasable to measure interactionsresulting from neutrinos. Whywas this so difficult? Because theneutrinos only interacted via theweak force. The incredibly vastmajority of them passed throughthe detector without leaving anytrace. Currently there’s an experiment inJapan called Kamland which isdesigned to detect neutrinos fromJapan’s working nuclear powerplants

Solar neutrinos The nuclear reactions in the Sunproduce neutrinos. Trillions of themare passing through your body everysecond. Why don’t you feel them?Because their probability ofinteracting is so small. An experiment set up by Ray Davis tolook for neutrinos from the Sun (in theHomestake Mine in South Dakota)found only 1/2 of the numberexpected (running from 1970 throughthe present) Have nuclear reactions in the Sunstopped? Within the last 2 years, it has beenunderstood that there are 3 types ofneutrinos and that the neutrinosproduced in the Sun metamorphizeinto another type (that can’t bedetected) before they reach the Earth.Whew!

Radioactive Dating We can often use radioactivity tomeasure the age of an object(artifact, fossil, etc) Consider 14C dating cosmic ray interactions in theupper atmosphere cause nuclearinteractions that produce 14Cfrom 14Nliving organisms breathe incarbon dioxide that has both 12Cand the radioactive 14Cso all living creatures have thesame ratio of 14C to 12C( 1.3X10-12)when the organism dies,however, it no longer absorbscarbon dioxide from the air, andso the ratio of 14C to 12Cdecreases Can measure therate for the reactionbelow per unit mass,and from it calculatehow long somethinghas been dead 1412C147N e- νthe greater the ratethe more recently ithas died

Carbon dating Works on samples fromabout 1 to 25,000 yearsago why not longer?half-life of 14C is 5730years, so longer than 5half-lives too small afraction of 14C is left (25 32so 1/32nd left) Examples: Dead Sea Scrolls date to1950 years agoIceman dates to 5300years agoShroud of Turin to 700years ago

Radioactivity Radioactivity can beclassified into 2groups unstable nuclei foundin nature (naturalradioactivity)nuclei produced in thelab through nuclearreactions (artificialradioactivity)Four radioactive series shownbelow. Uranium, Actinium andThorium are all found in nature.Neptunium is trans-uranic.

Decay chain for Thorium Start with 232Th half-life for first decayis 14 billions years End with 208Pb

Radiation damage Radiation damage in biologicalorganisms is primarily due toionization effects in cells normal function of a cell canbe disrupted when highlyreactive ions or radicals areformed as a result of ionizingradiation damage to a great number ofcells can lead to death cells which do survive theradiation may becomedefective and cancerous Can divide radiation damage into2 types somatic (to non-reproductivecells)genetic (to reproductive cells) Units of radiation damage rad: that amount of radiationthat deposits .01 J into 1 kg ofabsorbing materialrem is defined as the productof dose in rads and RBE(relative biologicaleffectiveness) factor

Radiation exposures Low level radiation fromcosmic rays, radioactiverocks, soil, air deliver adose of about 0.13rem/year Upper limitrecommended bygovernment is 0.5rem/year Acute whole-body doseof 500 rem results in amortality rate of 50% Natural sources of exposure cosmic rays: 14%radon: 58%food: 12%ground: 16% Equivalent exposure frommedical X-rays chest/teeth/arms and legs: afew days also equivalent to theradiation exposure from a 4hour plane flightbreast, spine, abdomen: afew monthsbarium enema: a few years

What about exposure from microwave ovens? E hc/λ

Nuclear fission Nuclear fission occurs when aheavy nucleus such as 235U splitsor fissions into 2 smaller nuclei In such a reaction the total massof the products is less than theoriginal mass of the heavynucleuswhere does the extra mass go?into kinetic energy of decayproducts, about 200 MeV (notjust of academic interest) Consider a slow neutroninteracting with a 235U nucleus(one possible reaction)10n 23592U14156921Ba 36Kr 30ncaptures slow-movingneutron Capture results in formation of236U*; excess energy of thisnucleus causes it to undergoviolent oscillations 236U nucleus becomeselongated Nucleus splits into 2fragments, emitting severalneutrons in the process 235U

Chain reactionAverage number of neutrons emitted is 2.5; when chain reactionoccurs fast, it’s a bomb; when reaction occurs slowly and controlledit’s a nuclear reactor

First chain reaction In 1942, Enrico Fermiand collaborators built anuclear pile underneaththe football stadium andobtained the firstcontrolled nuclear chainreaction Their measurementsconfirmed that theconstruction of an atomicbomb was a possibilityEnrico Fermi Physicist 1901 - 1954

Nuclear Reactor in a reactor have controlrods which can absorbneutrons to slow thereaction down

Operating principles

Two years later, James Chadwick and E.S. Bieler conclude that some strong force holds the nucleus together. Why? If protons in nucleus (and not electrons) then what keeps the repulsive force from driving the nucleus apart? Nucleus confined to a very small volume ( 10-14 m in d